VCUniversity Estudo Indigo

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ABSTRACT

HOLBERT, JR., RICHARD MOORE. Empirical and Theoretical Indigo Dye Models Derived from

Observational Studies of Production Scale Chain Rope Indigo Dye Ranges. (Under the direction of

Peter Hauser, Warren Jasper, Jon Rust, and Richard Gould.)

An observational study of production scale chain rope indigo dye ranges was conducted

using 100% cotton open end spun yarns to confirm previously published dye trends, investigate the

effects of dye range speed, and develop dye prediction models. To achieve these objectives, several

milestones were identified and systematically addressed. A comprehensive laboratory preparation

method was developed to ensure consistent yarn preparation. Equilibrium sorption experiments

were conducted to determine the functional relationship between dye bath concentration and pH to

indigo dye uptake in the cotton yarn. Additionally, the resulting shade from equilibrium sorption

data was expanded to create an innovative method of quantitatively characterizing indigo

penetration level of non-uniformly dyed yarns.

The following dye range set-up conditions were recorded for each observational point: yarn

count, number of dips, dye range speed, dwell length, nip pressure, dye bath indigo concentration,

dye bath pH, dye bath reduction potential, and oxidation time. All observations were conducted

after the dye range had been running for several hours and no feed rate adjustments were required.

Later the following measurements were taken to determine each response variable state: totalpercent chemical on weight of yarn, percent of fixed indigo on weight of yarn, and Integ shade

value.

Analysis of data from the observational study confirmed most previously published dye

trends relating to dye uptake, shade, and penetration level. Notably, the percent indigo on weight

of yarn as a function of dye bath pH was not confirmed. Although it was noted this relationship may

be dependent on the pH range evaluated during the observational study and not the broader

general trend. All other general trends were confirmed. Additionally several new dye range set-up

conditions were determined to significantly affect dye uptake, shade, and/or penetration level. Yarn

count, speed, and dwell time were deemed significant in affecting dye uptake behavior. Increasing

yarn count to finer yarns resulted in greater percent indigo on weight of yarn, Integ, and penetration



level. Increasing dye range speed resulted in less percent indigo on weight of yarn, lighter Integ

shade, and lower penetration level or more ring dyeing. And, increasing dwell time resulted in

lighter Integ shade.

Using the dye range set-up conditions and measured response variables from theobservational study data, empirical and dye theory models were constructed to predict percent

indigo on weight of yarn, Integ shade, and the resulting penetration level. An independent

production scale indigo dye range, which was not included in dye model creation, was used to

validate of each model for accurate prediction of percent indigo on weight of yarn, Integ shade, and

corresponding penetration level. The dye model predictions were compared to actual production

scale indigo dyed cotton yarns. By making adjustments in yarn porosity values the dye theory model

outperformed the empirical model in predicting final Integ shade although both models accurately

predicted the total percent indigo on weight of yarn.



Empirical and Theoretical Indigo Dye Models Derived from Observational Studies of Production Scale

Chain Rope Indigo Dye Ranges

by

Richard Moore Holbert, Jr.

A dissertation submitted to the Graduate Faculty of

North Carolina State University

in partial fulfillment of the

requirements for the Degree of

Doctor of Philosophy

Fiber and Polymer Science

Raleigh, North Carolina

2011

APPROVED BY:

Warren Jasper Richard Gould

Jon Rust Peter Hauser

Chair of Advisory Committee



ii

BIOGRAPHY

Richard Moore Holbert, Jr. was born on March 18, 1971 in Charlotte, NC. He graduated with a high

school diploma from North Mecklenburg High School in 1989. He received a Bachelor of Science

degree in Mechanical Engineering and Master of Science in Textile Engineering and Mechanical

Engineering from North Carolina State University in 1994 and 1997 respectively.

In 1997 he married Avian Kay and began working at Swift Denim in Erwin, NC denim facility. He

started working as a process engineer in the finishing and indigo dye house departments. After 8

years with the company he transferred to the Society Hill, SC piece dye plant in 2005. There he

assumed the role of director of global product development. In December 2010, Avian and he were

blessed with the arrival of Aleaha Louise Holbert.



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ACKNOWLEDGEMENTS

I would like to whole heartily thank my loving wife. After so many years of missed family weekends,

outings, birthdays, and occasional holiday gatherings; it is a wonder she has stayed by my side.

Without my laboratory assistant I doubt I would have ever finished this research.

To Geoff Gettilife and all the technicians at Swift Denim's Boland plant, I would like to thank you.

I'd like to thank my research committee. I know this process has taken longer than I (or you)

envisioned, but I believe this work is a perfect example of the "ends justifying the means".



iv

TABLE OF CONTENTS

List of Tables vi

List of Figures ix

List of Equations xv

1. Indigo Dyeing Principles: Review of Current Knowledge 1

1.1 Commercial Indigo Dyeing 2

1.2 Indigo Chemistry 7

1.2.1 Indigo Reduction or Vatting 7

1.2.2 Classification of Indigo Dye Species 10

1.2.3 Indigo dyeing Measurement Methods 14

1.3 Characteristics of Indigo Dyed Yarns 19

1.4 Dye Theory 32

1.4.1. Fundamental Sequence of Events during Dyeing 32

1.4.2 Fick's Law of Diffusion 341.4.3. Diffusional boundary Layer 41

1.4.4. Empirical Simplifications of Diffusion 44

1.5 Indigo Dyeing Experiments 49

1.5.1. Previous Investigations and Methods on Indigo Dyeing 49

1.5.2. Discussion of Previously Published Experimental Results 58

1.6 Summary of Key Developments and Identification of Deficiencies 83

2. Objectives of the Present Investigation 86

3. Experimental Methods and Procedures 89

3.1 Response Variables Definition, Collection Methods, and Evaluation Methods 89

3.1.1 Yarn Skein Definition and Creation 89

3.1.2 Running Yarn Skeins on Production Indigo Dye Range Equipment 89

3.1.3 Yarn Skein Evaluations 90

3.2 Determining Optimum Method for Laboratory Preparation 97

3.2.1 Analysis of Laboratory Preparation Time, Temperature, and Sodium Hydroxide

Concentration Affect on %Boil-off Loss 101


Concentration Affect on %IOWY after One and Six Dip Indigo Dyeing Conditions 106


Concentration Affect on Integ Shade Value after One and Six Dip Indigo Dyeing

Conditions 114

3.2.4 Analysis of Laboratory Preparation Time, Temperature, and Sodium HydroxideConcentration Affect on Penetration Factor after One and Six Dip Indigo Dyeing

Conditions 119

3.2.5 Determine Optimum Settings for Laboratory Preparation Procedure 126



v

3.3 Equilibrium Sorption Experiment to Determine %IOWY and Shade Relationship for

Uniformly Dyed Skeins 130

3.4 Observational Indigo Study: Establishing Breadth of Dye Conditions and

Convergence Test to Determine Conclusion of Study 141

4. Data Analysis from the Observational Study 146

4.1 Review of Main Parameter Affects on Response Variables Obtained from

Observational Study 146

4.2 Empirical Dye Models Based on Dye Range Parameters and the Resulting

Affect on Indigo Dye Response Variables 170

4.2.1 %COWY Empirical Model Generation 170

4.2.2 %IOWY Empirical Model Generation 176

4.2.3 Integ Empirical Model Generation 183

4.2.4 Penetration Level Empirical Model Generation 188

4.3 Theoretical Model for Indigo Dye Process 196

4.3.1 Derivation of Theoretical Dye Model 196

4.3.2 Algorithm to Calculate the Dye Coefficients 218

4.3.3 Spatial and Time Step Optimization 2194.3.4 Determination of Indigo Dyeing Coefficient Models 219

4.3.5 Algorithm to Calculate the %COWY, %IOWY, and Integ Shade 237

5. Empirical and Theoretical Dye Model simulation and validation 239

5.1 Simulation of Empirical and Dye Theory models on Third Independent Dye Range 239

5.1.1 Actual Versus Predicted %COWY 240

5.1.2 Actual Versus Predicted %IOWY 243

5.1.3 Actual Versus Predicted Integ Shade Value 246

5.1.4 Actual Versus Predicted Penetration Level 249

5.1.5 Summary of Dye Theory Model Compared with Empirical Model 252

5.2 Simulation of Empirical and Dye Theory Models to Actual Production Yarn 256

6. Summary of Results, Discussions, and Recommendations 267

References 274

Appendix 279



vi

LIST OF TABLES

1. Indigo Dyeing Principles: Review of Current Knowledge

Table 1-1: Typical Stock Mix. 9

Table 1-2: A typical indigo stock mix formula. 9Table 1-3: Additional indigo stock mix recipes. 10

Table 1-4: Estimated diffusion coefficients for disperse Red 11 (D, cm2/sec x 10-10). 43

Table 1-5: Regression values for three parameter emphirical solution. 48

Table 1-6: Concentration of alkali system. 49

Table 1-7: Etters 1989 data set. 51

Table 1-8: Annis and Etters 1991 data set. 52

Table 1-9: Etters 1991 Equilibrium sorption of indigo on cotton obtained from different

pHs in grams of dye per 100 grams of water(bath) or fiber. 54

Table 1-10: Dye concentrations required to yield equivalent shade at different pHs. 55

Table 1-11: % reflectance and corrected K/S values for different dyebath concentrations

and pH. 56

2. Objectives of the Present Investigation

3. Experimental Methods and Procedures

Table 3-1: Target dyed yarn sample weight for Methyl Pyrrolidinone extraction. 93

Table 3-2: Time, temperature, and sodium hydroxide concentration levels plus

response variable for one dip of indigo. 99

Table 3-3: Time, temperature, and sodium hydroxide concentration levels plus

response variable for six dips of indigo. 100

Table 3-4: ANOVA analysis results for laboratory preparation parameters on %Boil-off loss. 105

Table 3-5: ANOVA analysis results for laboratory preparation parameters on

%IOWY for one dip of indigo. 111Table 3-6: ANOVA analysis results for laboratory preparation parameters on

%IOWY for six dips of indigo. 113


Integ for one dip of indigo. 118


Integ for six dips of indigo. 119


penetration factor from one dip of indigo. 123


penetration factor from six dips of indigo. 125

Table 3-11: %IOWY and Integ shade data from equilibrium sorption experiment. 132

Table 3-12: Observational study parameters and potential range of values. 141

Table 3-13: Prime data set in the observational study. 142



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4. Data Analysis from the Observational Study

Table 4-1: ANOVA analysis results from the prime data set on %COWY. 171

Table 4-2: ANOVA analysis for %COWY from the entire data set. 173

Table 4-3: ANOVA analysis from the prime data set on %IOWY. 177

Table 4-4: Effects test from %IOWY ANOVA analysis for the entire data set

with pH component. 179

Table 4-5: ANOVA analysis for the %IOWY from the entire data set. 180

Table 4-6: ANOVA analysis of Integ shade from the prime data set. 183

Table 4-7: ANOVA analysis for Integ from the entire data set. 185

Table 4-8: ANOVA analysis results from the prime data set and penetration level. 189

Table 4-9: Effect tests for all data points with speed and pH interaction. 191

Table 4-10: Final empirical model ANOVA analysis for all data sets. 192

Table 4-11: ANOVA analysis results for fiber diffusion coefficient. 221

Table 4-12: ANOVA analysis results for yarn diffusion coefficient. 225

Table 4-13: ANOVA analysis for wet pick-up coefficient. 229

Table 4-14: ANOVA analysis results for wash reduction coefficient. 232

Table 4-15: ANOVA analysis results for oxidation rate coefficient. 235

5. Empirical and Theoretical Dye Model simulation and validation

Table 5-1: Canadian dye range set-up conditions used for simulation. 239

Table 5-2: ANOVA analysis results of empirical model to actual measured %COWY. 241

Table 5-3: ANOVA analysis results of dye theory model to actual measured %COWY. 242

Table 5-4: ANOVA analysis results of empirical model to actual measured %IOWY. 244

Table 5-5: ANOVA analysis results of dye theory model to actual measured %IOWY. 245

Table 5-6: ANOVA analysis results of empirical model to actual measured Integ. 247

Table 5-7: ANOVA analysis results of dye theory model to actual measured Integ. 248

Table 5-8: ANOVA analysis results of empirical model to actual measured

penetration level. 250

Table 5-9: ANOVA analysis results of dye theory model to actual measuredpenetration level. 251

Table 5-10: ANOVA analysis results of empirical model indirect penetration

level to actual measured penetration level. 256

Table 5-11: Production Yarn Dye Range Set-up Conditions. 257

Table 5-12: Measured, Empirical Model, and Dye Theory Model %IOWY and Integ values. 257


production yarn %IOWY. 259

Table 5-14: Calculated porosity value to fit Dye theory model %IOWY to

production yarn results. 259

Table 5-15: ANOVA analysis results of dye theory model to actual measured

production yarn %IOWY. 261


production yarn Integ. 262



viii

Table 5-17: ANOVA analysis results of dye theory model to actual measured

production yarn Integ. 264

Table 5-18: ANOVA analysis results of dye theory model calculated porosity

value to dye range speed. 265

6. Summary of Results, Discussions, and Recommendations

Table 6-1: Empirical model performance review. 271

Table 6-2: Dye theory model performance review. 271

Appendix Table A-3-1: % Reflectance of mock dyed 100% cotton yarns used to calculate K/S. 282

Table A-3-3: %IOWY and Integ shade data from equilibrium sorption experiment. 283

Table A-4-1: Prime and replica raw data set. 284

Table A-4-2a: Convergence test - standard errors from empirical model %COWY parameter. 370

Table A-4-2b: Convergence test - standard errors from empirical model %IOWY parameter. 370

Table A-4-2c: Convergence test - standard errors from empirical model Integ parameter. 371

Table A-4-2d: Convergence test - standard errors from empirical model penetration level

parameter. 371Table A-5-1: Independent dye range raw data set. 396



ix

LIST OF FIGURES


Figure 1-1: Typical dye range equipment to apply indigo dye. 2

Figure 1-2: Pre-scour section on long chain indigo dye range. 3Figure 1-3: Indigo dye boxes on long chain dye range. 4

Figure 1-4: Wash and dry section of long chain indigo dye range. 5

Figure 1-5: Re-circulation system on long chain indigo dye range to maintain dye

box uniformity. 6

Figure 1-6: Oxidized and reduced form of indigo dye. 8

Figure 1-7: Various forms of indigo: I - Oxidized, II - Reduced acid leuco,

III - Monophenolate, and IV - Biphenolate. 11

Figure 1-8: Fraction of leuco reduced indigo as a function of pH. 14

Figure 1-9: Specific Absorptivity of oxidized and reduced indigo as a function of wavelength. 15

Figure 1-10: Redox potential curve of reduced indigo undergoing oxidation

by sodium hypochlorite. 16

Figure 1-11: Calibration curve of Sahin laser diode spectrometer. 17

Figure 1-12: Kubelka-Munk analysis of downward and upward components of light flux. 19

Figure 1-13: Calculated R-square values for blue, red, and yellow dyes at various

surface reflectances. 24

Figure 1-14: Calculated y intercepts for blue, red, and yellow dyes. 25

Figure 1-15: Comparison of original K/S and corrected K/S for blue, red, and yellow dyes. 26

Figure 1-16: Examples of limited ring dyeing on the left, medium in the middle,

and high degree of ring dyeing on the right picture. 27

Figure 1-17: Pre-scour caustic concentration effect of dye uptake. 28

Figure 1-18: Typical reflectance values for indigo dyed denim yarn - 6.3/1 open end

yarn at 31 m/min, 2.3 g/l, 11.9 pH, and 6 dips. 29

Figure 1-19: Typical corrected K/S values for indigo dyed denim yarn - 6.3/1 open endyarn at 31 m/min, 2.3 g/l, 11.9 pH, and 6 dips. 29

Figure 1-20: Distribution of indigo dye and penetration level in denim yarn. 30

Figure 1-21: Basic sequence of events in dyeing fibers. 33

Figure 1-22: Graphical solution of Fick's 2nd Law for Diffusion in long cylinders. 38

Figure 1-23: Predicted fractional dye uptake as a functin of dimensionless time at

various flow rates. 42

Figure 1-24: Red 11 dye desorption at various oscillating speeds. 44

Figure 1-25: Mt / M∞ as a function of Dt/r2 for various values of E∞. 47

Figure 1-26: Effect of oxidation time on color. 58

Figure 1-27: Effect of reduction agent concentration on shade. 59

Figure 1-28: Effect of immersion time on shade. 60Figure 1-29: Chong's effect of immersion time on uncorrected K/S. 61

Figure 1-30: Relationship between number of dips and shade. 62

Figure 1-31: Chong's relationship between number of dips and uncorrected K/S. 63

Figure 1-32: Relationship between dye bath concentration and shade. 64

Figure 1-33: Chong's relationship between dye bath concentration and uncorrected K/S. 65



x

Figure 1-34: pH effect of shade with other parameters held constant. 66

Figure 1-35: K/S shade vs % indigo on weight of yarn at various pH’s. 67

Figure 1-36: Non-equilibrium Concentration of dye in fiber (g/100g) vs concentration

of dye in bath (g/100g). 68

Figure 1-37: Equilibrium isotherm for dye concentration in dye bath and fiber (g/100g). 69

Figure 1-38: Logarithmic plot of equilibrium isotherms for dye concentration. 70

Figure 1-39: Mean technical distribution as a function of dyebath pH. 71

Figure 1-40: Apparent reflectance absorptivity coefficient vs pH. 72

Figure 1-41: Reflectance absorptivity coefficient as a function of mean technical

distribution coefficient. 73

Figure 1-42: Relationship of Mono-ionic species of indigo and pH. 74

Figure 1-43: Relationship between mean technical distribution coefficient and

fraction of indigo existing as mono-ionic form. 75

Figure 1-44: Correlation of fractional distribution of apparent absorptivity

coefficient and mono-ionic form of indigo as a function of pH. 76

Figure 1-45: Indigo concentration in dye bath required to produce a given shade

depth at various pH’s from a 5 dip laboratory dyeing. 77

Figure 1-46: Effect of dye bath concentration and pH on dye uptake. 78Figure 1-47: Yarn dye uptake as a function of dye bath concentration and pH. 79

Figure 1-48: Corrected depth of shade as a linear function of indigo concentration

in yarn and dyebath pH. 80

Figure 1-49: Estimated concentration of unfixed indigo on yarn at corresponding

dye bath concentration and pH. 81



Figure 3-1: Relationship of maximum K/S shade shift as depth increases. 95

Figure 3-2: Relationship of K/S by wavelength as a function of %IOWY. 96

Figure 3-3: Relationship of time on %boil-off loss during laboratory preparation. 101

Figure 3-4: Relationship of sodium hydroxide concentration on %Boil-off loss

during laboratory preparation. 102

Figure 3-5: Relationship of temperature on %Boil-off loss during the laboratory preparation. 103

Figure 3-6: Interaction profile for time, temperature, and sodium hydroxide concentration

on %boil-off loss during laboratory preparation process. 104

Figure 3-7: %Boil-off loss model as a function of time (seconds), temperature (C),

and sodium hydroxide concentration (g/l) in laboratory preparation process. 106

Figure 3-8: Relationship of laboratory preparation time on %IOWY after one

and six dips of indigo dye. 107

Figure 3-9: Relationship of sodium hydroxide concentration during laboratory

preparation on %IOWY from one and six dips of indigo dye. 108Figure 3-10: Relationship of temperature during laboratory preparation on %IOWY

from one and six dips of indigo dye. 109


on %IOWY after one and six dips of indigo dye. 110



xi

Figure 3-12: %IOWY for one dip of indigo model as a function of time, temperature,

and sodium hydroxide concentration in laboratory preparation process. 112

Figure 3-13: %IOWY for six dips of indigo model as a function of time, temperature,


Figure 3-14: Relationship of laboratory preparation time on Integ shade value from

one and six dips of indigo dye. 115

Figure 3-15: Relationship of sodium hydroxide concentration during laboratory preparation

on Integ shade value after one and six dips of indigo dye. 116

Figure 3-16: Relationship of temperature during laboratory preparation on Integ shade

value after one and six dips of indigo dye. 117

Figure 3-17: Relationship of time during laboratory preparation on penetration factor

after one and six dips of indigo dye. 120

Figure 3-18: Relationship of sodium hydroxide concentration during laboratory preparation

on penetration factor after one and six dips of indigo dye. 121

Figure 3-19: Relationship of temperature during laboratory preparation on penetration

factor after one and six dips of indigo dye. 122


on penetration factor after one and six dips of indigo dye. 123Figure 3-21: Penetration factor for one dip of indigo model as a function of time, temperature,


Figure 3-22: Penetration factor for six dips of indigo model as a function of time, temperature,


Figure 3-23: Optimized laboratory preparation parameters incorporating prediction profiles

from %Boil-off loss and %IOWY from one dip of indigo dye. 128

Figure 3-24: Optimized laboratory preparation parameters incorporating prediction profiles

from %Boil-off loss and %IOWY from six dips of indigo dye. 129

Figure 3-25: %IOWY from 6.3/1, 7.1/1, 8.0/1, and 12.0/1 OE yarns compared to Etters20 data

under equilibrium sorption at pH 13 range. 133

Figure 3-26: %IOWY on 6.3/1, 7.1/1, 8.0/1, and 12.0/1 OE yarns compared to Etters

20

dataunder equilibrium sorption at pH 11 range. 134

Figure 3-27: Power function coefficients A and B as a function of dye bath pH. 135

Figure 3-28: Equilibrium sorption power function coefficients as a function of

monophenolate ionic form of indigo. 136

Figure 3-29: Comparison of calculated and measured %IOWY under equilibrium sorption

laboratory dyeing conditions as the dye bath concentration and pH were varied. 137

Figure 3-30: Relationship of Integ shade value for various yarn counts as %IOWY from

equilibrium sorption. 138

Figure 3-31: Relationship of %IOWY on the outside surface for various yarn counts as Integ

from equilibrium sorption. 139

Figure 3-32: Shape of K/S at 660 nm as a function of %IOWY from equilibrium sorption

experiments. 140

Figure 3-33: Range of observational study dye range set-up conditions and interactions. 143

Figure 3-34: Affect of additional replicated data sets on standard error of indigo dye bath

concentration parameter and four response variables after one dip of indigo. 145



xii


Figure 4-1: Number of dips affect on %COWY and %IOWY for all data points. 146

Figure 4-2: Build curve relationship for %COWY as a function of number of dips on

6.3/1 yarn count at similar speed, pH, and reduction potential. 147

Figure 4-3: Build curve relationship for %IOWY as a function of number of dips on

6.3/1 yarn count at similar speed, pH, and reduction potential. 148

Figure 4-4: Integ shade value as a function of number of indigo dye box dips for

all data points. 149

Figure 4-5: Integ shade value as a function of number of dips on 6.3/1 yarn count at

similar speed, pH, and reduction potential. 150

Figure 4-6: Penetration level for all data points as a function of the number of dips. 151

Figure 4-7: Penetration level as a function of number of dips on 6.3/1 yarn count at

similar speed, pH, and reduction potential. 152

Figure 4-8: %COWY for all data points as a function of dye bath concentration after

one, three, and six dips. 153

Figure 4-9: %IOWY for all data points as a function of dye bath concentration after

one, three, and six dips. 154

Figure 4-10: Integ shade value as a function of dye bath concentration at variousnumbers of dips. 155

Figure 4-11: Penetration level for all data points as a function of dye bath concentration

within each dip. 156

Figure 4-12: Illustrates %COWY, %IOWY, Integ, and penetration level varies with

yarn count and dye concentration after six dips. 158

Figure 4-13: Speed affect on %COWY, %IOWY, Integ, penetration level at various

dye bath concentrations after six dips of indigo on 6.3/1 yarn. 160

Figure 4-14: pH affect on %COWY, %IOWY, Integ, penetration level at various

dye bath concentrations after six dips of indigo on 6.3/1 yarn. 162

Figure 4-15: Reduction potential affect on %COWY, %IOWY, Integ, and penetration level

at various dye bath concentrations after six dips of indigo on 6.3/1 yarn. 164Figure 4-16: Dwell length affect on %COWY, %IOWY, Integ, and penetration level at

various dye bath concentrations after six dips of indigo on 6.3/1 yarn. 166

Figure 4-17: Dwell time affect on %COWY, %IOWY, Integ, and penetration level at


Figure 4-18: Nip pressure affect on %COWY, %IOWY, Integ, and penetration level at


Figure 4-19: Convergence test for empirical %COWY model. 172

Figure 4-20: Comparison of actual versus predicted %COWY for the entire data set. 175

Figure 4-21: %COWY prediction profile for dye range set-up condition affect on %COWY

from the empirical model. 176

Figure 4-22: Convergence test for the empirical %IOWY model. 178

Figure 4-23: Comparison of actual and predicted %IOWY from the final empirical model. 181

Figure 4-24: Prediction profile for %IOWY and dye range set-up parameters. 182

Figure 4-25: Convergence test for empirical model Integ. 184

Figure 4-26: Comparison of actual and empirical model predicted Integ shade values. 186



xiii

Figure 4-27: Prediction profile for Integ shade values as a function of each dye

range set-up conditions. 187

Figure 4-28: Convergence test for empirical model penetration level. 190

Figure 4-29: Comparison between actual and predicted penetration level. 194

Figure 4-30: Prediction profile of empirical model penetration level as a function of

dye range set-up parameters. 195

Figure 4-31: Nodal mesh arrangement and nomenclature for finite difference

method implementation. 205 Figure 4-32: Fiber diffusion coefficients for each yarn count as the oxidation rate changes. 215

Figure 4-33: Yarn diffusion coefficients for each yarn count as a function of oxidation rate. 216

Figure 4-34: Wet pick-up variation within yarn counts as a function of oxidation rate. 217

Figure 4-35: Standard deviations as a function of oxidation rate. 218

Figure 4-36: Comparison of model predicted and actual fiber diffusion coefficient. 222

Figure 4-37: Effective fiber diffusion functional relationship to dye range set-up conditions. 223

Figure 4-38: Comparison of model predicted and actual yarn diffusion coefficient. 226

Figure 4-39: Effective yarn diffusion functional relationship to dye range set-up conditions. 227

Figure 4-40: Comparison of model predicted and actual wet pick-up coefficient. 230

Figure 4-41: Dye theory model wet pick-up functional relationship to dye rangeset-up conditions. 231

Figure 4-42: Comparison of model predicted and actual wash reduction. 233

Figure 4-43: Dye theory model wash reduction functional relationship to dye range

set-up conditions. 234

Figure 4-44: Comparison of model predicted and actual oxidation rate. 236

Figure 4-45: Dye theory model oxidation rate functional relationship to dye range

set-up conditions. 237


Figure 5-1: Empirical model predicted %COWY compared to actual measured values. 240

Figure 5-2: Dye theory model predicted %COWY compared to actual measured values. 242Figure 5-3: Empirical model predicted %IOWY compared to actual measured values. 243

Figure 5-4: Dye theory model predicted %IOWY compared to actual measured values. 245

Figure 5-5: Empirical model predicted Integ compared to actual measured values. 246

Figure 5-6: Dye theory model predicted Integ compared to actual measured values. 248

Figure 5-7: Empirical model predicted penetration level compared to actual measured values. 249

Figure 5-8: Dye theory model predicted penetration level compared to actual measured

values. 251

Figure 5-9: Indigo build profile for Canadian dye range set-up on 443 shade

with 29 m/min, 1.26 g/l dye bath concentration and 12.2 pH. 253

Figure 5-10: Indigo build profile for Canadian dye range set-up on 418 shade with

32 m/min, 1.66 g/l dye bath concentration and 11.8 pH. 254

Figure 5-11: Indigo build profile for Canadian dye range set-up on 471 shade with

32 m/min, 2.09 g/l dye bath concentration and 12.1 pH. 254

Figure 5-12: Empirical model predicted indirect penetration level compared to

actual measured values. 255



xiv

Figure 5-13: Empirical model predicted %IOWY compared to actual measured values

from production yarns. 258

Figure 5-14: Dye theory model predicted %IOWY compared to actual measured values


Figure 5-15: Empirical model predicted Integ compared to actual measured values


Figure 5-16: Dye theory model predicted Integ compared to actual measured values


Figure 5-17: Functional relationship between theoretical porosity value and

dye range speed. 265




xv

LIST OF EQUATIONS


Equation 1-1: First law of thermodynamics. 6

Equation 1-2: Example calculation of percent indigo shade. 7Equation 1-3: Reaction of sodium dithionite and sodium hydroxide. 8

Equation 1-4: First ionization of indigo dye. 11

Equation 1-5: First associated equilibrium ionization constant. 12

Equation 1-6: Second ionization of indigo dye. 12

Equation 1-7: Second associated equilibrium ionization constant. 12

Equation 1-8: Indigo fractional form calculation based on pH and respective pka values. 13

Equation 1-9: Change in downward flux by Kubelka-Munk. 20

Equation 1-10: Change in upward flux by Kubelka-Munk. 20

Equation 1-11: Kubelka-Munk reflectance equation. 20

Equation 1-12: Kubelka-Munk equation for light absorbance and scattering. 21

Equation 1-13: Correction to Kubelka-Munk for light reflectance properties of mock dyed

substrate. 21

Equation 1-14: Corrected Kubelka-Munk to account for surface reflectance. 22

Equation 1-15: Relationship of K/S corrected to dye bath concentration. 22

Equation 1-16: L*, a*, and b* equations based on the tristimulus values as defined by CIELAB. 23

Equation 1-17: Calculation of Integ as a function of K/S values, average observer, and

standard light source. 23

Equation 1-18: Adjusting K/Scorr for non-uniformly distributed dye. 31

Equation 1-19: Fick's first law of diffusion. 35

Equation 1-20: Fick's second law of diffusion. 36

Equation 1-21: Expansion of Fick's second law of diffusion into cylindrical coordinate system. 36

Equation 1-22: Reduction of Fick's second law of diffusion to radial component only. 36

Equation 1-23: Non-steady state solution to equation 1-21. 37Equation 1-24: Solution of diffusion from constant initial concentration. 37

Equation 1-25: Hill's solution of dye concentration under infinite dye bath conditions. 39

Equation 1-26: Newman's solution of dye concentration under infinite dye bath conditions that

contain surface barrier effects. 40

Equation 1-27: Definition of L term utilized in Newman's dye concentration solution. 40

Equation 1-28: Othmer-Thakar relationship for diffusion coefficient in dilute aqueous solutions. 41

Equation 1-29: Vickerstaff one parameter approximate solution for dye distribution. 44

Equation 1-30: Urbanik two parameter approximate solution for dye distribution. 45

Equation 1-31: Etters three parameter approximate solution for dye distribution. 45

Equation 1-32: Etters empirical fit equation to calculate parameters in three parameter

approximate solution of dye distribution when L is 20 to infinity. 46Equation 1-33: Etters empirical fit equation to calculate parameters a in three parameter

approximate solution of dye distribution when L is 1 to 20. 46

Equation 1-34: Etters empirical fit equation to calculate parameters b in three parameter




xvi

Equation 1-35: Etters empirical fit equation to calculate parameters c in three parameter


Equation 1-36: Etters relationship for apparent diffusion coefficient and three parameter

estimates. 48

Equation 1-37: Calculation of Integ as a function of K/S values, average observer, and

standard light source. 57

Equation 1-38: Mono-ionic fraction form of indigo dye as function of pH. 73

Equation 1-39: Definition of technical distribution coefficient. 82

Equation 1-40: Approximation for technical distribution coefficient as a function of dye bath pH. 82

Equation 1-41: Empirical model of apparent reflectance absorptivity coefficient. 82



Equation 3-1: Calculation of %Boil off loss. 91

Equation 3-2: Calculation of %COWY. 91

Equation 3-3: Calculation of %IOWYwash. 91

Equation 3-4: Calculation of %IOWY by Methyl Pyrrolidinone extraction. 92Equation 3-5: Calculation of %IOWY in terms of 100% indigo paste from Methyl Pyrrolidinone

extracts. 93

Equation 3-6: Calculation of K/S from Kubelka-Munk. 94

Equation 3-7: Calculation of Integ shade value from K/S values. 94

Equation 3-8: Calculation of penetration factor from Integ and %IOWY. 97

Equation 3-9: %Boil-off loss as a function of time, temperature, and sodium hydroxide

concentration. 105

Equation 3-10: %IOWY as a function of time, temperature, and sodium hydroxide

concentration after one dip of indigo. 111

Equation 3-11: %IOWY as a function of time, temperature, and sodium hydroxide

concentration after six dips of indigo. 113

Equation 3-12: Calculation of penetration level as a function of measured %IOWY and

converted surface %IOWY from Integ shade reading. 130

Equation 3-13: Power function relationship of indigo dye bath concentration to %IOWY under

equilibrium sorption. 134

Equation 3-14: General relationships between indigo dye bath concentration and pH to

resulting %IOWY under equilibrium sorption. 136

Equation 3-15: Calculation of Integ shade based on %IOWY under equilibrium sorption. 139

Equation 3-16: Calculation of surface %IOWY from Integ shade values. 139


Equation 4-1: Empirical model %COWY as a function of dye range set-up conditions. 174

Equation 4-2: Empirical model %IOWY as a function of dye range set-up conditions. 181Equation 4-3: Empirical model Integ as a function of dye range set-up conditions. 186

Equation 4-4: Empirical model penetration level as a function of dye range set-up conditions. 193

Equation 4-5: Ozisik diffusion coefficient calculation in external medium. 197

Equation 4-6: Fick's first and second law of diffusion. 200

Equation 4-7: Transient second order partial differential of mass diffusion in radial direction. 200



xvii

Equation 4-8: Crank-Nicholson explicit finite difference model for mass diffusion. 201

Equation 4-9: Actual %IOWY based on maximum possible %IOWY and fractional relationship. 202

Equation 4-10: Crank's expression for the fractional relationship of dye pick-up. 202

Equation 4-11: Maximum %IOWY from equilibrium sorption experiments. 202

Equation 4-12: Fractional relationship between indigo leaving the dye bath stream and dye

diffused into the cotton fiber. 203

Equation 4-13: Initial dye distribution at t<0. 203

Equation 4-14: Dye bath concentration at the outside surface node. 203

Equation 4-15: Boundary condition at the center of the yarn due to symmetry. 204

Equation 4-16: Functional relationship of %IOWY at the surface related to Integ shade. 204

Equation 4-17: Relationship of surface %IOWY by Integ shade. 204

Equation 4-18: Nodal equation for center node. 206

Equation 4-19: Nodal equation for interior nodes. 206

Equation 4-20: Nodal equation for exterior node. 206

Equation 4-21: Expression for lambda and beta coefficients in the nodal equations. 206

Equation 4-22: Matrix example of all nodal equations in finite difference model. 207

Equation 4-23: Mogahzy's relationship for open end yarn radius as a function of yarn count. 207

Equation 4-24: Calculation of oxidized boundary layer as a function of wash reductioncoefficient, and %COWY and %IOWY from the previous dip. 208

Equation 4-25: Determining the reduced boundary layer concentration and quantity after the

nip process. 209

Equation 4-26: Explicit finite difference equation for oxygen distribution in the nodal mesh. 209

Equation 4-27: Rate of oxygen removal from the air stream. 209

Equation 4-28: Fraction of oxygen removed from the air stream as a function of total reduced

dye present. 210

Equation 4-29: Boundary conditions for solving finite difference equations. 210

Equation 4-30: Equations used to track the convergence of reduced indigo dye into oxidized

state. 211

Equation 4-31: Chemical reactions and intermediaries during the oxidation process. 212Equation 4-32: Relationship for the grams of auxiliary chemicals per gram of indigo present. 212

Equation 4-33: Calculation of the %COWY based on total indigo amounts. 213

Equation 4-34: Dye theory model effective fiber diffusion coefficient. 222

Equation 4-35: Dye theory model prediction equation of effective yarn diffusion coefficient. 226

Equation 4-36: Dye theory model prediction equation wet pick-up. 230

Equation 4-37: Dye theory model prediction equation of wash reduction. 233

Equation 4-38: Dye theory model prediction equation of oxidation rate. 236



Equation 6-1: Equations to calculate %IOWY as a function of dye bath concentration and pHunder equilibrium sorption conditions. 267

Equation 6-2: Expressions to relate penetration level of non-uniformly dyed yarns. 268



xviii

Appendix Equation A-1-1: oz/gal of 20% indigo related by %T by spectrophotometric method. 280

Equation A-1-2: Calculation of total alkalinity by titration method. 281



1

1 Indigo Dyeing Principles: Review of Current Knowledge

Indigo is a vat dye which was probably one of the oldest known coloring agents and has

been used to dye fabric for thousands of years. In fact, it is thought that this ancient dye was the

first naturally occurring blue colorant discovered by primitive man. The origin of the name “indigo”

can be traced back to the word “Indic” which means of India. Indigo has also been greatly valued by

the Chinese. Egyptian Mummy cloths have been discovered that were dyed with the “ntinkon”, a

blue dye having all the properties of indigo.

Today, the indigo used in commercial dyeing of denim yarn is no longer of natural origin.

After 12 years of research by Adolf von Baeyer, a method of laboratory synthesis of indigo was

discovered in 1880. By 1897 the first commercial form of indigo based on Baeyer’s method

appeared on the market. After the turn of the 20th century, synthetic indigo gradually replaced

natural dye worldwide. Over the last hundred plus years more indigo dye has been produced than

any other single dye.

Even though indigo is classified as a vat dye, it does not perform like other vat dyes because

it has little affinity for cotton. Compared to other vat dyes, indigo has inferior fastness properties.

But these poor performance properties are indeed the very nature of the dye which makes it so

popular. Due to the poor fastness properties, a desirable blue shade develops when indigo dyed

denim is laundered repeatedly.

If indigo was introduced today, not many dyers or chemists would be interested. In fact, it

might not even leave the lab compared to today’s requirements for commercializing a new dye.

Zollinger noted in 198819, “Were it not for the persistence of the denim fashion, indigo would hardly

be produced or used at all today.” This statement still rings true today. Given the extensive use of

indigo in commercial dyeing applications, one would speculate the literature would be filled with

fundamental experiments and knowledge of the use and driving properties of this important dye. At

last, until recently this is not the case. It wasn’t until the end of the 1980’s when the Southeastern

Section of the AATCC committee lead by investigations of J.N. Etters that significant research

revealed the physico-chemical mechanisms of the sorption of indigo by cellulosic materials.



3

The majority of denim yarns dyed with indigo utilizes the 6-dip (or more) continuous rope

dye range. A typical rope dye range will process 20 to 40 ropes of yarns at a time. The exact

number will be predetermined by machine layout and subsequent slasher restrictions. 300-400

individual yarns make up a single rope. The final number of ropes will equate to 2 to 4 slasher sets.

This characteristic allows the continuous rope dye range to produce uniformly dyed yarn at great

production rates in a variety of shades.

Before the cotton yarns can be dyed with indigo, the cotton must be prepared. The pre-

scouring process shown in figure 1-2 involves two main objectives. First the cotton is chemically

cleaned with a penetrant, sequestering agent, and sodium hydroxide solution. Typical sodium

hydroxide concentrations range from 10-25 g/l although higher levels (mercerization strength) are

used to create unique dye characteristics. The main purpose is to remove natural waxes and oils

from the cotton fibers. During this stage sulfur dyes are commonly added to enhance the final

indigo dye shade. Multiple wash boxes follow the scour box to rinse contaminants from the yarns.

The last benefit of the pre-scour section is to remove all excess air trapped in the yarns. Excess air in

the yarns will prematurely oxidize the reducing agent and possibly indigo in the dye boxes causing

the entire system to fall out of reduction.

Figure 1-2: Pre-scour section on long chain indigo dye range.1



4

After the last wash box in the pre-scouring section, the yarns are immediately immersed

into the first indigo dye box. There are two main ways to “build” the amount of indigo on weight of

yarn. 1. Indigo concentration in the dye boxes. 2. The total number of dips. Each “dip” is

characterized by submerging the yarn into the dye liquor for 15-60 seconds with a “W” type thread-

up. Then excess dye liquor is squeezed from the yarns by using 4-5 ton nip which typically produces

70 – 90% wet pick-up. “Skying” after each nip allows natural air oxidation of the leuco indigo.

Typical sky times are 1+ minute. By chaining multiple dips together as shown in figure 1-3, the

indigo shade can be built to the final desired depth. Most commercial dye ranges have 4 to 8

successive dye boxes although some extreme new machines are being manufactured with 12 indigo

dye boxes. The maximum amount of indigo applied in any one dye box is approximately 2% of 20%

indigo paste. Therefore, approximately 6 dips are required to produce a “12%” indigo shade.

Figure 1-3: Indigo dye boxes on long chain dye range.1

Following the dye boxes, the yarns are washed to remove excess alkali and any unfixedsurface dye. During this stage sulfur dye “tops” can be applied to further enhance the indigo shade.

Figure 1-4 shows washing begins with cool water around 80°F in the first wash box and the

temperature is gradually increased by 20 degrees in each subsequent box. The final wash box is



5

usually around 140°F. Just before drying begins, typically a beaming aid is applied to improve

beaming efficiency.

Figure 1-4: Wash and dry section of long chain indigo dye range.1

Of course the main purpose of indigo dyeing is to apply indigo to the yarn. Indigo dyeing

occurs in an infinite bath condition because uniform dye concentration is maintained throughout

the dyeing process by the addition of make-up dye. Uniform dye concentration throughout all the

dye boxes is therefore paramount. Uniformity is achieved by re-circulating the dye liquor while

additional dye is metered into the range. Typical circulation system is shown in figure 1-5. Each dye

box is cross connected by 4 inch pipes located at the bottom of each box. Dye liquor is pulled from

the bottom of the vats by a circulation pump. The circulated liquor plus indigo and chemical feed

make-up is returned to each box near the top. Dye overflow is typically on the top of the first dye

box. This overflow is typically captured and re-used later.



Figure

indig

contr

Equati

1-5: Re-circulat

Since dye

dye boxes c

ol volume un

ℎ

n 1-1: First la

ion system on l

liquor is circu

an be model

dergoing a p

ℎ

of thermodyn

ng chain indig

lated throug

d as one gia

ocess can b

=

mics

dye range to

h the dye bo

nt dye box.

expressed a

aintain dye bo

es to maint

he conserva

s equation 1

−

x uniformity. 1

in uniform c

tion of mass

1.

ncentration

principle for

6

, the

a



7

The purpose of measuring the indigo concentration in the dye liquor is to maintain a

constant dye concentration so the net change in mass within the control volume equals zero.

Therefore the total mass entering equals total mass leaving the dye box. Total mass entering the

dye box is generally known. The concentration of indigo stock mix is predetermined and the feed

rate is measured by flow meters. The total mass leaving the system is divided into two components.

1. Indigo pick-up in the cotton yarns. 2. Indigo in the overflow from indigo dye box. Typical indigo

shades are expressed in terms of % indigo shades. This is calculated by dividing the pounds of indigo

per hour by the pounds of cotton per hour. For example:

3.75 pound/gallon indigo stock mix

78.3 gallons/hour indigo stock mix feed rate

293.6 pounds of indigo/hour feed rate3673 pounds cotton/hour

293.6/3673=8.0% indigo shade

Equation 1-2: Example calculation of % indigo shade

The approach shown in equation 1-2 neglects the indigo mass component in the overflow.

For a more accurate % indigo shade calculation, the mass of the discharged indigo must be

considered. Additionally, unfixed indigo removed from the dye bath on the yarn but later removedduring the washing process must be accounted for. Due to the complexity of measuring these

discrepancies, many indigo dyers refer to equation 1-2 for its simplicity.

1.2 Indigo Chemistry

1.2.1 Indigo Reduction or Vatting

Reduced indigo is called leuco indigo and is yellow in color. Leuco indigo can dye cellulose

materials and will later be oxidized back to blue color. The traditional reducing agent is sodium

dithionite also called sodium hydrosulphite or simply hydro. Other reducing agents fill special

demands and have not gained large practical acceptance. Hydro is extremely sensitive to



8

atmospheric oxygen. Oxidation of hydro is accompanied by consuming sodium hydroxide, NaOH,

when atmospheric oxygen is present in the alkaline medium.

The reduction of indigo dye requires two chemical processes as shown in equation 1-3 and

figure 1-6. Caustic and sodium hydrosulfite react to liberate two hydrogen atoms which react withthe two carbonyl groups (C = O) on the indigo molecule. Additional sodium hydroxide reacts with C

– OH group to form C – ONa group which solubilizes the dye into leuco indigo.

+ 2 2 + 2

Equation 1-3: Reaction of sodium dithionite and sodium hydroxide

Figure 1-6: Oxidized and reduced form of indigo dye.1

The theoretical calculations of caustic and hydro in indigo stock mix are as follows. Themolecular weight of indigo, hydro, and caustic are 262.26, 174.11, and 40.01 respectively. From the

above two reactions 4 moles of 100% NaOH and 1 mole of 100% Na2S2O4 (Hydro) are required to

completely reduce 1 mole of 100% indigo. In commercial operations, excess sodium hydroxide and



9

hydrosulphite are used to reduce indigo. An example of a typical indigo stock mix formula is given in

table 1-1.

Table 1-1: Typical Stock Mix.

As is

#/Gal

As is

g/l

% OWI 100%

g/l

Total

Moles

Theory

Moles

Excess

Moles

Excess

g/l

Indigo 3.75 450 -- 90 0.343 0.343 -- --

Caustic 1.50 180 40 112.5* 2.813 1.372 1.441 57.6

Hydro 0.60 72 16 64.8 0.372 0.343 0.029 5.1

* Includes the caustic present in the Indigo paste (5.2%).

The excess caustic and hydro are present to ensure complete reduction is reached and

maintained for the life of the mix. Additionally the excess chemicals will reduce the required

auxiliary chemical feed rates to maintain the desired pH during the dyeing process. In order to

maintain proper reduction of the indigo in the dye boxes, a total hydro consumption factor based on

the weight of the Indigo (OWI) would be approximately 32%.

Other typical indigo stock mixes follow formulas in table 1-2 and 1-3. Table 1-2 formula will

produce a 3.75 lb/gal or 450 g/l indigo concentration. Vatting or reducing the indigo usually occurs

at 50° C in approximately 30 minutes. Properly vatted indigo is yellow or amber in color. The liquor

turns green in 12-15 seconds on clean glass as air oxidation begins.

Table 1-2: A typical indigo stock mix formula.1

Stock Mix concentration

Gallons Lbs Lbs/Gal oz/gal g/l

Indigo 20% Paste 320 3000 3.75 60 450

Sodium Hydroxide 50% 94 1200 1.50 24 180Liq. Hydro 170g/l 340 3250 4.06 65 490

Water 46 382 - - -

Total Volume 800



10

Table 1-3: Additional indigo stock mix recipes.13

Plant 20% Indigo

Paste (g/l)

50% Caustic

Soda (g/l)

Hydro (g/l) 50% Caustic

Soda (%I)

Hydro (%I)

1 450 143 68 31.77 15.11

2 414 140 54 33.77 13.09

3 382 140 71 36.79 18.554 400 118 60 29.5 15

5 450 136 69 30.02 15.33

6 420 121 64 28.17 15.33

7 450 150 75 33.33 16.67

8 381 120 63 31.49 16.54

9 400 270 64 67.5 16.5

1.2.2 Classification of Indigo Dye Species

Indigo dye can exist as four species as shown in figure 1-7:

I. oxidized or keto indigo.

II. Reduced nonionic acid leuco indigo.

III. Monophenolate ion of reduced indigo.

IV. Biphenolate ion of reduced indigo.

Both forms I and II are highly insoluble compounds of unknown solubility and virtually no

substantivity for cotton. The solubility of the other species III and IV can be calculated when given

the pKa’s of the reduced forms. These two ionic forms vary greatly with di-ionic form having the

higher solubility but lower substantivity. The mono-ionic form of indigo predominates in the lower

pH ranges of 11.



11

Figure 1-7: Various forms of indigo: I - Oxidized, II - Reduced acid leuco, III - Monophenolate, and IV - Biphenolate.17

Indigo can undergo a two-step ionization to produce the two ionic species: mono-ionic and

di-ionic or the monophenolate and biphenolate forms respectively. The relative amount of each

species is governed by the pH of the dye bath. The poorly water-soluble nonionic or ‘acid leuco’

form of reduced indigo can be abbreviated as H2I where H is hydrogen and I represents indigo. Thefirst ionization step produces the more soluble mono-ionic form of indigo, HI- as shown in equation

1-4.

↔ +

Equation 1-4: First ionization of indigo dye



12

The associated equilibrium ionization constant k1 is given by equation 1-5.

= [][]

[]

Equation 1-5: First associated equilibrium ionization constant

The second ionization step produces the even more soluble di-ionic form of indigo, I2- by equation 1-

6.

↔ +

Equation 1-6: Second ionization of indigo dye

The associated equilibrium ionization constant k2 is given equation 1-7.

= [

]

[]

Equation 1-7: Second associated equilibrium ionization constant

The fractional distribution of each indigo dye form in figure 1-7 is governed by the pH and respective

pKa values. The functional relationship for each form is given in equations 1-8.



13

= [] ,ℎ = ( − ) = (2 − − )

= [] , ℎ = ( − ) = ( − )

= [] , ℎ = ( + − 2) = ( − )

Equation 1-8: Indigo Fractional form calculation based on pH and respective pK values

A higher pKa value indictates weaker ionization. In fact, the autoprotolysis equilibrium of water has

a pKa = 14.00. The relatively high value of 14 indicates only a few water molecules are ionized.8

In 1993 the actual pK1 and pK2 values for reduced indigo were unknown. Etters used the

values found for tetra-, tri-, di-, and mono- sulphonic acid forms of indigo. He states when these

data are extrapolated to the zero sulponic acid form, i.e. conventional reduced indigo, reasonable

estimates for pK1 and pK2 with 95% confidence limits are made.25 Etters' reported pKa estimates

are: pK1 mean value is 7.97 (limits 7.19, 8.74) and pK2 mean value is 12.68 (limits 12.23, 13.08).

The pKa’s of the first and second ionization steps of the acid leuco of indigo were later

measured to be pK1 = 9.5 and pK2 = 12.7.19 By using these values it is possible to calculate the

fractional amount of each reduced species of indigo in the dye bath for a given pH. Figure 1-8

illustrates the mono-ionic form dominates at pH of 11.0 while the di-ionic form reins superior at pH

of 14.0. At traditional indigo pH dye ranges of 12.0 – 13.0, the mono-ionic to di-ionic form ratio is

basically 50/50.



14

Figure 1-8: Fraction of leuco reduced indigo as a function of pH.15

1.2.3 Indigo dyeing Measurement Methods

Indigo concentrations in the dye box are measured by three different methods: visual versus

standard, Spectrophotometric analysis, or gravimetric analysis. All of the above methods are

affected to some degree by sulfur contamination in the indigo boxes when a sulfur bottom is

applied. However, results should be relative to previous measurements, therefore comparative.

By far the most widely accepted indigo measurement system in commercial operations is

the %T measurement. This technique is based on the transmittance values of a spectrophotometer

reading a diluted and oxidized dye sample. A known aliquot of dye is diluted to a fixed volume with

water and allowed to oxidize. Usually the resulting measurement is compared to a predetermined

standard. By using Beer’s Law: A=ebc; where A is absorbance, c is concentration g/l, b is cell

thickness cm, and e is specific absorptivity L/gcm; the indigo dye concentration can be calculated.



15

The specific procedure is outlined in appendix A-1-2a. Since oxidized indigo is not water soluable,

the mixature must be constantly stirred to maintain uniform distribution.

Figure 1-9 graphically depicts the specific absorptivity of oxidized and reduced indigo. The

specific absorptivity is independent of concentration and cell thickness.

Figure 1-9: Specific Absorptivity of oxidized and reduced indigo as a function of wavelength.53

Caustic is necessary to dissolve the reduced indigo into the leuco-indigo form. Caustic is also

the regulator of the dyeing process. Excess caustic results in increase penetration making the shade

appear weaker. Not enough caustic results in poor crocking properties, increased ring dyeing,

streaked dyeing, and/or a precipitation in the vat. The total alkalinity caustic level can be measured

by titration method. The specific method is given in appendix A-1-2b.

Sodium hydrosulfite is required to reduce the indigo and keep the indigo dye boxes in the

proper dyeing condition. Excess hydro results in increased penetration, greener and brighter

shades, weaker dyeing, potential streaking, higher cost, and slower wash down. Too little hydro

results in increased surface dyeing, redder and duller shades, color of the dye liquor changing from



16

amber to green, and/or dyeings which are not fast to washing. Sodium hydrosulfite concentrations

can be determined by volumetric titration with iodine or with K3 [Fe(CN)6]. The end point is

determined either visually or potentiometrically.

The hydro level can be measured by four different methods: 1. Iodine titration. 2.

Potassium Ferricyanide titration. 3. Vatometer. 4. MV measurement of the oxidation reduction

potential (ORP) which is a composite value based on indigo, caustic and hydro concentrations.

Reduced indigo dye bath can be titrated with sodium hypochlorite to produce the following

potential curve, figure 1-10. Starting from -890 mV to point A on the curve (-850 mV), the potential

depends on the concentration of sodium hydrosulphite in the dye bath. When all the hydro is

consumed, the potential undergoes a sudden increase to point B which is about -695 mV. As indigo

is insoluble in the aqueous dye bath, the potential of the solution is therefore the potential of leuco

indigo. At point C the leuco indigo molecules are oxidized and the potential quickly rises.

Electrochemical titration methods to measure Indigo and hydro use potassium hexacyanoferrate (III)

as the titrant.

Figure 1-10: Redox potential curve of reduced indigo undergoing oxidation by sodium hypochlorite.46



17

Several alternative methods have been developed over the years to measure and monitor

indigo and sodium hydrosulfite concentrations. Westbroek51 used an electrochemical method using

multistep chronoamperometry. Photometric and spectrophotometric reflectance can be used to

determine indigo concentrations by potentiometric titration. However the system doesn’t

differentiate between unreduced indigo and leuco indigo in the dye bath. This is due to the

oscillation of potential used to remove indigo particles from the electrode. By applying a -0.90 mV

potential across the electrode, all indigo in the sample vessel is completely reduced to leuco indigo.

Sahin53 describes a laser diode spectrometer for monitoring indigo concentrations. A laser

diode absorption spectrometer with monochromatic radiaton emmited at 635 nm to measure

oxidized indigo absorption at the shoulder of a broad absorption peak. A linear calibration curve

between 10 and 150 mg/l is shown in figure 1-11 which corresponds to indigo concentrations in the

dye bath from 0.8 to 12 g/l (diluted with aerated water by a factor of 80). Typical dye bath indigo

concentrations ranges are 1 to 3 g/l. Sahin claims no interference due to sulfur compounds present

in dye bath which is a problem with electrochemical titration methods but no supporting evidence is

provided.

Figure 1-11: Calibration curve of Sahin laser diode spectrometer.53



18

Another method for monitoring indigo is the Flow Injection analysis (FIA)61. FIA is a Real-

time analytical technique for determining leuco indigo dye concentration in batch dye bath. 20 uL

sample was introduced in FIA and diluted with 5 different reducing agents. Absorbance

measurements are made at 406 nm (maximum absorption of leuco indigo) by fiber optic coupled

spectrometer. To prevent premature oxidation, nitrogen gas was continuously bubbled in.

While many automatic systems have been developed over the years, few have gained wide

acceptance. Most automatic methods have limited success due to poisoning of the system, either

build-up on potentiometric electrodes, blocking of valves, and/or peristaltic pumps failures.

Extraction of indigo on yarns and fabrics was historically carried out by pyridine reflux. A

given dyed sample of approximately 0.5 grams would have the indigo dye removed until the solution

siphoning from the fabric was colorless. The pyridine solution extract was then brought up to 250ml in a volumetric flask. Absorbance of the solutions at 608 nm is measured on either a single beam

spectrophotometer or a dual-beam diode array spectrophotometer. This particular method of

indigo on weight of yarn measurement is no longer utilized.

Recently Hauser and Merritt29 demonstrated the effective use of ferrous

sulfate/triethanolamine/sodium hydroxide or Fe/TEA/OH as the extraction solvent. Approximately

0.5 gram dyed sample is placed in flask then 100 ml of pre-prepared Fe/TEA/OH solution is added.

(Fe/TEA/OH is prepared by adding 5 g/l ferrous sulfate, 50 g/l triethanolamine, and 10 g/l sodium

hydroxide (pellets) to distilled water.) The extraction is carried out at 45° C for 90 minutes on a

stirring hot plate. After 90 minutes the solution is cooled to room temperature, volume topped off

to 100 ml, and absorbance measured at 406 nm. The solutions once again follow Beer’s law with

dilutions made by additional reducing solution if needed.



19

1.3 Characteristics of Indigo Dyed Yarns

To accurately describe and discuss the characteristics of indigo dyed yarn, a back ground

understanding of color measurement, shade, and ring dyeing is required. Color measurement andshade are physical measurements one can make to qualify the amount of dye on a textile substrate.

1.3.1 Color Measurement and Representation

1.3.1.a Kubelka-Munk Color Evaluation

Most opaque colored objects illuminated by white light produce diffusely reflected colored

radiation by light absorption and scattering. A function based on this fact was developed by Kubelka

and Munk in 1931. These researchers theorized that the ratio of the coefficient of light absorption,K, to the coefficient of light scattering, S, is related to the fractional reflectance of light Rd of a given

wavelength from the opaque substrate.

Consider the simple case of a light beam passing vertically through a very thin pigmented

layer of thickness dx in a paint film, figure 1-12. The downward (incident) and upward (reflected)

components can be considered separately by the absorption coefficient K and the scattering

coefficient S.

Figure 1-12: Kubelka-Munk analysis of downward and upward components of light flux.9

Surface of aint film

X dx

Substrate

I J



20

The downward flux (intensity I) is:

- decreased by absorption = -KIdx

- decreased by scattering = -SIdx

- increased by backscatter = +SJdx

To yield the change in downward flux, equation 1-9 is utilized.9

= − − + = −( + ) +

Equation 1-9: Change in downward flux by Kubelka-Munk

The upward flux (intensity J) is:

- decreased by absorption = -KJdx

- decreased by scattering = -SJdx

- increased by backscatter = +SIdx

To yield the change in upward flux, equation 1-10 is utliized.9

= − − + = −( + ) +

Equation 1-10: Change in upward flux by Kubelka-Munk

Solution of these differential equations for an isotropically absorbing and scattering layer of infinite

thickness leads to the widely used Kubelka-Munk equation, equation 1-11.9

= 1 + −

+ 2 /

Equation 1-11: Kubelka-Munk reflectance equation



21

This equation can be solved for K/S and the widely used form of K/S results in equation 1-12.9

= ()

Equation 1-12: Kubelka-Munk equation for light absorbance and scattering

This is the most widely known form of the equation and most used by textile professionals

directly or indirectly through specialty software programs. For the equation to be of practical value

it is necessary for the equation to be corrected to take into account light reflectance properties of

the textile substrate. One correction to this equation accounts for the light reflectance (Rm) from a

mock-dyed substrate, i.e., a substrate that has been subjected to a dyeing process containing all the

chemicals other then dye.9

= ()

− ()

Equation 1-13: Correction to Kubelka-Munk for light reflectance properties of mock dyed substrate

The range of applicability of the mock dyed corrected formula can be extended by

accounting for surface reflectance of the fabric. It is easily shown that as the dye content of a textile

substrate increases, less and less light is reflected from the substrate. However zero reflectance is

never achieved. Instead a low limiting value of reflectance is encountered that is insensitive to

further increases in concentration of dye in the substrate. This limiting value of reflectance is the

“surface reflectance”, Rs. By including Rs, the range of linearity is extended to higher concentrations

of dye. The final corrected K/S formula is given in equation 1-14.

9



22

= ()

() − ()()

Equation 1-14: Corrected Kubelka-Munk to account for surface reflectance.

Where Rd is the reflectance of light from the substrate containing a given concentration of dye, Rm is

the light reflectance from a mock-dyed substrate, and Rs is the so-called “surface reflectance”.

It is found that the resulting corrected K/S can be shown to be a linear function of dye

concentration in the textile substrate.9 In equation 1-15, "C" is the concentration of dye in the

substrate and “a” is the reflectance absorptivity coefficient. Since the reflectance absorptivity

coefficient is equal to the value of K/S that is obtained per unit concentration of dye in thesubstrate, the reflectance absorptivity coefficient is a measure of the “color yield” that is obtained

for a given system25. As the value of “a” increases, the greater the depth of shade for a given unit of

fixed dye.

= ∗

Equation 1-15: Relationship of K/S corrected to dye bath concentration.

The definition of reflectance absorptivity coefficient requires uniform dye distribution in the

cross section of the yarn. There is only one true reflectance absorptivity coefficient, “at”, for a given

dye/fiber system. Etters has estimated that the value of “at” for dyeings in which indigo is uniformly

distributed in the cross-section of the substrate is approximately 40 when the dye concentration is

expressed as grams of indigo per 100 g of fiber.33

A useful description to represent an object's color was defined by the Committee of the

Society of Dyers and Colourists in 1976 as the CIELAB system. This system defined three parameters

that related the color value of an object. The L* represents the light to dark aspect, a* describes the



23

red to green color shift, and the b* term describes the yellow to blue relationship. These values are

calculated using the equations in 1-16 that involve the tristimulus values which relate the measured

reflectance wavelength values, average observer, and the standard light source. All calculations

presented in this paper use a 10° observer and D65 standard light source. For more detailed review

please reference book 9 in the bibliography section: Colour Physics for Industry.

∗ = 116

− 16

∗ = 500[

−

]

∗ = 200[

−

]

Equation 1-16: L*, a*, and b* equations based on the tristimulus values as defined by CIELAB.

where = ∑ ∑

, = ∑ ∑

, and = ∑ ̂∑

Another method of expressing the overall color value from a sample is the Integ shade

value, equation 1-17. In this calculation the K/S at each wavelength is scaled by the average

observer and standard light source. The resulting Integ value increases in value as the overall color

depth increases.

= ∑

∗ E( + + )

Equation 1-17: Calculation of Integ as a function of K/S values, average observer, and standard light source.46



24

1.3.1.b Determination of Surface Reflectance, Rs

Etters summarized a method for the determination of Rs in 1991.18 To determine the Rs

value, make successive linear regression analyses of K/Scorr versus concentration for various values

of Rs until both a high value of R2 and a statistically optimum zero value for the intercept are found.

Etters plotted the R2 versus Rs values for blue, red, and yellow reactive dye on velour cotton in figure

1-13. It is revealed the R2 value for the blue dye is insensitive to surface reflectance with all the

values being greater than 0.99. On the other hand, R2 for the red dye exhibits much greater

sensitivity to surface reflectance, with the maximum R2 occurring at an Rs of about 0.01. R2 for the

yellow dye has only limited sensitivity to surface reflectance, with the R2 value reaching a maximum

between 0.020 and 0.025. The most important point made in figure 1-13 is that, for the present

series of dyes on the given velour substrate, the R

2

value that results from the use of an optimumvalue of Rs is only slightly improved over that which is obtained with an Rs of zero.

Figure 1-13: Calculated R-square values for blue, red, and yellow dyes at various surface reflectances.18



25

The intercepts of the linear regression lines obtained in the analysis of K/Scorr versus

concentration are given as a function of surface reflectance in figure 1-14. The zero intercept for

the red and yellow dyes occur at about the same value of surface reflectance: 0.0166 and 0.0163.

However the zero intercept for the blue dye occurs at a surface reflectance of 0.0128. Yellow dye is

most sensitive to surface reflectance while the blue dye is the least.

Figure 1-14: Calculated y intercepts for blue, red, and yellow dyes.18

From the R2 and intercept analysis, Etters determined he could use a surface reflectance of

1.5% for each dye. Plots of K/Scorr versus concentration in which both zero surface reflectance and

the common value of 0.015 are given in figure 1-15. In each case the linearity is significantly

improved by accounting for surface reflectance. The reflectance absorptivity coefficient (line slope)

is increased in each case. Recall the R2 analysis indicated only small improvement by accounting for

Rs would be expected. Yet, the surface reflectance had a dramatic visual impact on the correlation

of K/S versus concentration.



26

Figure 1-15: Comparison of original K/S and corrected K/S for blue, red, and yellow dyes.18

Corrected

Original

Original

Original

Corrected

Corrected



27

1.3.1.c Investigating the Ring Dyeing Property of Indigo Dyed Yarn

Ring dyeing is characterized by the inner layer of fibers containing little to no dye while the

outer layer is highly pigmented. During indigo dyeing, the degree of ring dyeing can be regulated by

pH of the dye bath or pretreatments used during pre-scour section. Typically pH 11 displays betterring dyeing, while pH 13 exhibits much greater penetration. Figure 1-16 illustrates the difference in

degree of ring dyeing between normal pre-scour and causticization as well as pH 13.3 vs pH 12.3.

Adsorption and absorption of dyestuff by textiles is strongly dependent on the nature, source, and

properties of the fibers and their surface activity.

Figure 1-16: Examples of limited ring dyeing on the left, medium in the middle, and high degree of ring dyeing on the

right picture.19

Indigo dyeing naturally produces a “ring dyed” effect where the dye concentration is greater

on the surface of the yarn then the interior or core of the yarn. This characteristic is a desirable part

of the indigo dyeing and produces the aesthetic high and low or uneven shade on the final product

after garment wet processing. As mentioned earlier, the ring dye effect can be further enhanced by

causticizing or even mercerization during the pre-scouring process. The figure 1-16 illustrates the

ring dye effect from a pre-scour and causticized warp yarn. The amount of caustic used during pre-

scouring also affects the %indigo pick-up on the cotton yarns. Figure 1-17 documents the change in

indigo pick-up or uptake given constant dye range parameters with only changes in the scour box.



28

Figure 1-17: Pre-scour caustic concentration effect of dye uptake.1

Typical % reflectance values for a 6 dip indigo shade are shown in figure 1-18. These were

measured from production dyeing on 6.3/1 open end 100% cotton yarn dyed at 31 m/min, 2.3 g/l,

11.9 pH, and 6 dips of indigo. When these % reflectance values are corrected for the mock

substrate, the K/S values as a function of wavelength can be calculated as demonstrated in figure 1-

19. Typically the wavelength of the minimum reflectance or the corresponding maximum K/S is

used for calculations. Color yield can be expressed as the depth of shade obtained for a given

amount of fixed dye. Color depth is usually expressed as K/S at the wavelength of minimum

reflectance.

Indigo Pick-up vs. Caustic Concentration in the Scour Box

0

2

4

68

10

12

14

1.5 5 10 20 30 45.5 61.2 80 88.2

50% NaOH Concentration (opg)

% I n

d i g o P i c k - u p

Mild Alkali Causticizing Mercerizing



29

Figure 1-18: Typical reflectance values for indigo dyed denim yarn - 6.3/1 open end yarn at 31 m/min, 2.3 g/l, 11.9 pH,

and 6 dips.

Figure 1-19: Typical corrected K/S values for indigo dyed denim yarn - 6.3/1 open end yarn at 31 m/min, 2.3 g/l, 11.9 pH,

and 6 dips.

% Reflectance Values of Typical 6 Dip Indigo Dye Shade

0

0.5

1

1.5

2

2.5

3

3.5

400 450 500 550 600 650 700

Wavelength (nm)

% R

e f l e c t a n c e

K/S Corrected Values of Typical 6 Dip Indigo Dye Shade

0

10

20

30

40

50

60

400 450 500 550 600 650 700

Wavelength (nm)

K / S

C o r r e c t e d



30

As previously illustrated in figure 1-16, microscopy has revealed that for indigo dye baths

having the same level of alkalinity, but buffered to different pH’s; the resulting distribution of dye

exhibits more or less ring dyeing. When the buffered dye bath pH decreases from 13.0 to 11.0 the

denim yarn progressively becomes more and more ring dyed. Associated with the increased ring

dyeing is more color yield. When a given concentration of dye (expressed as percent on the weight

of the yarn) is located in progressively fewer and fewer fibers, the concentration of dye in each dyed

fiber increases. Reflected light from the surface of the dyed yarn is therefore lower. Etters

proposed the relationship between depth of shade (K/S) and ring dyeing for a given concentration of

dye may be approximated by accounting for dye distribution within the yarn.22

r

p

Figure 1-20: Distribution of indigo dye and penetration level in denim yarn.22



31

The volume of a yarn can be defined as Vm =πr2 1, where the r is the yarn radius and using 1

as a unit length. The volume of yarn not occurred by dye when penetration is not complete (indigo

dyeing) can be expressed as Vi = π (r – pr) 2 1, where p is the penetration of the yarn expressed as a

fraction of the yarn radius, r. The volume of yarn that is occupied by dye then becomes Vd = Vm - Vi.

For a yarn of unit radius and length this equation reduces to Vd = π p (2 – p) and the fractional

volume of yarn occupied by dye can be expressed as Vf = p(2 – p).

The effective concentration of dye in the yarn is related to the actual concentration from a

shade stand point by Ce = Ca / Vf , where Ce is the effective concentration of dye in the yarn and Ca is

the actual concentration of dye in the yarn. When the fractional penetration of the yarn is 1.0, i.e.

uniform dye distribution in the cross section, Ce = Ca. But as penetration becomes less the effective

concentration of dye becomes greater.

When dealing with indigo dyed yarn the shade values or K/S are related to the effective dye

concentration not the actual, the previously discussed K/Scorr = a C can be adjusted for non-

uniformly distributed dye concentrations by substituting Ce.

= ∗ →

= () →

= ()

Equation 1-18: Adjusting K/Scorr for non-uniformly distributed dye

Where at in equation 1-18 is the true reflectance absorptivity coefficient for indigo that is

distributed uniformly in the cross section of the yarn (p=1). Ca is the actual concentration of dye in

the yarn cross section, and “p” is the fractional penetration of the yarn by the fixed dye.



32

1.4 Dye Theory

Numerous books and articles have been published on the topic of dye theory. This review is

intended to provide a fundamental background on key topics that are relevant to indigo-cotton dyesystem. This discussion will start with basic sequence of events during dyeing, then Fick’s laws of

diffusion, next diffusional boundary layer, and ending with empirical simplifications. More in-depth

discussion can be found in Weisz3 and McGregor4.

1.4.1. Fundamental Sequence of Events during Dyeing

Etters28 defined four fundamental steps which outline the path of dye molecules from the

bath to the fiber as illustrated in figure 1-21.

1. Diffusion of the dye in the external medium (usually water) toward the diffusional boundary

layer at the fiber surface.

2. Diffusion of dye through the diffusional boundary layer that exists at the fiber surface.

3. Adsorption of the dye onto the fiber surface.

4. Diffusion of dye into the fiber interior by absorption.



Figure

chem

1

2

3

4

5

6

denie

1-21: Basic seq

The rate o

ical paramet

. Denier of

. Liquor rati

. Distributio

applicatio

. Diffusion

. Fundame

. Thickness

Rate of dy

r of a given f

ence of events

f sorption of

rs.

iber, which i

o, the ratio o

n coefficient

medium an

oefficient of

tal nature of

of the diffusi

eing for a giv

iber increase

in dyeing fiber

dye by textil

proportion

f volume of

or ratio of th

d the fiber.

the dye in b

the dyeing s

onal bounda

en system is

, the surface

.28

materials is

l to radius o

ye bath to t

e equilibriu

th the applic

stem: infini

y layer at th

inversely pro

area decrea

controlled b

the cylinder

e volume of

concentrati

ation mediu

e or finite ba

fiber surfac

portional to

ses for a give

several fun

fiber.

fiber mass.

on of dye in

and the fib

th condition.

e.

he denier of

n mass of fib

amental ph

oth the

er.

the fiber. A

er available f

33

sico-

the

or



34

dye sorption. Accompanying the increased surface area that is associated with decreasing fiber

radius is a decreased distance that the dye on the exterior fiber surface must diffuse to “fill” the

fiber to an equilibrium fixation level. Lengths to diameter ratios for useful fibers are usually greater

then 1000, so the surface area contributions from the ends of the individual fibers are relatively

small and usually ignored.

Since dyeing on a continuous rope dye range is conducted under constant dye bath

concentrations, the process is defined as an infinite dye bath. Since the liquor ratio is infinitely high,

the exhaustion is zero.28 Under infinite dye bath conditions, since dye that is absorbed at the fiber

surface is in equilibrium with dye in the dye bath, diffusion of dye into the fiber interior will occur

from a constant surface concentration.28 From a mathematical standpoint, Etters has stated

“Sorption of dye from a constant surface concentration is a much simpler system from an

experimental and analytical point of view”.31 Some argue diffusion coefficient of dye in a fiber is

really the same as it is in the surrounding aqueous medium.28

“Rate of dyeing” is controlled by the rate of diffusion of dye “in fiber” unless a significantly

thick diffusional boundary layer exists at the fiber surface. If a diffusional boundary layer exists,

then rate of dyeing is influenced by rate of diffusion of dye in dyeing medium and fiber which may

possess different diffusion coefficients.28

One problem related to indigo dyeing is when dye becomes immobilized as diffusion

proceeds. When diffusion is accompanied by absorption, conventional equation of diffusion in one

dimension has to be modified to allow for immobilization.48

1.4.2 Fick's Law of Diffusion

Any discussion involving diffusion should begin with the some basic definitions.

1. Absorption: the process of absorbing. Absorb: to take up and make part of an existent whole.

2. Adsorption: the adhesion in extremely thin layer of molecules to the surface of solid bodies or

liquids with which they are in contact.

3. Desorption: the reverse of absorption or adsorption.

4. Sorption: the process of sorbing. Sorb: to take up and hold by either absorption or adsorption.



35

During the the indigo-cotton dyeing process, the following steps are assumed to occur. The

indigo dye molecules form a thin layer surrounding each cotton fiber. This process is adsorption of

dye to the fiber surface. Once the indigo dye molecules adhere to the fiber surface, indigo dye can

absorb into the fiber interior by absorption. This entire process can also be referred to as sorption

of indigo dye into the cotton fibers. If indigo dye is removed from the cotton fiber either from the

interior to the surface or from the surface to the surrounding bath, the process is referred to as

desorption.

Crank defines diffusion as the process by which matter is transported from one part of a

system to another as a result of random molecular motions.2 Etters defines the diffusion coefficient

as a measure of the rapidity of movement of a molecule through a given medium. As the value of

diffusion coefficient increases, the speed of movement of a molecule through the medium also

increases.28

The complicated process of dyeing is modeled on the diffusion principles outlined by Fick.

Fick recognized the relationship between diffusion and heat transfer by conduction. He adopted the

mathematical equations derived by Fourier to quantify diffusion. Fick’s first law of diffusion for one

dimensional isotropic medium is written in equation 1-19.

= − ∗

Equation 1-19: Fick's first law of diffusion.2

Here F is the rate of transfer per unit area of section, C the concentration of diffusing substance, D is

the diffusion coefficient, and x the space coordinate measured normal to the section.



36

Using Fick’s first law, Fick’s second law for diffusion in one dimension can be derived as

equation 1-20.

=

Equation 1-20: Fick's second law of diffusion.2

Furthermore, the equations can be expanded to multi-dimensions in cylindrical coordinate system

to describe diffusion in cylinders.

=

∗

+

+

∗

Equation 1-21: Expansion of Fick's second law of diffusion into cylindrical coordinate system. 2

Here x = r cos θ and y = r sin θ, where r, θ, and z are cylindrical coordinates. Equation 1-21 can be

solved by the method of separation of variables, method of Laplace transformation, or numerical

solutions when the diffusion coefficient can be assumed constant.

Modeling the dye process by considering diffusion in long circular cylinders reduces the 3-

dimensional equation to the following diffusion equation 1-22.

=

∗

Equation 1-22: Reduction of Fick's second law of diffusion to radial component only. 2



37

This equation is one dimensional since diffusion progresses radially into the yarn and is constant

around the yarn. No diffusion occurs along the axis of the yarn. The non-steady state solution for

solid cylinder with constant surface concentration and uniform initial internal concentration that

possesses the boundary conditions: C=f(r), at 0<r<a and t=0; and C=Co at r=a and t≥0, produces

equation 1-23.

= [1 − ∑

()/()] + ∑ ()/() ∗

∫ () ()Equation 1-23: Non-steady state solution to equation 1-21.

2

Here αn ‘s are the positive roots of Jo which are the Bessel function of the first kind of order zero.

If the concentration is initially uniform throughout the cylinder than equation 1-23 reduces

to equation 1-24 and is graphically depicted in figure 1-22.

= 1 − ∑ ()

(

)

Equation 1-24: Solution of diffusion from constant initial concentration.2

Here the C is the concentration within the cylinder, C1 is the initial uniform concentration within the

cylinder, and C0 is the constant surface concentration on the cylinder.



38

Figure 1-22: Graphical solution of Fick's 2nd Law for Diffusion in long cylinders.2



39

The sorption curves on figure 1-22 are defined by the dimensionless parameter Dt/a2.

Other formal solutions to the partial differential equation have been developed. However

there are certain limiting assumptions that must exist for the mathematical solutions to be valid.

1. It is assumed the diffusion coefficient is constant and not dependent on concentrations.

2. Equilibrium distribution coefficient of dye between fiber and dye bath is linear for a wide

range of concentrations, i.e. linear sorption isotherms.

3. All fibers are morphologically stable, homogenous, and uniformly accessible endless

cylinders.

4. No diffusional boundary layer exists in the dye bath and no “skin-core” effect exists in the

fiber. This results in instantaneous equilibrium between dye on fiber surface and dye in the

bath.

Given these assumptions Hill31 has developed a solution for infinite dye bath conditions in the

absence of surface barrier effects, equation 1-25.

= 1 − ∑

Equation 1-25: Hill's solution of dye concentration under infinite dye bath conditions.31

Here the βn’s are the positive transcendental Bessel roots given by J0 βn = 0 and is the fractional

equilibrium uptake of dye at a given time Mt and at equilibrium . An unfortunate limitation of

Hill’s infinite bath equation is that all of the four assumptions previously mentioned must be

present.

Newman31 developed an alternative solution for infinite dye bath conditions that does not

require assumption #4. Namely, Newman’s solution is applicable in the presence of surface barrier

effects. Due to this fact, Newman’s equation (equation 1-26) is particularly useful for diagnostic or

analytical work.



40

= 1 − ∑ ∗

( )

Equation 1-26: Newman's solution of dye concentration under infinite dye bath conditions that contain surface barrier

effects.31

Here the βn’s are the roots of the transcendental equation: βnJ1(βn) - LJ0(βn) = 0 in which J0 and J1

again are zero and first order Bessel functions, and the dimensionless parameter, L is defined by

equation 1-27.

=

Equation 1-27: Definition of L term utilized in Newman's dye concentration solution.

Here Dm and Ds are the diffusion coefficients of the diffusant in the external medium and polymer

respectively, K is the equilibrium distribution coefficient of the diffusant between the external

medium and the polymer, r is the radius of the cylinder, and δD is the thickness of the diffusional

boundary layer.

The diffusional boundary layer is a mechanical characteristic that impedes sorption or

desorption and is inversely proportional to the rate of flow of the external medium past the surface

of the cylinder. When the rate of flow of the external medium is very high, the thickness of the

diffusional boundary layer approaches zero and the value of “L” approaches infinity. As the value of

“L” approaches infinity, the βn2 /L2 drops out from Newman’s equation (equation 1-26) which then

becomes equivalent to Hill’s equation (equation 1-25).

These solutions may not directly apply to indigo dyed cotton yarn due to several underlying

assumptions. Namely the constant initial uniform concentration within the cylinder only applies

before the first dip where C1=0. Also the diffusion coefficient may not remain constant through



41

every dip of indigo. In fact it may be a function of the dye concentration within the yarn.

Furthermore, the “skin” of oxidized indigo dye on each yarn after the first dip may have a different

diffusion coefficient then the partially dyed cotton yarn.

In the absence of experimental data, the Othmer-Thakar

31

correlation can be used to

estimate the diffusion coefficient, Ds, of various substances in dilute aqueous solutions. The

Othmer-Thakar correlation was defined in equation 1-28.

∗ 10 = ..

Equation 1-28: Othmer-Thakar relationship for diffusion coefficient in dilute aqueous solutions.

Here Uw is the viscosity of water in centipoises and Vm is the molal volume of the diffusing substance

in ml per gram-mole. With the Ds value the “apparent diffusional boundary layer”, δD, can be

determined.

1.4.3. Diffusional boundary Layer

The diffusional boundary layer, δD, potentially impedes dye uptake by the fiber. The

thickness of diffusional boundary layer is proportional to the thickness of the hydrodynamic

boundary layer and the thickness of the hydrodynamic boundary layer is inversely proportional to

velocity of flow of the bath past the fiber surface. Figure 1-23 illustrates the effect of dye bath

movement on fractional dye uptake. In case #4 of E=0 (infinite dye bath conditions), at low flow

rate 50% uptake occurs at 0.4 dimensionless time units. Whereas 50% dye uptake occurs almost at

0.2 dimensionless time units at the higher flow rate.



42

Figure 1-23: Predicted fractional dye uptake as a function of dimensionless time at various flow rates.28

Etters evaluated Newman’s equation on Disperse Red 11 in stabilized, 40 denier, 13 filament

nylon 66 tricot using desorption experiments. The results are presented in table 1-4. There was

variation in the desorption data leading to uncertainty in the computation of not only the diffusion

coefficient but also the L value. In response, the approximate L values and apparent diffusion

coefficients were determined by utilizing the % CV minimization technique.



43

Table 1-4: Estimated diffusion coefficients for disperse Red 11 (D, cm2/sec x 10

-10).

31

Time (min) 15 opm (L=2) 30 opm (L=80) 90 opm (L=∞)

0.50 4.72 5.38 4.81

1.00 4.17 4.89 4.382.00 5.06 3.84 5.03

3.00 4.29 4.11 4.56

4.00 3.04 4.75 4.50

5.00 5.31 4.39 4.89

10.0 5.06 4.63 4.34

15.0 5.14 5.08 4.20

Mean 4.60 4.63 4.59

%CV 16.33 10.94 6.38

The experimental data was plotted according to Newman’s equation using the mean value

of the diffusion coefficient for each value of L. When 1- was plotted versus the square root of

time, an intercept on the root time axis was detected for lowest value of L, see figure 1-24. This

behavior is typical for systems in which a surface barrier exists in either the bath or the fiber. It is

also important to note, since an L value of infinity is found for the highest oscillation rate, no skin-

core effect is detected for the nylon fiber. If the value of L had not increased very much as the

oscillation rate of the bath increased, an argument could be made that the effect was caused by a

barrier that existed in the fiber surface rather than in the bath itself.



44

Figure 1-24: Red 11 dye desorption at various oscillating speeds.

1.4.4. Empirical Simplifications of Diffusion

The formal solution to Fick’s 2nd

law of diffusion is a grueling task even for a superior

mathematician. To simply the equations many empirical equations have been proposed over the

years. Three such exponential equations were compared for the efficacy in simulating the

functional relationship between

, Dt/r2, and L that is found by formal use of Newman’s equation

1-26.31 The equations that were examined are one, two, and three parameter exponential

equations. Vickerstaff suggested an empirical approximation using one parameter as shown in

equation 1-29.31

= 1 −

Equation 1-29: Vickerstaff one parameter approximate solution for dye distribution.



45

Urbanik was the among the first to use the two parameter equation to describe dye uptake which is

provided in equation 1-30.31

= 1 − ( )

Equation 1-30: Urbanik two parameter approximate solution for dye distribution.

Etters developed a three parameter equation to express the functional relationship as shown in

equation 1-31.31

= [1 −

]

Equation 1-31: Etters three parameter approximate solution for dye distribution.

Each of the three equations were fitted to data obtained by the use of formal solutions to

Newman’s equation for the

range of 0.05 to 0.95 at 0.05 intervals and associated values of Dt/r2

for values of L ranging from infinity to 1.0. The goodness of fit is expressed as adjusted R2. Etters’

three parameter equation provides the best fit of the three empirical exponential equations over a

very wide range of L. Only at very low values of L does the two parameter equation perform as well.

For the three parameter equation to have empirical utility for a wide range of L values, it is

necessary to express the parameters a, b, and c as a function of L. Etters derived the following

expression for L at a range of 20 to infinity.



46

=

Equation 1-32: Etters empirical fit equation to calculate parameters in three parameter approximate solution for dyedistribution when L is 20 to infinity.

31

Here PV equals a, b, or c in his three parameter equation for L range of 20 to infinity.

parameter a: q0=5.530554, q1=160.58898, q2=-1750.616, q3=37.494042, q4=-374.48753

parameter b: q0=1.2479036, q1=27.400938, q2=88.43848, q3=33.90477, q4=52.505626

parameter c: q0=0.3798136, q1=12.004462, q2=-6.8204581, q3=11.003091, q4=5.3552691

For L range from 20 to 1, the three equations shown in equations 1-33, 1-34, and 1-35

accurately express the parameter values of a, b, and c which are utilized in equation 1-30.

= + ln

+ +

Equation 1-33: Etters empirical fit equation to calculate parameter a in three parameter approximate solution for dye

distribution when L is 1 to 20.31

Here: q0=4.098044891, q1=3.024653177, q2=-2.49630292, q3=2.59232464

= + + ln

+

Equation 1-34: Etters empirical fit equation to calculate parameter b in three parameter approximate solution for dye

distribution when L is 1 to 20.31

Here: q0=1.179748591, q1=-0.14496394, q2=0.094386506, q3=0.001282442



48

As shown in Figure 1-25, the above technique results in a series of nearly straight lines

corresponding to various values of equilibrium bath exhaustion, E∞. The slope of each line defines

the parameter b and the line intercept I (at Dt/r2

=1) gives the parameter a, a=eI

. Table 1-5

summarizes the regression values for a, b, and c for various E∞. For infinite dye bath conditions,

E∞= 0, table 1-5 gives the following values: a=5.3454, b=1.1299, and 1/c=2.3.

Table 1-5: Regression values for three parameter emphirical solution.10

E∞ a b 1/c

0.995 13.4067 0.1150 0.06250.98 10.6394 0.1619 0.17

0.95 9.0635 0.2177 0.32

0.90 8.1074 0.2904 0.52

0.75 7.2074 0.4742 1.00

0.50 6.5849 0.7373 1.60

0.30 6.1410 0.9319 2.00

0.00 5.3454 1.1299 2.30

Rearranging Etter’s three parameter equation permits the direct calculation of the apparent

diffusion coefficient D as shown in equation 1-36.

= [(

)

)]

Equation 1-36: Etters relationship for apparent diffusion coefficient and three parameter estimates.31



49

1.5 Indigo Dyeing Experiments

The methods and procedures used by various experimenters will be presented in one

section for direct comparison. The cotton yarn and fabric substrate from each experiment should benoted as well as the dye procedure. Later the actual results from all experiments have been

grouped together. This will facilitate discussion of a particular topic based on all available analysis.

1.5.1. Previous Investigations and Methods on Indigo Dyeing

Southeastern Section of AATCC 1989 Experiment15

The Southeastern Section Research Committee published a paper in 1989 investigating the

effect of dye bath pH on color yield. This study used 8/1’s yarn knitted into tube form having aflattened width of about 2 inches. The dye baths used 20% indigo paste, sodium hydrosulfite power,

sodium hydroxide pellets, and potassium phosphate buffered alkalis.

The dye baths were prepared by mixing the required amount of dye, 150 ml of the selected

type of stock alkali solution, and 15 grams of sodium hydrosulfite with 500 ml of water at 90° C for 2

minutes. The dye baths were then diluted to a volume of 3 liters with room temperature water and

cooled to room temperature of 25° C.

For each group of dyeings made at a measured dye bath pH, the indigo dye bath

concentrations consisted of 2.0, 1.5, 1.0, 0.5, and 0.2 g/l (based on 100% indigo). The concentration

of alkali (hydrated form) in stock solution is outlined in table 1-6.

Table 1-6: Concentration of alkali system.

Group A 60.1% Sodium hydroxide

Group B 37.0% Sodium hydroxide

Group C 37.5% Potassium Phosphate Buffer 1Group D 36.0% Potassium Phosphate Buffer 2

Group E 39.3% Potassium Phosphate Buffer 3

Group F 39.2% Potassium Phosphate Buffer 4

Group G 37.7% Potassium Phosphate Buffer 5



50

Lengths of tubing weighing 7.5 grams each were wet out in room temperature baths

containing 5 g/l of wetting agent and squeezed to 71% wet pick-up. These were then placed into a

three liter dye bath containing a specified dye concentration at a given pH. The dwell time in the

dye bath was 15 seconds, followed by a squeeze and skying time of 45 seconds. Each dyeing

consisted of five, 15 second dips in the dye bath followed by squeezing and 45 second aeration.

After all dyeings had been completed, the knitted tubes were rinsed together three times in a 90° C

water bath, squeezed by a padder after each rinse, and finally air dried. Since the liquor ratio from

which the dyeings were made was 400/1, dye uptake can be considered to be occurring from

essentially an infinite bath. Following this assumption, the concentration of dye at the fiber surface

does not change during the course of dyeing.

The dye on the knitted tubes was determined by hot pyridine extractions. The pyridine

extractions were diluted to 25 ml in a volumetric flask. The absorbance was measured on a

spectrophotometer at a wavelength of 612 nm. Using known absorbance versus concentration

data, the calculated dye content on the denim yarn was determined.

Reflectance values from 400 to 700 nm at 20 nm intervals were measured on all dyeings and

a mock dyed sample by a spectrophotometer with ultraviolet and specular reflectance contributions

using C2 illuminant.

The following was assumed for the analysis and results summarized in table 1-7.

1. There was sufficient reducing agent in the dye bath at all times to completely reduce all of the

indigo.

2. Ionic strength is approximately constant over all dye bath conditions.

3. Solubility does not limit the concentration of any salt in the bath.



51

Table 1-7: Etters 1989 data set.15

Group pHDyebath(g/L)

Dye in Fiber(g/100g) Reflectance Crock

A 13.3 0.2 0.03 17.79 4

A 13.3 0.5 0.06 12.73 3

A 13.3 1 0.15 8.81 4 A 13.3 1.5 0.26 6.04 3

A 13.2 2 0.42 3.94 3

B 13.2 0.2 0.02 17.69 4

B 13.1 0.5 0.1 9.34 4

B 13.1 1 0.28 4.76 3

B 13.1 1.5 0.39 3.63 3

B 13.1 2 0.61 2.97 3

C 12.3 0.2 0.06 7.37 4

C 12.3 0.5 0.24 3.39 3

C 12.3 1 0.51 2.33 3

C 12.2 1.5 0.66 2.11 2

C 12.1 2 0.81 2.02 2

D 11.4 0.2 0.09 4.68 4

D 11.4 0.5 0.28 2.46 3

D 11.3 1 0.53 1.98 2

D 11.3 1.5 0.77 1.88 2

D 11.2 2 1.01 1.95 2

E 11.2 0.2 0.08 4.67 4

E 11.2 0.5 0.26 2.47 2

E 11.1 1 0.54 1.96 2

E 11 1.5 0.77 1.89 2

E 10.9 2 1.1 2.01 2

F 10.4 0.2 0.13 4.09 4

F 10.3 0.5 0.34 2.24 3

F 10 1 0.62 2.1 2

F 9.8 1.5 0.92 1.89 1

F 9.4 2 1.15 2.32 1

G 7.7 0.2 0.04 11.87 4

G 7.7 0.5 0.08 9.84 3

G 7.7 1 0.13 9.04 3

G 7.8 1.5 0.15 7.75 2

G 7.8 2 0.22 6.61 2



52

Annis and Etter 1991 Experiment19

In May 1991 Annis and Etters published results from an experiment designed to investigate

dye uptake and resulting color yield as influenced by dye bath pH. The same material, laboratory

simulations of indigo dyeing, and analytical techniques used by the Southeastern Section of AATCCwere used in this experiment except 0.25 g/l indigo concentration was used instead of 0.20 g/l. The

experimental results are summarized in table 1-8.

Table 1-8: Annis and Etters 1991 data set.19

pH Cb Cf Rd pH Cb Cf Rd

9.3 1 0.63 0.02 12.8 1.5 0.27 0.034

8.5 0.25 0.05 0.12 9 0.5 0.15 0.0412.1 0.25 0.08 0.063 11.9 2 0.6 0.022

13.1 2 0.62 0.03 11.2 2 1.06 0.017

10.5 2 1.18 0.017 13 2 0.52 0.028

11 1 0.53 0.021 12.5 0.5 0.13 0.056

11.2 0.25 0.11 0.038 13.3 1.5 0.285 0.044

13.1 1.5 0.405 0.036 13.3 1 0.15 0.088

11.3 0.5 0.265 0.026 7.8 1.5 0.18 0.076

11.8 2 0.8 0.019 7.8 2 0.22 0.06

12.3 2 0.84 0.02 12.2 0.5 0.24 0.031

12.3 1 0.47 0.024 13.3 2 0.44 0.031

12.8 1 0.2 0.046 11.1 1.5 0.78 0.0187.7 0.25 0.048 0.18 9.8 2 1.18 0.018

10.3 1 0.64 0.02 10 0.25 0.165 0.037

10.8 0.5 0.27 0.025 11.4 1.5 0.76 0.019

10.8 0.25 0.108 0.04 10.4 1.5 0.885 0.019

7.7 1 0.15 0.048 12.3 1.5 0.63 0.022

13.1 0.5 0.09 0.1 11.3 1 0.52 0.02

7.7 0.5 0.08 0.099 10.3 0.5 0.335 0.023

13.3 0.5 0.065 0.159 9.5 1.5 0.9 0.019

13.1 1 0.26 0.046 7.7 0.25 0.044 0.191



53

Etters 1991 Experiment20

In December 1991, Etters published results from an experiment investigating the effect of

pH and dye concentrations on fiber dye uptake under equilibrium conditions. 8/1’s cotton yarn

knitted into tubes was dyed with indigo, sodium hydrosulfite, and sodium hydroxide or proprietarybuffered alkali solution. Dye baths were prepared by mixing the required amount of dye with either

20 grams of NaOH to obtain dye bath pH of 13.1-13.3 or with 100 ml of buffered alkali solution to

obtain dye bath pH of 11.1-11.3. 10 grams of sodium hydrosulfite and 600 ml of de-ionized water at

80° C were then added to each mixture and stirred for 30 seconds to facilitate dye reduction to

leuco form. The total volume was then increased to 2 liters with de-ionized water at room

temperature. The following indigo dye concentrations were prepared (expressed as 100% pure

indigo): 0.05, 0.10, 0.175, 0.25, 0.375, 0.50, 0.625, 0.75, 1.00, 1.125, 1.25, 1.5, 2.00, and 2.50 g/l.

To perform the dyeings, the knitted tubes were wet out at room temperature in baths

containing 5 g/l wetting agent. The tubes were then rinsed three times in warm de-ionized water

and squeezed to 71% pick-up. A 1 g sample of the rinsed knit tube was attached to the sample

holder of the dyeing machine and placed into an 850 ml dye bath which contained the specified dye

amount and pH. Since the liquor ratio was 850/1, infinite dye bath conditions were in effect.

Preliminary experiments revealed that the mean relative dye uptakes for 0.1 and 1.0 g/l dye bath

concentrations at dyeing times of 2, 4, and 8 hours at 25° C were 0.978, 0.933, and 0.930

respectively. Eight hours appeared to be more than sufficient to achieve a close approximation to

equilibrium. Cross sections of yarn and fibers were examined to confirm complete penetration after

8 hours. So all dyeing was conducted over 8 hours with agitation at 25° C in covered cylinders. After

dyeing, the samples were exposed to air for 30 seconds to promote dye oxidation, rinsed with warm

de-ionized water, and squeezed to about 71% pickup. The samples were then dried overnight at 65°

C in an oven.

Fiber dye content was determined by using pyridine extraction technique. 20 to 60 mg

dried sample from each dye condition was weighed, stored in a desiccator with anhydrous CaSO4 for

24 hours, and weighed again. Dye was extracted using pyridine at about 80° C. The resulting dye

solutions were built to 25 ml in a volumetric flask and the absorbance of each solution was

measured at a wavelength of 610 nm using a spectronic colorimeter. Using known absorbance



54

versus concentration data, the dye content was calculated. The results of the equilibrium sorption

experiment were summarized in table 1-9.

Table 1-9: Etters 1991 Equilibrium sorption of indigo on cotton obtained from different pHs in grams of dye per 100

grams of water(bath) or fiber.20

Cb Cf (pH=13.2) Cf (pH=11.2) Cb Cf (pH=13.2) Cf (pH=11.2)

0.005 0.075 0.316 0.075 0.635 1.557

0.005 0.077 0.314 0.0875 0.649 1.679

0.01 0.139 0.553 0.0875 0.652 1.727

0.01 0.14 0.561 0.1 0.753 1.742

0.0175 0.195 0.69 0.1 0.729 1.837

0.0175 0.189 0.7 0.1125 0.81 2.098

0.025 0.296 0.933 0.1125 0.767 1.971

0.025 0.3 0.917 0.125 0.872 2.1110.0375 0.361 1.047 0.125 0.838 2.147

0.0375 0.342 0.999 0.15 0.907 2.34

0.05 0.472 1.239 0.15 0.927 2.517

0.05 0.444 1.296 0.2 1.251 3.181

0.0625 0.513 1.409 0.2 1.191 3.024

0.0625 0.525 1.459 0.25 1.44 3.518

0.075 0.547 1.535 0.25 1.465 3.418

Etters 1994 Experiment27

To investigate shade sensitivity as a function of pH, Etters designed an experiment at two

different pH levels and small permutations of pH were introduced. The experiment utilized 8/1’s

denim yarn knitted into tubes with a flattened width of 4.5 cm and weight of 7.2 grams per 30 cm

length.

The dye baths were three liters in total volume to ensure infinite dye bath conditions. Table

1-10 outlines the dye concentrations utilized in the experiment.



55

Table 1-10: Dye concentrations required to yield equivalent shade at different pHs.27

K/S pH 11.0 pH 12.5

50 0.5 g/l 1.7 g/l

100 1.0 g/l 3.2 g/l

200 2.1 g/l 6.5 g/l

In addition to the indigo dye concentration, 2.0 g/l of sodium hydrosulfite was maintained in all dye

baths. pH of 11.0 was obtained by using 50 g/l of commercial buffered alkali, Virco Buffer ID. A

nearly equivalent total alkalinity amount of sodium hydroxide was used to obtain 12.5 pH. The dye

bath pH was then adjusted downward with the addition of sodium bisulfite and upward with sodium

hydroxide.

The knitted tubes were wet out at room temperature in a solution containing 1.5 g/l sodium

dioctyl sulfosuccinate, wetting agent, and passed through a pad. The tubes were then rinsed with

de-ionized water and squeezed again. Finally the tubes placed into a fresh bath of de-ionized water

until needed.

To dye each tube, the excess de-ionized water was squeezed from the tube prior to

immersion into the dye bath at room temperature for 15 seconds. The excess dye liquor was then

squeezed from the tube to 70% pick-up and air oxidized for 45 seconds. This process was repeated

4 times on each tube to simulate a 5 dip dye range. After all dyeings were completed, the tubes

were rinsed together with warm water until the rinse water appeared to be colorless. After drying

all the tubes, reflectance measurements were collected using a LabScan 6000 spectrophotometer.

Corrected K/S values were calculated based on the 660 nm wavelength reflectance. The results are

summarized in table 1-11.



56

Table 1-11: % reflectance and corrected K/S values for different dyebath concentrations and pH.27

Cb (g/l) pH %Rc K/S Cb (g/l) pH %Rc K/S

0.5 10.6 2.52 48 1.7 12.1 2.29 62.2

0.5 10.8 2.5 48.9 1.7 12.3 2.38 55.8

0.5 11 2.48 50 1.7 12.5 2.47 50.5

0.5 11.2 2.51 48.4 1.7 12.7 2.59 44.8

0.5 11.4 2.53 47.5 1.7 12.9 2.74 39.3

1 10.6 2.01 97 3.2 12.1 1.9 123.9

1 10.8 2 98.9 3.2 12.3 1.95 110.1

1 11 1.99 101 3.2 12.5 1.99 101

1 11.2 2 98.9 3.2 12.7 2.05 89.8

1 11.4 2.01 97 3.2 12.9 2.12 79.6

2.1 10.6 1.77 184.1 6.5 12.1 1.7 248.9

2.1 10.8 1.75 198.9 6.5 12.3 1.72 226.2

2.1 11 1.75 198.9 6.5 12.5 1.75 198.9

2.1 11.2 1.76 191.2 6.5 12.7 1.78 177.5

2.1 11.4 1.77 184.1 6.5 12.9 1.81 160.2

Chong 1995 Experiment29

The material used in the experiment was 16/1’s yarn woven in a 2x1 twill with 78x50

construction. One standard dipping consisted of immersing the material into a leuco indigo dye

bath for 1 minute followed by immediate air oxidation for 3 minutes. 5 successive dips were chosen

as the standard procedure. After dyeing, the material was thoroughly rinsed and soaped at boil for

10 minutes in a soaping bath containing 1.5 g/l of Lissapol NX. The standard dye bath consisted of

the following formula.

Indigo dye – 2 g/l

Sodium dithionite – 6 g/l

Caustic soda – 5 g/l

Sandozin NI – 0.2 g/l

The reduction of indigo dye was carried out at 80° C for 10 minutes.

After each dyeing the color yield as expressed by Kubelka-Munk K/S at 660 nm was

calculated.



57

Xin 2000 Experiment46

In 2000 Xin, Chong, and Tu studied the effects of indigo, caustic, and hydro concentrations,

immersion time, and number of indigo dips on the depth of shade. They used a 100% cotton 7/1’s

open end yarn loosely knitted into fabric as the dyeing substrate. The fabric was boiled for 30minutes in a solution of Sandopan DTC (1 g/l, wetting agent) and caustic soda (1.5 g/l) with a liquor

ratio of 30:1. The fabric was then air dried.

The basic dye bath formula utilized 2 g/l of 100% indigo, 4 g/l of sodium hydrosulphite

(85%), and 4 g/l sodium hydroxide. The fabric was dyed at room temperature with each dip

immersed for 30 seconds. The excess liquor was removed by squeezing to 80% wet pick-up and air

oxidized for 2 minutes. Five dips were simulated for all experiments except on the effect of dips.

After dyeing each fabric was thoroughly rinsed with warm water.

To evaluate the dyed samples spectrophotometric analysis was conducted. The K/S value at

660 nm and an Integ value, expressed in equation 1-37, were used.

= ∑

∗ E( + + )

Equation 1-37: Calculation of Integ as a function of K/S values, average observer, and standard light source.46

Here: E λ spectral power distribution of illuminant and (x λ + y λ + z λ) is the standard observer

function. As the maximum absorption wavelength shifts to less than 660 nm for samples with high

shade depth, the Integ value was used instead of the traditional K/S values.



58

1.5.2. Discussion of Previously Published Experimental Results

1.5.2.a Oxidation Time Effect on Indigo Dye Uptake

To achieve the progressive build-up of indigo dye it is important to ensure adequate

oxidation time after each immersion. If complete oxidation is not allowed to occur, desorption of

indigo dye from the cotton yarn will result in weaker dye build-up. As part of Chong’s 1995

experiment the effect of oxidation time was evaluated. While the K/S values have not been

corrected, the results are still relative. Figure 1-26 shows the effect of oxidation time on the color

depth. Complete oxidation is achieved after 60 seconds. Oxidation times in excess of 60 seconds

are not required to completely develop the indigo shade.

Figure 1-26: Effect of oxidation time on color.29

Effect of Oxidization Time on Depth of Shade

10

15

20

25

30

30 60 90 120 150 180

Oxidization Time (sec)

K / S



59

1.5.2.b Amount of Reduction Agent Effect of Indigo Dye Uptake

The effect of excess hydro was investigated by Xin and the results displayed in figure 1-27.

Only a minor change in dye yield was observed between 0 g/l to 0.25 g/l (excess). Greater excess

hydro concentrations beyond 0.25 g/l had no appreciable impact on dye yield. There is of coursethe limiting case, when excessive hydro actually doesn’t permit complete oxidation during the

skying phase. In this case, reduced indigo can be stripped from the yarn and the depth of shade

reduced.

Figure 1-27: Effect of reduction agent concentration on shade.46



60

1.5.2.c Immersion Time Effect of Indigo Dye Uptake

Xin's investigation into immersion time effects on indigo dye uptake is shown in figure 1-28.

Any immersion time greater than 20 seconds does not affect the dye yield significantly. Dye yield

had slight changes between 0 to 20 seconds. Typical indigo dye ranges have 20 to 30 seconds ofimmersion time.

Figure 1-28: Effect of immersion time on shade.46

Chong29 also investigated the effect of increasing immersion time on color depth. In figure

1-29, an immersion time of 30 seconds appears to be adequate. Prolonged immersion time does

not increase the color depth because the oxidized indigo on the material may be re-reduced by the

reducing agents present and causes desorption of the indigo. These two separate experiments

support each other’s conclusions.



61

Figure 1-29: Chong's effect of immersion time on uncorrected K/S.29

1.5.2.d Number of Dips Effect of Indigo Dye Uptake

As previously stated indigo dye has a low affinity for cotton. To increase the depth of shade

multiple dips are widely utilized. Xin explored the impact of multiple dips on the resulting shade

with results shown in figure 1-30. The effect of number of dye dips produced results as expected.

As the number of dips increased, the shade darkened. After the 8th dip the change in depth of shade

significantly decreases but does continue to darken. Also notice the cast shifts from greenish dark

blue to redder less blue shade as the number of dips increase.

Effect of Immersion Time on Depth of Shade

10

15

20

25

30

15 30 45 60 75 90

Immersion Time (sec)

K / S



62

Figure 1-30: Relationship between number of dips and shade.46

Since the color depth of indigo dyed yarns relies on the progressive build-up of color

through successive dipping and oxidation, the number of dips is the prime factor determining the

final color yield. As shown in figure 1-31, the optimum color yield is achieved after about 10 dips.

Chong29 and Xin46 independently confirm the results.



63

Figure 1-31: Chong's relationship between number of dips and uncorrected K/S.29

1.5.2.e Dye Bath Concentration Effect of Indigo Dye Uptake

The effect of dye concentration was studied by immersing knitted fabric into the simulated 5

dip method with varying dye bath concentrations by Xin46. The first graph in figure 1-32 illustrates a

rapidly decreasing L* value with increasing dye concentrations until ~2 g/l, after which the level of

decrease lightness slows down and tends to level off. The cast shift is displayed in the second graph

of figure 1-32 with the shade shifting more red and yellow as dye concentration was increased. The

final graph in figure 1-32 confirms the increasing depth of shade trend as indigo dye bathconcentration was increased.



64

Figure 1-32: Relationship between dye bath concentration and shade.46

Chong29 examined the effect of indigo dye bath concentration on color yield as shown in

figure 1-33. The affinity of indigo dye is very low, as is its build-up property. Hence increased color

depth cannot be achieved solely by increasing the dye concentration. In fact the color yield remains

fairly flat after 3 g/l.



65

Figure 1-33: Chong's relationship between dye bath concentration and uncorrected K/S.29

1.5.2.f The Affect of pH on Indigo Dye Uptake

Since leuco indigo is a weak acid, the pH of the dye liquor will have a significant effect on

dye yield. This can be explained by ionization which changes the substantivity of the dye to cotton

fiber. The highest substantivity of dye for the cotton fiber can be achieved at about pH 10.0. Thus

the degree of ring dyeing would be higher at pH 11.0 then more conventional pH region of 12.0-

13.0. The effect of pH on depth of shade and the corresponding cast shift is illustrated in figure 1-

34.



66

Figure 1-34: pH effect of shade with other parameters held constant.46

Although the maximum Integ shade in graph 3 of figure 1-34 reveal that color yield is much

greater for a dyeing conducted at pH 11 then it is for a dyeing conducted at pH 13, a more detailed

picture is given in figure 1-35. At a given indigo on weight of yarn concentration, the color yield will

be greater at lower pH. Maximum color yield occurs in pH range of 10.5 to 11.5 and decreases as

the dye bath pH is increased. It was suggested that it is owing to the higher affinity and lower

solubility of the monophenolate form of indigo present at this pH range.



Figure

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67

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69

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The mean

n by indigo c

chnical distr

ical distribut

antivity asso

ugh this info

ercial dyein

ath pH is mai

ic plot of equili

technical dis

oncentration

ibution coeff

ion coefficien

iated with ri

mation is ba

s tend to co

ntained with

brium isother

tribution coe

in dye bath.

icient, K, and

t decreases

ng dyeing an

sed on labor

firm the con

in the range

s for dye conce

fficient is cal

In figure 1-3

the coefficie

ith increasi

color yield

tory dyeings

stancy of su

of 10.8 to 11

ntration.20

ulated by di

9 the relatio

nt of variati

g pH and th

ecome mor

according to

stantivity of

.2.

iding the ind

ship betwee

n of %CV are

%CV increa

variable wit

Etters30, the

indigo for de

igo concentr

n dye bath p

given. The

es. This me

h increasing

results from

nim yarn wh

70

ation

H

ns

pH.

en



71

Figure 1-39: Mean technical distribution as a function of dyebath pH.30

Ring dyeing of yarns can be increased by dyeing conditions that promote a very fast initial

strike of the dye for the fiber surface. The rapid exhaustion of the dye onto the fibers in the exterior

regions of the yarn will lead to decreased dyeing of the fibers in the yarn interior. Recall the

expression derived by Etters, K/S = at[Cf /(2p – p2)]; where at is the true value of the reflectance

absorptivity coefficient, i.e., the value for uniform distribution of dye in the yarn cross-section, Cf is

the concentration of dye in the yarn, and p is the fractional penetration of fixed dye in the yarn

cross-section. This equation will hold approximately unless a severe concentration gradient exists

within the dyed ring or colorant layer becomes translucent. The values of p have been roughly

estimated by microscopy to be 0.65, 0.33, 0.20, and 0.20 for pH ranges 13, 12, 11, and 10

respectively33.



practi

appa

dye b

ring d

betw

Figure

plott

from

may

incre

baths

Etters' eq

cal indigo dy

ent coefficie

ath pH is illu

yeing and an

en pH 10.8

1-40: Apparent

Figure 1-4

d as a functi

other dye ba

e concluded

sing substan

. The fact th

ation makes

eing process

nts. The rela

trated in fig

increasing a

nd 11.2, the

reflectance abs

1 illustrates t

on of the tec

th pH’s. As t

from figure

tivity and str

at the appar

use of the tr

s true reflec

tionship bet

re 1-40. As

parent refle

greatest col

orptivity coeffi

he apparent

nical distrib

e distributio

-41 that the

ike of indigo

nt reflectanc

ue reflectanc

tance absorp

een appare

he dye bath

ctance absor

r yield is ach

ient vs pH.30

reflectance a

ution coeffici

n coefficient

yarn ring dy

for cotton fib

e absorptivit

e absorptivit

tivity coeffici

t reflectanc

pH decrease

ptivity coeffi

ieved.

bsorptivity c

ents with ad

increases, th

ing phenom

er that is ass

y coefficient

y coefficient.

ents must be

absorptivity

from 13 to

cient. It has

efficients of

itional data

e color yield

enon is highl

ociated with

found in th

However in

replaced by

coefficient

1 there is m

een found t

figure 1-40

points added

also increase

correlated

lower pH dy

se experime

72

nd

ore

at

s. It

ith

nts



73

are pH dependent can be explained by the effect of pH on the distribution of dye in the cross-

section of yarn. As the degree of ring dyeing increases so does the apparent absorptivity coefficient.

Figure 1-41: Reflectance absorptivity coefficient as a function of mean technical distribution coefficient.30

Etters15 proposed the effect of pH on distribution coefficient and apparent absorptivity

coefficient is due to the ionized form of the dye molecule in the dye bath. The fraction of reduced

indigo that exists as the mono-ionic form is given by equation 1-38.

=

Equation 1-38: Mono-ionic fraction form of indigo dye as a function of pH.15



Here

Mean

abov

and c

furth

exists

Figure

reduc

excep

fracti

indig

pK1 and pK2

values of m

pH 11.5 the

ontinues to d

r to produc

as mono-ion

1-42: Relations

The mean

e indigo that

tionally high

on of indigo

has a much

re the pKa v

no-ionic for

fraction of i

ecrease as p

the more so

ic and half h

hip of Mono-io

technical dis

exists as a m

linear correl

hat exists in

higher subst

alues associa

are plotte

digo that exi

H increases.

luble di-ionic

s di-ionic fo

ic species of in

tribution coe

ono-ionic fo

tion betwee

mono-ionic f

antivity for c

ted with the

in figure 1-

sts as a mon

This is due t

form. At dy

m.

digo and pH.30

fficients are

m at various

n the substa

rm. Etters15

tton fiber th

two step ion

2 as a functi

-anion begi

more of the

e bath pH of

lotted as a f

dye bath pH

tivity of indi

concluded t

en does the

ization of red

n of dye bat

s to drop off

mono-ionic

12.7 about h

unction of th

’s, figure 1-4

go for cotton

hat the mon

di-ionic form.

uced indigo1

h pH. It is no

rather sever

orm ionizin

alf of the indi

e mean fract

. There is a

fiber and th

-ionic form

74

.

ted

ely

go

ion of

f



Figure

form.3

dept

indig

appa

yarn

regio

into a

functi

1-43: Relations

Recall red

for a given

that exists

ent affinity o

urfaces incr

It is readil

of maximu

fractional fo

on of pH, th

hip between m

ced indigo c

mount of fix

s a monoph

f the mono a

ases, leadin

seen that th

reflectance

rm and supe

relationship

an technical di

an exist in t

ed dye is sho

nolate ion in

nion form.

to a more ri

e fractional

absorptivity

rimposing on

becomes cl

stribution coeff

o forms: mo

wn to be hig

dye bath. T

s the affinity

ng dyed yarn

mount of th

. By converti

top of the fr

arer, figure

icient and fract

nophenolate

ly correlate

he correlatio

increases, t

.

e mono-ioni

ng the appar

actional amo

-44. Only at

ion of indigo ex

ion or biphe

with the fra

n is explaine

e strike rate

form is maxi

ent reflectan

unt of mono

low pH valu

isting as mono-

olate ion. S

ctional amou

as an increa

of the dye fo

mum near t

ce absorptivi

ionic form a

s does this

75

ionic

hade

nt of

sed

r the

e

ty

a



76

relationship break down. This can be explained by the superficial staining of the yarn by the acid

leuco form (II). Based on these results, it is reasonable to postulate that the mono-ionic form is the

principal species absorbed by the cotton. Or at least mono-ionic form has the highest apparent

affinity for cotton.

Figure 1-44: Correlation of fractional distribution of apparent absorptivity coefficient and mono-ionic form of indigo as a

function of pH.15



1.5.2.

dye u

demodept

prod

is req

the c

Figure

labora

figur

dye i

in the

speci

g Interrelatio

Given the

ptake, penet

nstrates the(K/S) at vari

ce a rather

uired to pro

oss section o

1-45: Indigo co

tory dyeing30

.

When the

1-46. It is s

the dye bat

dye bath inc

ied range. It

nship of Dye

strong effect

ration, and s

mean indigoous dye bath

ark shade (K

uce the sam

f yarn.

centration in d

dye uptake d

own the ma

h. Maximum

reases the m

could be tha

Concentrati

dye bath co

ade; a more

concentratio pH values. F

S = 100) is a

shade dept

ye bath require

ata is plotte

ximum uptak

uptake occu

aximum upt

t all of the d

n and pH on

centration a

in-depth dis

n in the dyeor example t

bout 3 g/l at

h at pH 11.0.

d to produce a

vs. dye bat

e at a partic

rs between p

ke occurs at

e extracted

Shade

nd pH indep

ussion is wa

bath neededhe indigo co

pH 12.5. But

This is the r

given shade de

pH, the foll

lar pH depe

H 9.25 – 10.

lower and lo

rom the knit

ndently hav

rranted. Fig

to produce acentration r

only 1 g/l of

sult of dye d

pth at various p

wing relatio

ds on the co

. As the con

wer pH value

ted yarn tub

on the resu

re 1-45

given shadeequired to

indigo in dye

istribution w

H’s from a 5 di

ship develo

ncentration

centration o

s within the

was not in f

77

lting

bath

ithin

s,

f

dye

act



78

“taken up” by the fiber. Some of the dye may have been merely precipitated within the knitted yarn

bundle.

Figure 1-46: Effect of dye bath concentration and pH on dye uptake.15

In figure 1-47 dye uptake is shown to increase linearly with increasing concentration of dye

in the dye bath. The linear relationship holds for all dye bath pH values but the slopes of the lines

are shown to increase as dye bath pH decreases from 13.3 to ~10 range. As pH continues to

decrease to the 7.7 range, the dye uptake slopes drop sharply.



79

Figure 1-47: Yarn dye uptake as a function of dye bath concentration and pH.15

The linear relationship between K/S and concentration of dye in the substrate is illustrated

in figure 1-48. The slope of each pH range corresponds to the various apparent reflectance

absorptivity coefficients. The apparent absorptivity coefficients increase as the pH is decreased

from 13.3 to ~ 11.0 pH. As the pH is further decreased to 10.0 the absorptivity coefficients

decrease. And as the pH is reduced to 7.7 the line slope decreases to the extent that is

superimposed on the line slope obtained at pH 13.3.



80

Figure 1-48: Corrected depth of shade as a linear function of indigo concentration in yarn and dyebath pH.15

Since less indigo dye bath concentration is required at lower pH values to achieve a desired

shade, less indigo is washed off of the yarn at the conclusion of dyeing. In figure 1-49 the

concentration of unfixed indigo has been estimated by Etters30 as a function of both concentrations

of dye in the dye bath and dye bath pH. As the dye bath pH decreases, the amount of oxidized

indigo that is trapped between the fibers in the denim yarn is decreased. Therefore, less dye is

available to be washed off of the yarn.



Figure

1.5.2.

yarn

deriv

Etter

coeffi

obtai

tubes

math

conc

conc

1-49: Estimate

h Empirical i

The Holy

nd shade to

d. But an e

21. In this m

cient, indigo

The empir

ed from bot

as previousl

ematical mo

The techn

ntration of d

ntrations ar

concentration

digo dye mo

rail for indig

various cont

pirical mod

del the dye

on weight of

ical model is

h investigati

outlined. B

el.

ical distributi

ye in the fib

expressed i

of unfixed indi

del

o dyers worl

ollable dye r

l based on a

bath indigo c

yarn, and su

based on the

ns is based

y analyzing t

on coefficien

r, Cf , divided

terms of gr

o on yarn at co

wide would

ange param

5 dip labora

oncentration

bsequently t

Southeaster

n 5 dip, 15 s

ese two dat

t, K, is define

by the conc

ms of dye p

rresponding dy

be a dye mo

ters. This o

ory experim

and pH is us

e final yarn

n Section15 a

econd imme

a sets, Etters

d in equatio

ntration of

r 100 grams

e bath concent

el relating i

e equation h

ent has been

ed to predict

shade.

nd Annis res

sions of knit

21 developed

1-39 to equ

ye in the dy

of fiber or w

ation and pH.30

digo on wei

as not yet be

proposed by

the distribut

arch19. The

ed denim ya

the followin

al the

bath, Cb. Th

ater.

81

ht of

en

ion

data

rn

e



82

=

Equation 1-39: Definition of technical distribution coefficient.21

A regression analysis explains 86% of the variability of K in terms of the variability of pH and the

relationship was defined in equation 1-40.

= + ()

Equation 1-40: Approximation for the technical distribution coefficient as a function of dye bath pH.21

Here the components are defined: a = 0.9623 and b = -0.000331.

Given the pH and dye concentration of the dye bath, one can calculate the technical distribution

coefficient, K, and subsequently the dye concentration in the fiber, Cf .

The second part of the empirical model is based on the relationship between pH and the

apparent reflectance absorptivity coefficient, a. Recall K/Scorr = a Cf . A regression analysis explains

94% of the variability of apparent reflectance absorptivity in terms of variability around pH. The

empirical model for apparent reflectance absorptivity coefficient was defined by Etters in equation

1-41.

=

Equation 1-41: Empirical model of apparent reflectance absorptivity coefficient.21

Here i=-46.3280, b=6.4373, c=0.4733, d=-0.0905, and e=0.0030.

Given the dye bath pH one can calculate the apparent absorptivity coefficient, a. Using the

calculated value for a and Cf , one can estimate the shade of the dyed fabric in terms of K/Scorr.



83

1.6 Summary of Key Developments and Identification of Deficiencies

The head indigo dyer responsible for daily production quality is always relentlessly searching

for new methods, procedures, and technology to reduce variability in the indigo dyeing process.Their shade control war chest includes some basic qualitative rules of thumb for indigo dyeing.

1. If the shade drifts green and light, reduce the hydrosulfite.

2. If shade drifts red, reduce caustic and/or slightly increase hydro.

3. If changing green and dull, increase caustic.

4. If drifting red and dull, increase hydro.

5. A gradual increase or decrease in depth, if on cast, is corrected by changing the indigo feed rate.

6. If increase in depth is accompanied by bronzing, increase hydro and/or decrease dye feed rate.

While these qualitative measures can not be forgotten, further improvements in shade control and

prediction can only be made with definitive quantitative measures.

To the aim of reducing the art of dyeing and increasing the science of dyeing, much

improvement has been made over the last 20+ years. Through many laboratory experiments we

now have a much greater understanding of indigo dye uptake, penetration distribution, and

corresponding shade as it relates to dye bath concentration, pH, and number of dips. Finally an

empirical model has been proposed to relate the desired dye outcome to measurable and

controllable dyeing parameters. Unfortunately the head indigo dyer cannot take these relationships

directly to production environment due to the key underlying assumptions.

Let’s begin the discussion with where all the indigo dye goes from a macroscopic scale. It

may sound elementary, yet no model has been published to accurately account for all the indigo

dye. We know how much indigo is fed to the range. But how much is removed during washing? At

the overflow? Current indigo dye terminology expresses % indigo on weight of yarn as a function of

pounds per minute of indigo and pounds per minute of cotton. This relationship does not account

for either. Attempts have been made to explain the amount of dye removed during washing yet

these have not been substantiated with actual production data.



84

No attempt has been made to relate classical diffusion theory to the experimental data for

dyeing denim yarn with indigo. Many of the expressions and terms have been employed but not the

actual diffusion solutions. In as such, the diffusion coefficient for the indigo-cotton dye system has

not been completely explored or expressed. More specifically the potential dependence on dye

bath pH, dye concentration in the dye bath, dye concentration in the yarn, boundary layer, and/or

other yet unknown parameters is not fully understood.

All of the experimental data presented in the literature are based on laboratory dyeings.

While this research certainly explains the relationship of variable effects on measurable responses, it

does not directly provide quantitative relationships on production dye equipment. There are four

fundamental issues that may affect the results.

The substrates used in the experiments have been some form of fabric either knitted tubesor woven twills. In either case, the interlacing or interloping of yarns may affect the amount of dye

uptake. This is due to where the two yarns cross; dye is not allowed to contact the yarn surface. As

a result, the measured dye concentration in fiber will probably be less than the results on actual

production yarns. Furthermore, the fabric structure makes any measured shade values (K/S)

depend on the substrate. While these are probably relative to each other, the shade values will not

directly correlate to production dyed denim yarns.

In all of Etters non-equilibrium experiments, a 15 second immersion time was used. While

this is a viable dwell time for indigo dyeing, not every dye range matches this time exactly. Chong29

and Xin46 have demonstrated the significant effect immersion times less than 30 seconds have on

the resulting shade. Any indigo dyer with immersion times different than 15 seconds must proceed

cautiously when applying Etters’ relationships.

The vast majority of indigo dyed cotton experiments have been conducted with simulated 5

dip dye range set-up. While 5 dip dyeing may represent a significant amount of the denim yarn

dyed, it is certainly not the only set-up. In fact the majority of denim shade spectrum produced falls

within the 2 to 8 dip range. Once again, Chong29 and Xin46 have demonstrated the significant affect

number of dyes has on the resulting shade. Since indigo dye uptake and/or degree of penetration



85

may be affected by previous dye applications (i.e. previous dip), relationships derived from 5 dip

simulations may not translate to more or fewer dips.

The movement of dye bath during the simulated laboratory experiments may affect the final

dye uptake and penetration. More specifically, no discussion of agitation during dyeing experimentswas mentioned. Dye bath agitation has been well documented to have a significant effect on

disperse dye uptake on polyester. While the same relationship may not hold true for indigo-cotton

system, the contrary has not be demonstrated. Furthermore, it may not be possible to recreate real

world boundary layer development in the laboratory.

Etters’ empirical indigo dye model appears to accurately predict yarn shade and dye uptake

given certain dye range parameters, specifically dye bath concentration and pH. However this

model is derived from very specific laboratory conditions involving: substrate, number of dips,immersion time, and agitation (boundary layer development). Furthermore, the indigo penetration

is modeled as a step function. All of these issues may have some affect on Etters’ empirical indigo

dye model. More importantly since no actual production data was given for comparison or

compared to classical diffusion theory, at the very least it raises some doubt.



86

2 Objectives of the Present Investigation

Although there is a long history of dyeing denim yarn with indigo, the process of dyeing with indigo

still remains largely an art and not a science. - Zhou48

In an ideal world to investigate the effect of yarn count, number of dips, immersion time,

dye bath pH, speed, and dye bath concentration on yarn uptake of dye and the resulting shade; a

systematic design of experiment would be conducted. At last, this researcher has yet to find a

denim manufacture willing to “blindly” produce a million+ yards of denim fabric that would be

required for such an experiment. As a result, an indigo-cotton dye observational study is proposed

that would gather key processing parameters and yarn samples during "actual indigo dyeing”

process. It is hoped the resulting data and relationships provide more refined insight into the

indigo-cotton dye system.

By processing yarn skeins through an actual indigo dye range it is put forth many of the

issues surrounding laboratory experiments will be avoided. While certain dye parameters cannot be

controlled by the experimenter, others can actually be more easily manipulated. Furthermore,

careful selection of various production shades should yield adequate variation in the dyeing

parameters to produce reliable results.

For each set of skeins processed, the following dye range set-up conditions were monitored.

1. Date and time skeins were processed.

2. Production shade number, dye range, and location.

3. Production yarn count and total number of ends per ball

4. Production indigo, caustic, and hydro feed rates to the dye range.

5. Dye range speed

6. Immersion time (dye dwell time)

7. Sky time (oxidation time)

8. Chemical checks made by the technician (g/l of indigo, mV potential, vatometer, pH, and %

alkalinity.

9. Yarn count of skeins and the sequence of dye boxes that they were processed through.



87

The following response variables were measured.

1. Greige weight of skein and shade

2. Laboratory prepared weight of skein and shade

3. Dyed but unwashed weight of skein and shade

4. Dyed and laboratory washed weight of skein and shade- All weight measurements will be conducted according to AATCC methods.

5. Shade readings will include the CIELAB L*, a*, b* values using 10° observer and D65

illuminant; and % reflectance from 400 to 700 nm at 20 nm intervals.

6. %IOWY determination by 1-Methyl-2-Pyrrolidinone extraction

Data analysis involved comparing chemical on weight of yarn measurements to actual

production parameters. Determination of fixed versus unfixed indigo dye on yarn was calculated

from before and after washed skeins.

An empirical model based on analysis of indigo on weight of yarn and shade values was

developed. This model was based on two different indigo dye ranges. This should yield a more

reliable and transferable indigo-cotton dye model. Next the diffusion coefficients were calculated

for various dyeing set-ups and analysis identified key influential parameters. To validate the

empirical dye model, comparisons were evaluated to classical diffusion theory and previously

published laboratory experiments.

A reliable indigo model would improve quality control by removing the “art” of indigo

dyeing and replacing with the “science” of indigo dyeing. At the very least a better understanding of

the indigo dye process would allow the production dyer to better control the process. Most

optimistically an accurate indigo-cotton dye model would allow product development to design dye

range set-ups to produce new and unique dye shades possessing shade and penetration

characteristics never before imagined.

While much research has been conducted in the field of chain rope indigo dyeing, many

questions still remain unanswered. Specifically a rigorous math and science based model to explain

dye pick-up, final shade, and dye penetration. Previous research has indicated dye bath

concentration, immersion time, number of dips, pH, and reduction potential have a significant effect

on the dye on weight of yarn and the resulting shade. Furthermore little research actually specifies



88

quantitative changes and instead focuses on general trends and qualitative relationships. This

researcher submits that dye range speed would also have a significant contribution to dye pick-up

and shade. Furthermore, the specific quantity of indigo on weight of yarn and resulting shade was

predicted given fundamental dye range parameters.

Ideally, a design of experiment would be evaluated to determine the effect of each listed

variable. Alas, laboratory dye equipment has restrictions on dwell length and immersion time over a

range of typical dye range speeds. Not to mention limitations on dye bath volume and maintaining

chemical equilibrium. Furthermore, such an experiment cannot be conducted on production dye

equipment since strict and specific dye conditions must be maintained in order to ensure proper

shade on bulk production orders. However, an observational study of indigo dyeing may be

conducted on production bulk equipment without adversely affecting bulk orders. Specifically, dye

pick-up or percent indigo on weight of yarn and shade can be measured on skeins while noting the

various dye range parameters. While the researcher cannot change the dye range parameters to a

specific value in a study, multiple evaluations over a range of production dyeings will allow

determination of parameter affects on response variables.

At the conclusion of the study, mechanical dye range parameters: speed, immersion thread-

up length, oxidation time, and number of dips coupled with dye bath conditions: indigo dye bath

concentration, pH, and reduction potential effects will be evaluated on response variables % indigo

on weight of yarn, shade, and dye penetration. Insight will be gained regarding equilibrium sorption

of indigo dyed cotton yarns by maximum dye up take and resulting shade. This information was

presented to quantify the level of indigo penetration when ring dyeing conditions exist. Last the

relationships will be viewed under Fick's laws of diffusion. The extension to diffusion equations will

explain the cause and effect and allow a rigorous mathematical model to be developed. Specifically

the diffusion coefficients for the cotton-indigo interface will be determined.



89

3 Experimental Methods and Procedures

To evaluate production indigo dyeing without influencing actual production orders, skeins of

cotton yarns were tied onto the production yarns during the dyeing process. By running skeins

instead of looking at actual production yarns, effects of boil off efficiency, washing after boil off,

washing after indigo dyeing, and sulfur dye bottom or top were eliminated. Additionally, yarn skeins

were prepared in a laboratory to ensure consistent base for dyeing from skein to skein.

Additionally, skeins were made from the same yarn package to remove inconsistencies from yarn

package to package. These precautions provided consistent base from dye set-up to set-up since

bulk production yarns will most certainly vary over the observational time frame.

3.1 Response Variables Definition, Collection Methods, and Evaluation Methods

3.1.1 Yarn Skein Definition and Creation

A yarn skein consists of evenly wound yarns from the same yarn count to produce a uniform

loop. The loop can then be tied at the top to maintain integrity while being handled. A yarn skein

was made by winding a specific yarn count into a loop of approximately 80 centimeters in length,

100 loops, and weighing roughly 4 to 8 grams. The specific length, number of loops and weight

wasn't critical. The weight for each skein was later measured and documented. The specific yarn

counts used for this study were 6.3/1, 7.1/1, 8.0/1, and 12.0/1 English cotton count formed on an

open end Schlafhorst spinning frame.

3.1.2 Running Yarn Skeins on Production Indigo Dye Range Equipment

Laboratory prepared yarn skeins were tied onto a production dye range in multiple locations

by the use of a 100% polyester spun thread. The polyester thread was strong enough to ensure the

skein remained tied to the production rope while easily broken when pulled off later. Also note the

100% polyester thread will not be dyed by indigo and therefore will not interfere during the dyeing

process. A simple loop knot was tied around the yarn skein with 8 inches extra thread on both sides

of the knot. While the dye range was running, a simple, loose double knot was formed around the

production rope. With one swift motion starting above the head, tighten the first knot followed by



90

the second knot to secure the skein to the production rope. With practice, the procedure becomes

effortless.

Most indigo dye ranges have walkways and platforms around the wash boxes, after the boil-

off box, as well as the indigo dye boxes. These allow operators to access the production cottonropes to repair lost or broken ends while the dye range remains operational. This researcher used

these access points to tie on the yarn skeins. Following standard production procedures the skeins

would be immersed in at least one wash box before entering the indigo dye boxes. The wash box

would remove trapped air in and around the cotton fibers as well as provide uniform water pick up.

To pull off the yarn skeins a simple good grip and quick pull breaks the polyester thread.

Ideally this process should be conducted while the polyester thread and production rope interface

was in direct contact with a steel roller in the sky or oxidation section after each indigo box. Thecontact point provides stability to the production yarn thereby resisting the pulling motion. To avoid

a dye range stop, pull down (perpendicular to the roller axis of rotation), never across (parallel to

the roller axis)! Any parallel motion can pull the production rope out of track.

3.1.3 Yarn Skein Evaluations

Once the yarn skeins were processed, critical information was measured and recorded.

These measured values will later be the response variables used to evaluate dye range parameter

effects. The first group of response variables was dry weight measurements which were conducted

on the yarn skeins in accordance to AATCC 20A section 8 (Moisture Content) method. All weights

were measured on a Mettler AE100 scale. The weight was recorded before laboratory preparation

and noted as "greige" weight. After the skeins had been laboratory prepared the weight was

recorded as "boil-off" weight. The weight was measured after processing through the dye range.

This last weight measurement was recorded as "dyed" weight. Finally, the dyed yarn skeins were

washed in the laboratory and identified as "washed" weight.

The “%Boil-Off Loss” was defined as the difference in Greige weight and Boil-off weight

divided by the Greige weight as shown in equation 3-1.



91

% =

Equation 3-1: Calculation of %Boil off Loss.

Given the boil-off and dyed weight, the total percent chemical on weight of yarn (%COWY)

was calculated according to equation 3-2. Note this was the total chemical amount on weight of

yarn after dyeing. This number has fixed and unfixed indigo dye as well as residual sodium

hydroxide and other salts resulting from oxidation.

% =

Equation 3-2: Calculation of %COWY.

The skeins were washed in the laboratory using warm water of ~40°C. Washing of the yarn

skeins was necessary to simulate dye range set-up and remove unfixed dye and chemical residuals

from the yarn. Each skein was passed under running water until the water was clear of color. The

final washed percent indigo on weight of yarn (%IOWYwash) was calculated by dividing the difference

between Washed weight and Boil-off weight by the Boil-off weight, equation 3-3.

% =

Equation 3-3: Calculation of %IOWYwash.

The final method used to determine %IOWY after the yarn skeins had been washed was

Spectrophotometric Methyl Pyrrolidinone extraction. This method was ultimately chosen for later



92

data analysis due to greater acceptance and use in literature. The following Methyl Pyrrolidinone

method to measure the %IOWY was provided by Clariant Inc.

1. Prepare the solvent solution as follows: (sufficient for one sample)

To a 400 ml beaker, add:

200 ml of distilled water7.2 grams of sodium hydroxide (50%)

4.0 grams of sodium hydrosulfite (90%)

After the sodium hydrosulfite was dissolved, add 120 ml of 1-Methyl-2-Pyrrolidinone

Cool to ambient temperature and pour into a graduated cylinder. Then fill to the 400 ml mark with

distilled water and mix well before use.

2. Weigh out yarn per Table 3-1 and place in a 250 ml volumetric flask. Add the solvent solution

prepared in step #1 to the mark. Add a 1.5 inch magnabar and stir for 15 minutes.

Note: At the end of this time, the indigo on the yarn should be completely reduced. The yarn

should be devoid of color unless sulfur dye was present on the yarn.

3. Recheck the volume in the flask by removing the magnabar. If necessary, add solvent solution

prepared in step #1 to bring back up to the 250 ml mark in the flask and mix well.

4. To a 100 ml volumetric flask, add 80 - 90 mls of the solvent solution prepared from step #1.

Pipette 5.0ml of the solution from step #3, being careful to wipe off any excess from the outside of

the pipette.

Note: Dip the point of the pipette into the solvent solution to prevent oxidation of the reduced

indigo.

5. Dilute to the 100 ml mark with the solvent solution prepared in step #1.

6. On a suitable spectrophotometer, record the absorbance of the solvent solution prepared in step

#1 at 406 nm using a 1cm cell. [Current study used a Thermo Spectronic 20D+.]

7. Measure the maximum absorbance of the sample solution prepared in step #5 at 406nm. Adjust

the sample absorbance by adding or subtracting the absorbance of the blank solution measure in

step #6.

8. Calculation by equation 3-4:

%% =∗.

Equation 3-4: Calculation of %IOWY by Methyl Pyrrolidinone extraction.



93

Table 3-1: Target dyed yarn sample weight for Methyl Pyrrolidinone extraction

Anticipated Indigo Concentration Amount of Yarn to Weigh

5 - 7% 1.5 - 2.0 grams

8 - 12% 1.0 - 1.5 grams

13 - 17% 0.5 - 1.0 grams

18 - 30% 0.4 - 0.7 grams

The resulting %IOWY calculated from the Spectrophotometric Methyl Pyrrolidinone

extractions were expressed in terms of 20% paste. This convention has its roots from the days when

20% indigo paste was the only commercially available concentration. Today 20%, 40% and even

42% indigo paste is commercially available. To express the indigo dye concentration more

generically the above value was divided by 5 to make the units %IOWY in terms of 100% indigo as

outlined in equation 3-5. This final form was used in all subsequent analysis and will here forth be

known simply as %IOWY.

% =% %

Equation 3-5: Calculation of %IOWY in terms of 100% Indigo paste from Methyl Pyrrolidinone extracts.

The next response variable was a calculation based on the actual shade of the dyed and

washed yarn skein. The relationship K/S shade was expressed as a function of the % reflectance of

the dyed sample minus the % reflectance of a mock sample at various wavelengths. The mock

sample was the same yarns as the dyed sample processed the same way except without any actual

indigo dye involved. Of course all mock dyed samples were created in the laboratory by padding

dye bath chemicals minus the indigo on the yarn skeins. The mock dyed yarn % reflectance values

are referenced in appendix section A-3-1. Higher values indicate a “darker” shade or in this case

greater transfer of indigo during the dyeing process. Lower K/S values correspond to lighter shades

with less dyed on weight of yarn and/or more penetration into the yarn structure. The equation for



94

K/S was given in equation 3-6. The %reflectance values were measured on a Hunterlab ColorQuest

XE running on Gretag-Macbeth SLI-Form software.

=

( %)

∗ %−

( %)

∗ %

Equation 3-6: Calculation of K/S from Kubelka-Munk.

To ensure accurate and repeatable shade measurements the yarn skeins were wrapped

around a white plastic board 6 centimeters wide. By pulling the yarns tight during the wrapping

process, the individual yarns were straight without any knots or twists and parallel to one another.

The shade was measured with a 1 inch port on the spectrophotometer. The shade software

automatically averages three individual readings. By moving the yarn skein between individual

readings the average % reflectance was calculated. Furthermore each dyed yarn skein was

measured on three separate occasions. The three separate readings were later averaged in

Microsoft's Excel spreadsheet which resulted in the % reflectance values at each wavelength

representing nine different readings.

To represent the total shade over many wavelengths in one number, the value of Integ has

been developed. As pointed out by Xin46 the Integ value has greater importance when evaluating

shade over a wide range of depths as the maximum absorption wavelength tends to shift at greater

depths of shade. In equation 3-7, Eλ equals the spectral power distribution of the illuminant. The xλ

+ yλ + zλ function was the standard observer function. All shade evaluations were conducted using

D65 illuminant with a 10° observer.

= ∑

∗ E

(

+

+

)

Equation 3-7: Calculation of Integ shade value from K/S values.



95

Graphical representation of the K/S by wavelengths further illustrates the shift Xin was

referring. Figure 3-1 shows the K/S by wavelength from multiple dips of 6.3/1 OE yarn in 3.0 g/l

indigo dye set-up at 31 meters per minute and 12.0 pH. The maximum K/S value shifts from 660 nm

at one dip to 640 nm at 3 dips. By the time dip 6 and 7 occur, the maximum K/S value occurs at 580

nm. Since the wavelength of maximum K/S shade shifts, no single wavelength will accurately

describe the change in shade as a function of dye concentration or location. For reference the Integ

shade value for the same dips of figure 3-1 was 24.2, 64.8, 95.1, and 103.9 respectively.

Figure 3-1: Relationship of maximum K/S shade shift as depth increases

In addition to the shifting maximum wavelength, the K/S shade value was non-linear as a

function of %IOWY. In the past this had been corrected by Etters and others by adjusting the K/S

value for higher %IOWY. This approach worked for relatively low %IOWY values. However as the

%IOWY or degree of ring dyeing was increased the K/S value not only was non-linear but non-

unique. In figure 3-2 at 580 nm the K/S shade becomes non-linear at approximately 1.25% IOWY. At

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

45.0

50.0

400 450 500 550 600 650 700

K / S s h a d e v a l u e

Wavelength (nm)

K/S Shade Values by Wavelength for Typical 3.0

gm/lit Indigo Dye Set-up

1 dip 3 dip 6 dip 7 dip



96

660 nm the K/S shade value becomes non-linear at 0.75 %IOWY. Furthermore K/S660nm reached a

maximum value at 1.25 %IOWY. With continued increase in %IOWY the K/S660nm shade value

actually decreased in value. No amount of mathematical correction could compensate for this

relationship. Figure 3-2 illustrates the relationship of Integ to %IOWY. While this function was

certainly not linear, at least the values are unique over the entire %IOWY range and possessed

greater change in value at higher %IOWY measurements. Therefore Integ shade value was used for

all future calculations related to shade.

Figure 3-2: Relationship of K/S by wavelength as a function of %IOWY

The final response variable was a calculation based on the shade of the yarn and %IOWY,

equation 3-8. This response variable qualifies the “location” of the indigo in the cross section of the

yarn. A relatively lower penetration factor value indicates more indigo penetration into the cross

section of the yarn, while a higher value indicates less penetration. Of course this value is relative to

other skeins dyed under similar conditions.

0.0

20.0

40.0

60.0

80.0

100.0

120.0

0.000% 0.500% 1.000% 1.500% 2.000% 2.500% 3.000% 3.500%

I n t e g o r K / S S h a d e V a l u e

%IOWY

Integ and K/S Shade at 580nm and 660nm vs %IOWY

580nm 660nm Integ



97

Penetration Factor =

%

Equation 3-8: Calculation of penetration factor from Integ and %IOWY.

3.2 Determining Optimum Method for Laboratory Preparation

During the indigo dyeing process, 100% cotton yarn was run through the dye range to

produce a specific desired shade. The cotton yarn was first exposed to the “Boil-Off” box, which

contained chelate, wetter, sodium hydroxide, and water (and sometimes sulfurs dyes). The purpose

of this box was to prepare the yarn for the subsequent indigo dye boxes. The experimenter wished

to conduct an observational study of the various parameters that affect the indigo dye process. But

one key parameter was the boil-off box, which was not a desired part of the study. To overcome

this obstacle, skeins were prepared in a laboratory thereby bypassing the boil off box on the dye

range. This would allow other factors of interest to be studied without the negative impact of boil-

off box variation and/or sulfur dye from regular production.

Previously published articles on indigo dyeing have used a variety of preparation methods.

Some researchers have used room temperature distilled water. Some have used water and wetters.

Finally, a few have used water, wetters, and sodium hydroxide. What was the best laboratory

preparation process? What characteristics does a good laboratory procedure possess?

Some initial trials run and intuition from this experimenter indicated: the dwell time,

temperature, and amount of sodium hydroxide played a major role in the laboratory preparation

process. The use of chelates was ultimately only important in bulk production equipment designed

to run continuously for hours. The experimenter wished to develop a laboratory preparation

procedure, which was robust in design. Ideally, reasonably small changes in time, temperature,

and/or sodium hydroxide concentration have little to no effect on the degree of dyeing. Or at the

very least the experimenter needs to understand the amount of error the lab preparation procedure

can impart on the research to be conducted.

To understand the laboratory preparation procedure better, the experimenter conducted a

design of experiment based on central composite design with axial components that were



98

orthogonal and inscribed with 4 replicated center points under two blocks. The three factors of

interest were time the skeins were allowed to “cook”, temperature the skeins were “cooked”, and

sodium hydroxide concentration of the bath used for "cooking". Time was measured with a

stopwatch in minutes with a range of 20 to 40 minutes. Temperature was measured with a

thermometer with a range of 76 °C to 100 °C. The sodium hydroxide concentration was measured

on weight basis with a range from 0 to 15 grams per liter where a measured weight of sodium

hydroxide was added to a measured volume of water. The sodium hydroxide used in this

experiment was a 50% solution not dry weight and the units were actually X g/l of 50% sodium

hydroxide.

The two blocks of the design of experiment consisted of the actual indigo dyeing process.

Block #1 was the skeins run through only one dip of indigo. Block #2 was the skeins run through six

dips of indigo. While six dips of indigo represents typical indigo dyeing set-up, one dip of indigo

produced the most extreme case with the yarn skein exposed to the least amount of indigo. This

should accentuate any variation in the yarn skeins from the laboratory preparation procedure.

Using SAS's JMP 8.0 statistical software package, the central composite experimental design

was laid out and the package automatically created a randomized run order. Following this run

order each laboratory preparation recipe was mixed with 3.785 liters of water, brought to the

correct temperature, and yarn skein added for the desired amount of time. After the required time,

the yarn skein was removed from the boil-off mixture and washed under hot water at 40°C for 5

minutes. The washing process again mirrors actual indigo dye range set-up, which was to remove

residual boil-off mixture from the cotton yarn.

Table 3-2 details the level of each variable and the order in which it was conducted in the

laboratory. This run order list was used for block #1, one dip of indigo. There were 4 response

variables that were measured at each level of the laboratory preparation procedure. These

consisted of the %Boil-Off Loss, %IOWY, Integ shade, and penetration factor as defined in section

3.1.



99

Table 3-2: Time, temperature, and sodium hydroxide concentration levels plus response variable for one dip of indigo

Pattern Time

(min)

Temperature

(°C)

NaOH

(g/l)

%Boil-Off

Loss

%IOWY Integ Penetration

Factor

Run

Order

a00 20 88 7.5 2.00% 0.307% 23.0 75.01 1

+-- 37 79 2.25 1.34% 0.115% 23.3 201.47 2

000 30 88 7.5 2.11% 0.270% 22.4 82.86 3

A00 40 88 7.5 2.62% 0.283% 27.2 96.23 4

+++ 37 96 12.7 2.62% 0.306% 23.3 75.98 5

0A0 30 100 7.5 2.77% 0.310% 26.4 85.26 6

000 30 88 7.5 2.34% 0.336% 23.2 69.10 7

++- 37 96 2.25 2.26% 0.341% 25.4 74.54 8

00A 30 88 15 2.26% 0.348% 21.6 62.07 9

00a 30 88 0 1.46% 0.202% 23.4 115.78 10

000 30 88 7.5 2.21% 0.312% 25.3 81.05 11

-+- 23 96 2.25 2.37% 0.240% 23.1 96.06 12

0a0 30 76 7.5 1.32% 0.155% 23.3 150.37 13

+-+ 37 79 12.7 1.43% 0.085% 23.3 272.92 14

--+ 23 79 12.7 1.71% 0.104% 23.3 223.49 15

--- 23 79 2.25 1.27% 0.019% 23.2 1232.46 16

-++ 23 96 12.7 2.94% 0.261% 22.7 86.77 17000 30 88 7.5 2.20% 0.296% 22.2 75.09 18

Table 3-3 details the run order in the laboratory for block #2, six dips of indigo. This list was also

randomized and the corresponding measured response variables were included.



100

Table 3-3: Time, temperature, and sodium hydroxide concentration levels plus response variable for six dips of indigo

Pattern Time

(min)

Temperature

(°C)

NaOH

(g/l)

%Boil-Off

Loss

%IOWY Integ Penetration

Factor

Run

Order

+-+ 37 79 12.7 1.47% 1.818% 98.4 54.13 1

-++ 23 96 12.7 2.89% 2.190% 96.5 44.08 2

a00 20 88 7.5 2.02% 2.043% 97.3 47.62 3

-+- 23 96 2.25 2.19% 2.109% 96.0 45.50 4

++- 37 96 2.25 2.63% 2.059% 93.9 45.60 5

0A0 30 100 7.5 2.68% 2.158% 95.6 44.30 6

--- 23 79 2.25 1.09% 1.869% 100.1 53.56 7

+-- 37 79 2.25 1.30% 1.902% 91.0 47.86 8

000 30 88 7.5 2.19% 2.224% 93.4 41.99 9

000 30 88 7.5 2.41% 2.159% 100.9 46.73 10

00a 30 88 0 1.26% 1.940% 93.5 48.21 11

A00 40 88 7.5 2.79% 2.073% 97.0 46.80 12

000 30 88 7.5 2.28% 2.250% 94.3 41.94 13

0a0 30 76 7.5 1.02% 1.719% 100.3 58.33 14

+++ 37 96 12.7 3.52% 2.208% 99.4 45.02 15

000 30 88 7.5 2.11% 2.034% 100.5 49.43 16

--+ 23 79 12.7 1.18% 1.637% 95.1 58.06 1700A 30 88 15 2.22% 2.167% 98.9 45.65 18

The data analysis was broken into five parts. Part 1 involved the boil-off loss during the

laboratory preparation process. This does not involve the indigo dyeing process and does not

require separating one dip of indigo versus six dips of indigo. In other words, the experimenter had

a completely replicated central composite design with axial components. The remaining parts

involved analyzing the data after the indigo dyeing process and therefore must take into

consideration the amount of indigo applied from either one or six dips. Part 2 involved %IOWY after

one and six dips of indigo. Part 3 involved Integ shade value after one and six dips of indigo. Part 4

involved penetration factor after one and six dips of indigo. Finally, the optimum laboratory set-up

was determined from the results in previous parts. While the exact indigo dye conditions were not

of major importance in determining preparation parameter affects, for the record the production

shade consisted of 3 g/l indigo dye bath concentration, 12.5 pH, 31 m/sec, and 8.6 meter dwell

length. The skeins were prepared as outlined in section 3.2 (table 3-2 and 3-3), processed through

the range as discussed in section 3.1.2, and all yarn evaluations were conducted as detailed insection 3.1.3.



101

3.2.1 Analysis of Laboratory Preparation Time, Temperature, and Sodium Hydroxide Concentration

Affect on %Boil-off Loss

Figure 3-3 illustrates the affect of time on the %Boil-off loss for all data points. The general

trend was slightly greater %Boil-off loss as dwell time increased. However the effect was minimal asthe average value shifts from 2.0% at 20 minutes to 2.25% at 40 minutes. Furthermore the

correlation of %Boil-off loss and time was extremely low as indicated by the R2 value of 0.025. This

low correlation was due to the high variability around the average value at each evaluated time and

the relative low time dependence. This does not necessarily mean time doesn't play a significant

role in %Boil-off loss but instead the affect of time could be over shadowed by other parameters.

Figure 3-3: Relationship of time on %boil-off loss during laboratory preparation

The effect of sodium hydroxide concentration in the boil off box is illustrated in figure 3-4.

As with time, sodium hydroxide concentration causes a slight increase in %Boil-off loss as the

concentration was increased. Unlike time, sodium hydroxide appears to reach a plateau at ~11 g/l.

R² = 0.025

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

3.50%

4.00%

20 25 30 35 40

% B o i l - o f f L o s s

Time (minutes)

Relationship of Time on %Boil-off Loss during

Laboratory Preparation



102

Further increases in concentration appear to have a little effect on average. Also as with time, the

correlation of the effect was minimal with a R2 value of 0.148. Again the low correlation was due

the high variability of %Boil-off loss at various levels of sodium hydroxide concentration.

Figure 3-4: Relationship of sodium hydroxide concentration on %Boil-off loss during laboratory preparation

With very low correlations of time and sodium hydroxide concentration to %Boil-off loss,

one would expect the temperature to play a major role during the laboratory preparation process.

Based on all %boil-off loss values as a function of temperature, it does play a significant role. As

temperature was increased the %Boil-off loss also increased in a non-linear fashion as seen in figure

3-5. The R2 value was 0.687 which indicates a fairly strong single parameter correlation.

Furthermore, the degree of change was rather large with 1.25% at 76°C and increasing to 2.75% at

100°C. This means the %Boil-off loss more than doubles over the range of temperatures evaluated.

R² = 0.148

0.00%

0.50%

1.00%

1.50%2.00%

2.50%

3.00%

3.50%

4.00%

0 2 4 6 8 10 12 14 16


Caustic Concentration (g/l)

Relationship of Sodium Hydroxide Concentration on

%Boil-off Loss during Laboratory Preparation



103

Figure 3-5: Relationship of temperature on %Boil-off loss during the laboratory preparation

Before a mathematical model of %Boil-off loss can be constructed, possible parameter

interactions must be evaluated. Interactions were easy to identify graphically as two curves will

cross when each is held constant by one parameter while a second parameter is varied. Figure 3-6

shows the interactions of all parameters on %Boil-off loss. The left column of graphs show the

interaction of time with temperature (middle graph) then sodium hydroxide concentration (bottom

graph). The middle column of graphs show the interaction of temperature with time (top graph)

and sodium hydroxide concentration (bottom graph). The right column of graphs shows the

interaction of sodium hydroxide concentration with time (top graph) and temperature (middle

graph). Since none of the curves on any graph cross each other, there were no significant

interaction effects on %Boil-off loss.

R² = 0.687

0.00%

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%3.50%

4.00%

70 75 80 85 90 95 100


Temperature (C)

Relationship of Temperature on %Boil-off Loss during

Laboratory Preparation



104

Figure 3-6: Interaction profile for time, temperature, and sodium hydroxide concentration on %boil-off loss during

laboratory preparation process

The interaction profile does however illustrate that time and sodium hydroxide

concentration independently can play a major role in %Boil-off loss even though the R2 values from

figures 3-3 and 3-4 were very low. For example, the lower left hand graph of %Boil-of loss as a

function of time and sodium hydroxide concentration shows a change in time and sodium hydroxide

concentration causes a linear change in %Boil-off loss. Specifically, as the sodium hydroxide

concentration was held constant at 0 g/l, the increase in time causes a linear increase in %Boil-off

loss. The upper right hand graph shows that as time was held constant an increase in sodium

hydroxide concentration causes a non-linear increase in %Boil-off loss. Graphical depictions of

single parameter affects on %Boil-off loss highlight these detailed changes in the overall variation of

the experiment. A more rigorous analysis was needed to determine the significance of each

parameters affect on %Boil-loss.

An ANOVA analysis of time, temperature, and sodium hydroxide concentration on %boil-off

revealed the statistically significant parameters as well as created a model to predict %Boil-off loss

as a function of those parameters. Table 3-4 summarizes the ANOVA analysis results after removing

0.01

0.02

0.03

0.04

%

B o i l -

o f f L o s s

0.01

0.02

0.03

0.04

%

B o i l -

o f f L o s s

0.01

0.02

0.03

0.04

%

B o i l -

o f f L o s s

Time

76

100

0

15

2 0

2 5

3 0

3 5

4 0

2040

Temperature

0

15

8 0

8 5

9 0

9 5

1 0 0

2040

76

100

NaOH

0 5 1 0

1 5

T i m e

T em p er a t ur e

N a OH

Interaction Profiles

(min)

(C)

(g/l)

%Boil-off Loss Interaction Profile



105

insignificant interaction effects. The parameter estimates indicate time, temperature, and sodium

hydroxide concentrations each have a statistically significant affect as the P-value for each was less

the 0.0059. Furthermore the analysis indicates the second order effect of temperature was

statistically significant with a P-value of 0.0411. This finding was graphically supported in figure 3-5

since the R2 value for second order trend curve was higher than a linear trend line. The summary of

fit produces a R2 of 0.89 for this model compared to the actual data points. Furthermore the

analysis of variance calculates a P-value less than 0.0001 for this model. Both values indicate high

correlation and significance for the model compared to actual data points.

Table 3-4: ANOVA analysis results for laboratory preparation parameters on %Boil-off loss

The model was constructed using the estimates from the parameter estimates section in

table 3-4, equation 3-9.

% − = −1.634 ∗ ( − 88.03) + 7.41 ∗ +

−6.683 ∗ ( − 7.64) + 4.69 ∗ + 1.942 ∗ − 0.05178

Equation 3-9: %Boil-off loss as a function of time, temperature, and sodium hydroxide concentration.



106

This equation was represented in the prediction profiler graph shown in figure 3-7. Now the

main effects were more easily identified. The time increased the %Boil-off loss linearly while sodium

hydroxide concentration and temperature increase have a non-linear increasing affect. Importantly,

the maximum effect of sodium hydroxide on %Boil-off loss occurs at 11 g/l regardless of time or

temperature. The true relationship could be a plateau was reached at 11 g/l were further increases

in concentration have little affect on %Boil-off loss. Recall the average effect illustrated in figure 3-

4. These results will later be coupled with effects of time, temperature, and sodium hydroxide

concentration affects on %IOWY, Integ, and penetration factor to determine the optimum

laboratory values.

Figure 3-7: %Boil-off loss model as a function of time (minutes), temperature (C), and sodium hydroxide concentration

(g/l) in laboratory preparation process


Affect on %IOWY after One and Six Dip Indigo Dyeing Conditions

The %IOWY after one and six dips of indigo as a function of time was illustrated in figure 3-8.Inspection of one dip dyeing represented by X's and solid trend line, showed poor correlation which

is statistically supported by the low second order polynomial R2 value of 0.046. While the

correlation coefficient was obviously very low the general trend was an increasing %IOWY value

% B o

i l -

o f f L o s s

0 . 0

3 0 2 1 1

± 0

. 0 0 2 3 3

2 0

2 5

3 0

3 5

4 0

7 5

8 0

8 5

9 0

9 5

1 0 0 0 5

1 0

1 5

Time min Temperature (C) NaOH (g/l)

%Boil-off Loss Prediction Profile for Laboratory Preparation Process



107

until approximately 32 minutes. After 32 minutes the amount of %IOWY decreases with further

increase in time. The %IOWY after six dips of indigo as represented by O's and dotted trend line

likewise showed poor correlation which is supported by the second order polynomial with a R2 value

of 0.034. As with one dip, the %IOWY after six dips as a function of time appears to reach a critical

value at 32 minutes. Further increases in time result in slightly lower %IOWY. While the effect of

time appears to have more importance at one dip, the same effect can be seen after six dips. The

time affect was highly variable, particularly after one dip, and thus difficult to draw immediate

conclusions on the role time plays in the laboratory preparation procedure.

Figure 3-8: Relationship of laboratory preparation time on %IOWY after one and six dips of indigo dye

Unfortunately the effect of laboratory preparation sodium hydroxide concentration on

%IOWY was similar to the effect of time. The best curve fit after one dip was by second order

polynomial with a R2 value of 0.086. Increasing sodium hydroxide concentration resulted in

increasing %IOWY until 9 g/l. Further increases in concentration resulted in decreased %IOWY as

R² = 0.046

R² = 0.034

0.000%

0.500%

1.000%

1.500%

2.000%

2.500%

0.000%

0.050%

0.100%

0.150%

0.200%

0.250%

0.300%

0.350%

0.400%

20 25 30 35 40

% I O W Y ( s i x d i p s )

% I O W Y ( o n e d i p )

Time (minutes)

Effect of Time on %IOWY from One and Six Dips of Indigo

One Dip Six Dips



108

illustrated in figure 3-9. For six dips the best curve fit was described as essentially constant with a R2

value of 0.037. Again, the poor correlation was due to high variability in the data points and limited

effect sodium hydroxide concentration during the laboratory preparation process played in %IOWY.

Figure 3-9: Relationship of sodium hydroxide concentration during laboratory preparation on %IOWY from one and six

dips of indigo dye

The effect of temperature during laboratory preparation had a major impact on %IOWY.

After one dip of indigo the best curve fit was by a second order polynomial with a R2 value of 0.708.

After six dips of indigo the second order polynomial R2 value was 0.743. The same general trend

was seen after one and six dips of indigo. Under both dyeing conditions as the temperature was

increased from 76°C, the %IOWY increased. The maximum %IOWY occurred at 94°C as shown in

figure 3-10. Furthermore, the change in %IOWY appears to flatten out at 94°C. The data points

indicate temperatures higher then 95°C do not produce a true change in %IOWY. Also notice the

R² = 0.086

R² = 0.037

0.000%

0.500%

1.000%

1.500%

2.000%

2.500%

0.000%

0.050%

0.100%

0.150%

0.200%

0.250%

0.300%

0.350%

0.400%

0 2 4 6 8 10 12 14 16

% I O W Y

( s i x d i p s )

% I O W Y

( o n e d i p )

Sodium Hydroxide Concentration (g/l)

Effect of Sodium Hydroxide Concentration on %IOWY from

One and Six Dips of Indigo

One Dip Six Dips



109

variability around the curve fit appeared to reduce at higher temperatures for both one and six dip

dyeings.

Figure 3-10: Relationship of temperature during laboratory preparation on %IOWY from one and six dips of indigo dye

The interaction of the parameters on %IOWY were also evaluated to determine if

any significant effect was attributed. Figure 3-11 shows the interaction profiles for time,

temperature, and sodium hydroxide concentration on %IOWY after one and six dips of indigo.

Inspection of all graphs in figure 3-11 revealed no interactions exist as no curves cross. Temperature

appears to be the only major influence on the %IOWY after one and six dips of indigo.

R² = 0.708

R² = 0.743

0.000%

0.500%

1.000%

1.500%

2.000%

2.500%

0.000%

0.050%

0.100%

0.150%

0.200%

0.250%

0.300%

0.350%

0.400%

70 75 80 85 90 95 100

% I O W Y ( s i x d i p s )

% I O W Y ( o n e d i p )

Temperature (°C)

Effect of Temperture on %IOWY from One and Six Dips of

Indigo

One Dip Six Dips



110

Figure 3-11: Interaction profile for time, temperature, and sodium hydroxide concentration on %IOWY after one and six

dips of indigo dye

A full ANOVA analysis was conducted on %IOWY after one dip of indigo by time, sodium

hydroxide concentration, and temperature during laboratory preparation. The analysis revealed the

second order effect of time and sodium hydroxide concentration to be insignificant. Furthermore,

the first order effect was actually determined to be insignificant as illustrated by the high P-values in

the parameter estimates from table 3-5. Time had a P-value of 0.6761 while sodium hydroxide

concentration was 0.4675. In fact, the only statistically significant parameter effect was the first andsecond order temperature along with intercept (P-value 0.0010, 0.0176, and 0.0259 respectively).

Even though time and sodium hydroxide concentration parameters were determined to be

insignificant, it is customary to leave the first order parameters in model calculations especially since

the equation will be later joined with other models that may have all three parameters. The

summary of fit for the resulting model was 0.71 with a P-value of 0.0029. Both indicate the model

produced a reasonable fit that was statistically significant compared to the data points.

%IOWY Interaction Profile for One Dip %IOWY Interaction Profile for Six Dips

(min) (min)

(C) (C)

(g/l) (g/l)



111

Table 3-5: ANOVA analysis results for laboratory preparation parameters on %IOWY for one dip of indigo

The exact model was constructed by pulling the parameter estimates from table 3-5 and

equation 3-10 was created.

% = −7.312 ∗ ( − 88.29) + 8.425 ∗ +

1.0 ∗ + 2.345 ∗ − 0.05075

Equation 3-10: %IOWY as a function of time, temperature, and sodium hydroxide concentration after one dip of indigo.

This equation was used to build the prediction profiler graphs shown in figure 3-12. These curves

finally illustrate the significance of temperature during laboratory preparation on %IOWY. They also

show the low dependence of %IOWY on time and sodium hydroxide concentration. The 95%

confidence intervals were also calculated and plotted as blue dotted curves. The best overall

combination yields confidence intervals of ±0.0896% with a mean value of 0.2946% indigo on weight

of yarn.



112

Figure 3-12: %IOWY for one dip of indigo model as a function of time, temperature, and sodium hydroxide

concentration in laboratory preparation process

A full ANOVA analysis was conducted on %IOWY after six dips of indigo by time, sodium

hydroxide concentration, and temperature during laboratory preparation. The results are presented

in table 3-6. Just like one dip of indigo the parameter estimates indicate the first and second order

term of temperature were statistically significant with P-values of ≤0.0001 and 0.0148 respectively

for six dips of indigo. Time and sodium hydroxide concentration were left in the model calculations

even though each was determined to be insignificant. The summary of fit for the model was

calculated to be R2 of 0.76 and the analysis of variance had a P-value of 0.0006. Both indicate the

model was a good fit and statistically significant compared to the data used to create the model.

% I O W Y

0 . 0 0 2 9 4 6

± 0 . 0

0 0 8 9 5

2 0

2 5

3 0

3 5

4 0

7 5

8 0

8 5

9 0

9 5

1 0 0 0 5

1 0

1 5

%IOWY Prediction Profile on One Dip of Indigo for Laboratory Preparation Process




113

Table 3-6: ANOVA analysis results for laboratory preparation parameters on %IOWY for six dips of indigo

Using the parameter estimates from table 3-6, equation 3-11 for 6 dips of indigo was

created.

% = −1.386 ∗ ( − 87.78) + 1.901 ∗ +

2.64 ∗ + 3.081 ∗ + 0.0032114

Equation 3-11: %IOWY as a function of time, temperature, and sodium hydroxide concentration after six dips of indigo.

This equation was also graphically represented in figure 3-13. These curves finally illustrate

the significance of temperature on %IOWY. They also show the low dependence of %IOWY on time

and sodium hydroxide concentration. The 95% confidence intervals are at minimum value when

time equals 30 minutes based on the blue dotted confidence curves. The best overall combination

yields confidence intervals of ±0.1654% with a mean value of 2.143% IOWY. While the magnitude of

confidence intervals for six dips of indigo is two times greater than one dip, the mean %IOWY at six

dips is almost ten times greater than one dip. Therefore, the overall confidence after six dips of

indigo is actually greater than after one dip of indigo.



114

Figure 3-13: %IOWY for six dips of indigo model as a function of time, temperature, and sodium hydroxide



Affect on Integ Shade Value after One and Six Dip Indigo Dyeing Conditions

The general trend for time's effect on Integ shade value from both one and six dip dyeings is

shown in figure 3-14. After one dip of indigo, increasing boil-off time caused the Integ shade value

to increase which indicates the indigo color became darker. The trend has an overall R2 value of

0.245 which indicated a poor overall correlation. The general trend is for constant Integ shade value

from 20 minutes till 30 minutes. At 30 minutes a high degree of variability exists in Integ shade

value. Further increases in time result in increased Integ shade values.

During six dips of indigo dyeing, time had the opposite effect on Integ shade value as

reflected in figure 3-14. As the time increased the Integ shade value decreased indicating the indigo

color becomes lighter. The trend has an overall R2 value of 0.021 which indicates a very poor overall

correlation. Over the entire time span the Integ shade value ranged from 91 at 37 minutes to 101 at

30 minutes. This is a change of 10 Integ shade value units or less than 10%. The general trend for

Integ as a function of time after six dips of indigo dyeing is that of constant value. Neither the one

% I O W Y

0 . 0

2 1 4 2 9

± 0 . 0

0 1 6 5 4

2 0

2 5

3 0

3 5

4 0

7 5

8 0

8 5

9 0

9 5

1 0 0 0 5

1 0

1 5

%IOWY Prediction Profile on Six Dips of Indigo for Laboratory Preparation Process




115

dip nor the six dip indigo dyeing condition exhibited a major contribution to Integ shade value due

to time.

Figure 3-14: Relationship of laboratory preparation time on Integ shade value from one and six dips of indigo dye

Next sodium hydroxide concentration during laboratory preparation was evaluated after

one and six dips of indigo. Both dyeing conditions exhibited a plateau as the sodium hydroxide

concentration was increased. Figure 3-15 shows the apex is approximately 6 g/l for one dip and 11

g/l for six dips. Continued increasing concentration levels beyond these values resulted in

decreasing Integ values for both dip conditions. However, both dyeing conditions exhibited poor

correlation as reflected in the R2 values of 0.187 and 0.182 for one and six dips respectively. The

poor correlation can be explained by the relatively small change in Integ values over a wide range of

concentrations coupled with the high variability associated with each concentration. At 7.5 g/l

concentration the variability of Integ shade value dramatically increased compared to lower

R² = 0.245

R² = 0.021

75.0

80.0

85.0

90.0

95.0

100.0

105.0

20.0

22.0

24.0

26.0

28.0

30.0

32.0

34.0

20 25 30 35 40

I n t e g ( s i x d i p s )

I n t e g ( o n e d i p )

Time (minutes)

Effect of Time on Integ from One and Six Dips of Indigo

One Dip Six Dips



116

concentrations. As the concentration is further increased the variability appears to reduce while the

overall Integ shade value also decreased.

Figure 3-15: Relationship of sodium hydroxide concentration during laboratory preparation on Integ shade value after

one and six dips of indigo dye

Unlike previous %IOWY analysis, temperature doesn't play a major role in Integ shade value

variation. After one dip of indigo, the general trend was increased Integ shade as the temperature

was increased from 88°C to 100°C. However the changes in Integ shade values were small and the

overall R2 correlation was low at 0.122 as shown in figure 3-16. After six dips of indigo the general

trend was decreased Integ shade as the temperature was increased from 88°C to 100°C. However,

the changes in Integ shade values were small and the overall R2 correlation was low at 0.015 as

shown in figure 3-16. At 88°C the variability increased considerably under both one and six dip

dyeing conditions and appears to decrease as the temperature is increased. Like the other two

parameters, temperature has a high degree of variability so a detailed ANOVA analysis was needed

to confirm insignificance.

R² = 0.187

R² = 0.182

75.0

80.0

85.0

90.0

95.0

100.0

105.0

20.0

22.0

24.0

26.0

28.0

30.0

32.0

34.0

0 2 4 6 8 10 12 14 16




Effect of Sodium Hydroxide Concentration on Integ from One

and Six Dips of Indigo

One Dip Six Dips



117

Figure 3-16: Relationship of temperature during laboratory preparation on Integ shade value after one and six dips of

indigo dye

The full ANOVA analysis involving first and second order plus interactions of parameters was

shown in table 3-7 for one dip indigo dyeing condition. The P-values calculated in parameter

estimates shown no statistically significant effect for all values except the intercept which of course

was meaningless. This conclusion was further supported by relatively low R2 in the summary of fit

and high P-value in analysis of variance results. As a result, the Integ shade value from one dip of

indigo was not used to optimize the laboratory preparation procedure.

R² = 0.122

R² = 0.015

75.0

80.0

85.0

90.0

95.0

100.0

105.0

20.0

22.0

24.0

26.0

28.0

30.0

32.0

34.0

70 75 80 85 90 95 100



Temperature (°C)

Effect of Temperture on Integ from One and Six Dips of

Indigo

One Dip Six Dips



118

Table 3-7: ANOVA analysis results for laboratory preparation parameters on Integ for one dip of indigo

The full ANOVA analysis involving first and second order plus interactions of parameters was

shown in table 3-8 for six dip indigo dyeing condition. The P-values calculated in parameter

estimates showed no statistically significant effect on all values except the intercept which of course

was meaningless. This conclusion was further supported by relatively low R

2

in the summary of fitand high P-value in analysis of variance results. No statistically significant effect from time,

temperature, or sodium hydroxide concentration on Integ shade value for six dips of indigo existed.

This is the same results as seen in one dip of indigo dye. As a result, the Integ shade value from six

dips of indigo was not used to optimize the laboratory preparation procedure.



119

Table 3-8: ANOVA analysis results for laboratory preparation parameters on Integ for six dips of indigo


Affect on Penetration Factor after One and Six Dip Indigo Dyeing Conditions

Since time, temperature, and sodium hydroxide concentration were determined to have

insignificant effect on Integ shade value and penetration factor is a function of Integ shade value

and %IOWY, this researcher expects the penetration factor to have the same relationship as the

inverse of %IOWY. For completeness, the full analysis was presented. First, notice a high degree of

variability in the penetration factor presented in figure 3-17 after one dip of indigo. The extremely

low levels of %IOWY at shorter times produced high penetration factor values. With all data points

the R2 correlation was very low at 0.088. If the single point at 1200+ penetration factor was

removed, the function was flat with R2 of 0.057. Time doesn't appear to affect penetration factor

after one dip of indigo.



120

A similar relationship exists for six dips of indigo on penetration factor as a function of time.

The high degree of variability in the penetration factor presented in figure 3-17 continues for six

dips. While the range of penetration factors from six dips is smaller than one dip, the overall

variation is high. With all data points the R2 correlation was very low at 0.03 and is basically

constant over all times.

Figure 3-17: Relationship of time during laboratory preparation on penetration factor after one and six dips of indigo

dye

The same observations can be made in regards to sodium hydroxide concentration influence

on penetration factor after one and six dips of indigo. Very poor correlation exists as illustrated in

figure 3-18 with R2 values of 0.094 and 0.011 for one and six dips respectively. If the 1200+

penetration factor value was removed, the resulting trend after one dip of indigo was flat with a R2

value of 0.049. Sodium hydroxide concentration doesn't have a major affect on penetration factor.

R² = 0.088

R² = 0.03

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

0.00

200.00

400.00

600.00

800.00

1000.00

1200.00

1400.00

20 25 30 35 40

P e n e t r a t i o n F a c t o r ( s e x d i p s )

P e n e t r a t i o n F a c t o r ( o

n e d i p )

Time (minutes)

Effect of Time on Penetration Factor from One and Six Dips

of Indigo

One Dip Six Dips



121

Figure 3-18: Relationship of sodium hydroxide concentration during laboratory preparation on penetration factor after


The temperature effect on penetration factor after one and six dips of indigo was discussed.

Under both indigo dyeing conditions the penetration factor decreased as the temperature was

increased, figure 3-19. This was the opposite trend as shown for %IOWY as a function of

temperature, refer back to figure 3-10. After one dip the general trend in figure 3-19 isn't as

pronounced due to the greater variation in penetration factor values which was reflected in the R2

value of 0.246. However, after six dips the general trend has a much stronger correlation as

reflected in the R2 value of 0.729. Both dyeing conditions exhibit reduce variation as the

temperature is increased. The penetration factor reaches the minimum value at approximately 95°C

and does not vary further as temperature continues to increase.

R² = 0.094

R² = 0.011

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

0.00

200.00

400.00

600.00

800.00

1000.00

1200.00

1400.00

0 2 4 6 8 10 12 14 16

P e n e t r a t i o n F a c t o r ( s i x d

i p s )

P e n e t r a t i o n F a c t o r ( o n e

d i p )


Effect of Sodium Hydroxide Concentration on Penetration

Factor from One and Six Dips of Indigo

One Dip Six Dips



122

Figure 3-19: Relationship of temperature during laboratory preparation on penetration factor after one and six dips of

indigo dye

Evaluation of parameter interaction was shown in figure 3-20 for both one and six dip indigo

conditions. As with %IOWY, no actual parameter interactions were detected. Furthermore, the only

major change in penetration factor occurs as a result of temperature as evident in large change from

76°C to 100°C in the second row of graphs for both one and six dip conditions.

R² = 0.246

R² = 0.729

0.00

10.00

20.00

30.00

40.00

50.00

60.00

70.00

0.00

200.00

400.00

600.00

800.00

1000.00

1200.00

1400.00

70 75 80 85 90 95 100

P e n e t r a t i o n F a c t o r ( s i x d

i p s )

P e n e t r a t i o n F a c t o r ( o n e

d i p )

Temperature (°C)

Effect of Temperture on Penetration Factor from One and Six

Dips of Indigo

One Dip Six Dips



123

Figure 3-20: Interaction profile for time, temperature, and sodium hydroxide concentration on penetration factor after


The full ANOVA analysis results after one dip of indigo were shown in table 3-9. The

parameter estimates with statistical significance was determined to be first and second order

temperature represented by P-values of 0.0021 and 0.0293 respectively. The R2 of 0.68 and P-value

of 0.0050 for the complete model indicate reasonable agreement that was statistically significant to

the actual data points. While the overall agreement was lower than for %IOWY, this was somewhat

expected given the greater degree of variability especially with the 1200+ penetration value.

Table 3-9: ANOVA analysis results for laboratory preparation parameters on penetration factor from one dip of indigo

50100

150200

250

P . F .

50100150

200

250

P . F

.

50100

150200

250

P . F .

Time

76

100

015

2 0

2 5

3 0

3 5

4 0

2040

Temperature

015

8 0

8 5

9 0

9 5

1 0 0

2040

76

100

NaOH

0 5 1 0

1 5

T i m e

T em p er a t ur e

N a OH

Interaction Profiles

40

45

50

55

60

P . F .

40

4550

55

60

P . F

.

40

45

50

55

60

P . F .

Time

102.5

015

2 0

2 5

3 0

3 5

4 0

2040

Temperature

015

7 5

8 5

9 5

1 0 5

2040

102.5

NaOH

0 5 1 0

1 5

T i m e

T em p er a t ur e

N a OH

Interaction Profiles P.F. Interaction Profile for One Dip P.F. Interaction Profile for Six Dips

(min) (min)

(C) (C)

(g/l) (g/l)



124

The prediction profiler, figure 3-21, further agrees with the inverse of %IOWY. Time and

sodium hydroxide concentration have little influence on penetration factor regardless of

temperature. While an increasing temperature causes a decrease in penetration factor. This trend

was governed by the %IOWY at each temperature level. At low temperatures, the %IOWY was low

while at higher temperatures the amount of %IOWY increased. Therefore dividing a relatively

constant Integ shade value by low %IOWY at low temperatures produces a high penetration factor

and low penetration factor at high temperatures since the %IOWY was higher. Since no new

information regarding laboratory preparation process was gleamed, this relationship will not be

used to determine the optimum laboratory preparation procedure.

Figure 3-21: Penetration factor for one dip of indigo model as a function of time, temperature, and sodium hydroxide


The full ANOVA analysis results after six dips of indigo were shown in table 3-10. The

parameter estimates with statistical significance was determined to be first and second order

temperature represented by P-values of 0.0001 and 0.0171 respectively. The R2 of 0.75 and P-value

of 0.0007 for the complete model indicated reasonable agreement that was statistically significant

to the actual data points. However, the overall agreement was less than previous %IOWY analysis.

Penetration Factor Prediction Profile on One Dip of Indigo for Laboratory Preparation




125

Table 3-10: ANOVA analysis results for laboratory preparation parameters on penetration factor from six dips of indigo

The prediction profiler, figure 3-22, further agrees with the inverse of %IOWY. Time and

sodium hydroxide concentration have little influence on penetration factor regardless of

temperature. While increasing temperature causes a decrease in penetration factor. Just like one

dip of indigo, this trend was governed by the %IOWY at each temperature level. At low

temperatures, the %IOWY was low while at higher temperatures the amount of %IOWY increased.

Therefore, dividing a relatively constant Integ shade value by low %IOWY at low temperatures

produces a high penetration factor and low penetration factor at high temperatures since the

%IOWY was higher. This relationship will not be used to determine the optimum laboratory

preparation procedure.



126

Figure 3-22: Penetration factor for six dips of indigo model as a function of time, temperature, and sodium hydroxide


3.2.5 Determine Optimum Settings for Laboratory Preparation Procedure

By joining the prediction formulas of %Boil-off loss and %IOWY at one dip, the prediction

profile illustrated in figure 3-23 was generated. The desired outcome was flat or very little change in

%Boil-off loss and %IOWY at specific values of time, temperature, and sodium hydroxide

concentration. The first row of graphs in figure 3-23 illustrated the relationship between %Boil-off

loss as a function of time, temperature, and sodium hydroxide concentration. The second row of

graphs illustrated the relationship between %IOWY as a function of time, temperature, and sodium

hydroxide concentration. Again, these were the same relationships previously determined in the

ANOVA analysis. The third row of graphs represents the combined response by placing equal

importance to %Boil-off loss and %IOWY. This sequence of graphs was used to determine the

optimum setting for each parameter.

The first column of graphs shows the total effect of time on each response variable and the

corresponding desire function. As one can see increasing time caused increase in %Boil-off loss and

no affect on %IOWY which resulted in very little overall affect on the total desire function.

Therefore, any value of time greater than 20 minutes will produce consistent and repeatable %Boil-

off loss and more importantly %IOWY. Given 30 minutes was the center point of the design of

Penetration Factor Prediction Profile on Six Dips of Indigo for Laboratory Preparation




127

experiment and therefore has the greatest replicated data points, this researcher selected 30

minutes for time value under one dip of indigo.

The second column of graphs illustrated the total effect of temperature on each response

variable and the corresponding desire function. According to %Boil-off loss the ideal temperaturevalue lays greater than 100° C. However, the %IOWY function indicated temperature values greater

than ~95° C have no additional impact. Therefore the combined desire function of %Boil-off loss

and %IOWY actually flattens out at 95° C. As a result, temperatures greater than 95° C had lower

sensitivity to changes which of course was desired, therefore temperature values greater than 95° C

were preferred.

The third column in figure 3-23 corresponds to sodium hydroxide concentration effect on

%Boil-off loss and %IOWY. Here 11 g/l was determined to have the greatest %Boil-off loss while noconcentration level significantly impacts %IOWY. The combined desire function indicates

concentration levels greater than 11 g/l had no additional impact. Therefore, any level greater the

11 g/l was preferred.



128

Figure 3-23: Optimized laboratory preparation parameters incorporating prediction profiles from %Boil-off loss and

%IOWY from one dip of indigo dye

Similar prediction profile graphs were created for six dips of indigo, figure 3-24. Following

the same logic as discussed with one dip of indigo produced the following results. The first column

shows time levels greater the 30 minutes yields little to no impact on the overall desire function.The second column illustrated the highest level of desire function to occur at 100° C and doesn't

flatten out. However, more detailed review shows temperature levels greater the 95° C has little

additional impact on the %IOWY. The third column for sodium hydroxide concentration mirrors the

results for one dip of indigo. Concentrations greater than 11 g/l have little or no additional effect on

%Boil-off loss or %IOWY.

0.015

0.02

0.025

0.03

r

e d F o r m u

l a

B o

i l - o f f L o s s

0 . 0

3 0 2 1 1

0

0.005

0.01

0.015

0.02

P r e

d F o r m u

l a

I O W Y B y

D i p

0 . 0

0 2 8 2 3

0 0

. 2 5

0 . 7

5 1

D e s

i r a b i l i t y

0 . 3

6 3 6 6 7

2 0

2 5

3 0

3 5

4 0

30

Time

7 5

8 0

8 5

9 0

9 5

1 0 0

100

Temperature

0 5 1 0

1 5

11

NaOH

1 6

1

Dip #

0

0

. 2 5

0 . 5

0

. 7 5 1

Desirability

Prediction Profiler Optimized Prediction Profile on One Dip of Indigo for Laboratory Preparation Process

Time (min) Temperature (C) NaOH (g/l)



129

Figure 3-24: Optimized laboratory preparation parameters incorporating prediction profiles from %Boil-off loss and

%IOWY from six dips of indigo dye

Additional observations made during the experiment were controlling the temperature of

the solution was the most difficult of the three factors. The time and sodium hydroxide

concentration were the easiest. Temperature levels of 100°C were easily maintained at atmospheric

conditions by just maintaining a slow boil in the preparation bath. Combining the above comments

with the results from the analysis of one and six dip indigo dyed skeins yields the following optimum

laboratory preparation procedure. These specific laboratory preparation parameters were used on

all following trials.

Time: 30 minutes

Temperature: 100°C

Sodium hydroxide concentration: 12.7 g/l of 50% caustic soda

0.015

0.02

0.025

0.03

r e d F o r m u

l a

B o

i l - o f f

L o s s

0 . 0

3 0 2 1 1

0

0.005

0.01

0.015

0.02

P r e

d F o r m u

l a

I O W Y B y

D i p

0 . 0

2 1 2 3 1

0

0 . 2

5

0 . 7

5 1

D e s

i r a b i l i t y

0 . 9

6 4 2 8 6

2 0

2 5

3 0

3 5

4 0

30

Time

7 5

8 0

8 5

9 0

9 5

1 0 0

100

Temperature

0 5 1 0

1 5

11

NaOH

1 6

6

Dip #

0

0 . 2

5 0

. 5

0 . 7

5 1

Desirability

Prediction Profiler Optimized Prediction Profile on Six Dips of Indigo for Laboratory Preparation Process

Time (min) Temperature (C) NaOH (g/l)



130

3.3 Equilibrium Sorption Experiment to Determine %IOWY and Shade Relationship for Uniformly

Dyed Skeins

In 1991 Etters20 published equilibrium sorption curves for %IOWY as a function of dye bath

concentration and pH. Unfortunately this data did not contain shade information. With the shadeinformation from uniformly dyed yarns, the shade of ring dyed yarns could be converted into

equivalent %IOWY on the "visible" surface of yarn. This value compared to actual %IOWY would

give a measurement of dye penetration into the yarn structure. This method would give a more

quantitative measurement of dye penetration as opposed to qualitative such as penetration factor

discussed in section 3.1.3. Specifically penetration level was defined by equation 3-12.

Penetration Level = %M

%I

Equation 3-12: Calculation of penetration level as a function of measured %IOWY and converted surface %IOWY from

Integ shade readings.

Here the %IOWY in the numerator was measured by Pyrrolidinone extract as discussed in

section 3.1. The %IOWY converted from Integ shade value in the denominator was the %IOWY that

corresponds to the measured Integ shade value if the dying had been conducted under uniform

dyeing conditions, i.e. uniform dye concentration distribution in the cross section of the yarn. The

penetration level values will vary from 1.0 to 0.0 with 1.0 corresponding to uniformly dyed cross

sections of yarn and 0.0 representing ideal ring dyed yarn with all dye located on the very outer

perimeter of the yarn.

To collect the shade information a series of laboratory dyeings were conducted. Eight

different stock mixes were made up and diluted to specific dye bath concentrations. Each dye bath

contained 3 liters of volume and at most 4 yarn skeins were dyed in each bath. Approximately 30

grams of cotton (4 times 7 grams/skein) to 3000 grams of dye bath followed 100:1 liquor: cotton

ratio. The initial dye bath pH was also measured. Then up to 4 skeins that had been pre-wet out

and nipped to 70% wet pick-up were submerged into the dye bath suspended by plastic hooks to



131

keep the skeins from lying on top of each other. The top of each dye mix was covered with plastic

film to prevent air oxidation of the dye. After 14 hours of dyeing time, each skein was pulled from

the dye bath and run through a laboratory pad nip to squeeze excess dye from the yarn to

approximately 70% wet pick-up. The skeins were then allowed to air oxidize for 3 minutes prior to

laboratory washing at 40°C. The washing process was deemed completed when the wash water was

void of color. Once the skeins were dried, the shade was measured as previously discussed and

finally the %IOWY was measured by Pyrrolidinone extraction. Table 3-11 listed the specific dye bath

concentration, pH, and resulting %IOWY and Integ shade for 6.3/1 yarn counts. The remaining yarn

counts and measured values are provided in appendix section A-3-3.



132

Table 3-11: %IOWY and Integ shade data from equilibrium sorption experiment

Yarn Count Dye Bath g/l Dye Bath pH %IOWY Integ Shade Stock Mix #

6.3 0.308 11.1 1.19% 27.9 2

6.3 2.548 11.2 2.97% 63.5 8

6.3 0.641 12.25 1.09% 31.3 1

6.3 0.17663 12.8 0.30% 7.6 46.3 1.2287 12.8 1.14% 30.6 6

6.3 1.602 12.72 1.65% 42.4 1

6.3 1.602 12.72 1.66% 43.7 7

6.3 2.564 12.9 2.07% 47.9 7

6.3 8.413 12.8 4.59% 75.1 2

6.3 0.01577 13.17 0.02% 1.2 3

6.3 0.03494 13.3 0.04% 2.3 6

6.3 0.49612 13.19 0.52% 13.4 5

6.3 1.99985 13.21 1.50% 35.3 3

6.3 3.8843 13.24 2.21% 49.9 5

6.3 4.487 13.14 2.70% 58.1 7

6.3 4.487 13.14 2.68% 57.1 1

6.3 6.3355 13.1 3.32% 63.3 4

6.3 9.61464 13.31 4.05% 69.4 3

6.3 14.0149 13.2 4.94% 75.6 6

6.3 14.422 13.2 5.65% 77.2 8

6.3 19.2293 13.43 6.20% 77.7 5

6.3 20.191 13.3 6.68% 81.8 8

6.3 24.037 13.2 8.10% 89.5 2

6.3 29.95 13.2 8.38% 91.3 4

Graphical representation of the equilibrium sorption data revealed the same correlation

previously published by Etters20. Namely the %IOWY follows a Freundlich isotherm or power

relationship between %IOWY and dye bath concentration at different dye bath pH values. Also

note the %IOWY was independent of the yarn count. In figure 3-25 the equilibrium sorption data at

pH ranges 13.1 to 13.3 were illustrated. The "X" marks were Etter's 1991 data points. The other

points were 6.3/1, 7.1/1, 8.0/1, and 12.0/1 yarn count data from current equilibrium sorption

experiment. The curve fit was Etter's 1991 data points extended above and below the original datarange to encompass the range of current values.



133

Figure 3-25: %IOWY from 6.3/1, 7.1/1, 8.0/1, and 12.0/1 OE yarns compared to Etters20

data under equilibrium sorption

at pH 13 range.

The same relationship was illustrated in figure 3-26 for pH ranges of 11.0 to 11.2. Once

again the current experimental results mirror Etter's 1991 data. Both sets of data are almost

perfectly modeled by a power function.

y = 0.007303x0.734588

R² = 0.996

0.01%

0.10%

1.00%

10.00%

100.00%

0.01 0.1 1 10 % I O W Y ( g m I n d i g o / 1 0 0 g m c o t t o

n )

Dye Concentration (g/l)

Equilibrium Sorption Relationship at 13.1 to 13.3 pH

6.3 7.1 8 12 Etters 1991



134

Figure 3-26: %IOWY on 6.3/1, 7.1/1, 8.0/1, and 12.0/1 OE yarns compared to Etters20

data under equilibrium sorption at

pH 11 range.

By combining all current equilibrium sorption data with Etter's 1991 data, a general

relationship between dye bath concentration and pH affect on total %IOWY was revealed. The

power functions at various pH values were summarized in equation 3-13 in the general form.

At each pH: % = ∗

11.2 pH: % = 0.019156 ∗ .

12.8 pH: % = 0.010734 ∗ .

13.2 pH: % = 0.007448 ∗ .

Equation 3-13: Power function relationship of indigo dye bath concentration to %IOWY under equilibrium sorption.

y = 0.019156x0.583135

R² = 0.992

0.10%

1.00%

10.00%

100.00%

0.01 0.1 1 10

% I O W Y ( g m I n d i g o / 1 0 0 g m c o t t o n

)


Equilibrium Sorption Relationship at 11.0 to 11.2 pH

6.3 8 Etters 1991



135

When the component values of the power functions were graphed as a function of pH, the A

component increased with decreasing pH and the B component increased with increasing pH. The

trend for each was shown in figure 3-27. Furthermore the shape of the component A was very

reminiscent of the monophenolate ionic form of indigo dye as a function of pH.

Figure 3-27: Power function coefficients A and B as a function of dye bath pH.

By converting figure 3-27 into a function of monophenolate ionic indigo dye as it varies with

pH, the regression between all three points becomes linear as shown in figure 3-28. Component A

now increased as the monophenolate fraction increased which occurs as pH decreased. Component

B now decreased with an increase in the monophenolate fraction which occurs as the pH decreased.

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0

0.005

0.01

0.015

0.02

0.025

11 11.5 12 12.5 13 13.5

V a l u e o f C o m

p o n e n t B

V a l u e o f C o m

p o n e t A

pH

Coefficients of Equilibrium Sorption %IOWY Power

Function

Component A Component B



136

Figure 3-28: Equilibrium sorption power function coefficients as a function of monophenolate ionic form of indigo.

These linear equations for component A and B as a function of monophenolate ionic indigo

dye fraction which were actually a function of pH were used in the general power function to relate

%IOWY to dye bath concentration under equilibrium sorption. The specific results were given in

equation 3-14.

ℎ =

..

= 0.016492 ∗ ℎ + 0.003465

= −0.244296 ∗ ℎ + 0.816158

% = ∗

Equation 3-14: General relationships between indigo dye bath concentration and pH to resulting %IOWY under

equilibrium sorption.

y = 0.016492x + 0.003465

R² = 0.999981

y = -0.244296x + 0.816158

R² = 0.999384

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0

0.005

0.01

0.015

0.02

0.025

0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

V a l u e o f C o m p o n e n t B

V a l u e o f C o m p o n e t A

Value of Monophenolate Indigo Dye Fraction as a Function of pH

Coefficients of Equilibrium Sorption %IOWY Power

Function

Component A Component B



137

Figure 3-29 shows the results of theoretical %IOWY at 11.2, 12.2, 12.8, and 13.2 pH. The

curves at various pH levels were the theoretical values based on equation 3-14. The individual data

points were all available points of equilibrium sorption as a function of dye bath pH and

concentration. While equation 3-14 was certainly not the only possible solution from regression to

fit the data available, it possesses certain elegance by combining the characteristic nature of

Freundlich isotherm and monophenolate ionic fraction into one equation. This represents the

maximum amount of dye pick-up under equilibrium sorption (M∞) that can be achieved given these

two important chemical dye range parameters.

Figure 3-29: Comparison of calculated and measured %IOWY under equilibrium sorption laboratory dyeing conditions as

the dye bath concentration and pH were varied.

0.01%

0.10%

1.00%

10.00%

100.00%

0.01 0.1 1 10

C a l c u l a t e d % I O W

Y ( g m I n d i g o / 1 0 0 g m c o t t o n )


Calculated Equilibrium Sorption Relationship atVarious pH's

11.2 pH 12.8 pH 13.2 pH Power (11.2 pH)

Power (13.2 pH) Power (12.2 pH) Power (12.8 pH)



138

The shade of the yarns as a function of %IOWY can now be investigated. The relationships

were later used to determine the penetration level for each dye range set-up observation. The

Integ shade value of a particular yarn was converted into the corresponding %IOWY from

equilibrium sorption. Then the penetration level was calculated when compared to the actual

%IOWY. The specific Integ shade values from each yarn count as a function of %IOWY from

equilibrium sorption is featured in figure 3-30. The %IOWY and Integ relationship starts off linear at

low %IOWY values. As the %IOWY increased the resulting change in Integ shade value had less

effect. Therefore the %IOWY and Integ relationship is non-linear but does possess unique values

over the entire range of %IOWY. The best model fit resulted in equation 3-15 that would allow Integ

shade calculations based on the %IOWY under equilibrium sorption.

Figure 3-30: Relationship of Integ shade value for various yarn counts as %IOWY from equilibrium sorption.

I n t e g



139

= 45.60937 + (592.19421 ∗ %) − (9928.5539 ∗ (% − 0.045773)) +(1.83538 ∗ (% − 0.045773)) − (1.52245 ∗ (% − 0.045773)) + (4.27080 ∗(% − 0.045773))

Equation 3-15: Calculation of Integ shade based on %IOWY under equilibrium sorption conditions.

The inverse relationship was actually required in order to calculate the penetration level.

Switching the independent and dependent variables produced the relationship for calculating the

%IOWY on the outside surface as a function of Integ shade value. The relationship is displayed in

figure 3-31 and resulting equation listed as equation 3-16.

Figure 3-31: Relationship of %IOWY on the outside surface for various yarn counts as Integ from equilibrium sorption.

% = −0.02646 + (9.5386

∗ ) + (1.3593

∗ ( − 55.2088)

) +(3.909 ∗ ( − 55.2088)) + (2.4244 ∗ ( − 55.2088)) + (6.4303 ∗( − 55.2088))

Equation 3-16: Calculation of surface %IOWY from Integ shade values.

% I O W Y o n O u t s i d e S u r f a c e



140

As previously discussed K/S660nm cannot be used for %IOWY conversion involving equilibrium

sorption data. The relationship was not only non-linear but it was non-unique as shown in figure 3-

32. In fact most researchers who have used K/S660nm have adjusted or "corrected" the curve to

create a linear relationship. However, the correction was based on slope at very low dye

concentrations and projected to about 3.0 %IOWY. While this correction was certainly an

acceptable manner to handle the non-linearity at low %IOWY values, it was apparent at much higher

%IOWY values the correction loses all meaning. For this reason the researcher has decided to use

Integ shade value instead of K/S660nm.

Figure 3-32: Shape of K/S at 660 nm as a function of %IOWY from equilibrium sorption experiments.

0.0

5.0

10.0

15.0

20.0

25.0

30.0

35.0

40.0

0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00

K / S a t 6 6 0 n m

%IOWY from Equilibrium Sorption

K/S at 660nm as a Function of %IOWY

6.3 7.1 8 12

Poly. (6.3) Poly. (7.1) Poly. (8) Poly. (12)



141

3.4 Observational Indigo Study: Establishing Breadth of Dye Conditions and Convergence Test to

Determine Conclusion of Study

The dye range conditions consist of two different attributes: mechanical parameters and

chemical parameters. Mechanical parameters were the yarn count, dye range speed, immersiondye bath thread-up length, oxidation thread-up length, nip pressure, and number of dye bath dips.

The chemical parameters were the indigo dye bath concentration, pH, and reduction potential.

When a set of yarn skeins was processed in the dye range, each parameter was measured and

recorded. As previously discussed, the response variables were %COWY, %IOWY, Integ shade, and

penetration level. The range of each parameter must be understood prior to beginning the study

and a game plan developed to justify ending the study. Table 3-12 lists the specific parameters

available from all bulk production dye range conditions at this researcher's disposal.

Table 3-12: Observational study parameters and potential range of values

Parameter Minimum Value Maximum Value

Yarn Count 6.3/1 12.0/1

Speed (m/sec) 26.5 36.6

Immersion Length (meter) 8.6 11.4

Oxidation Length (meter) 36.0 37.0

Number of dips 1 7

Dye concentration (g/l) 0.75 3.25pH 11.0 13.0

Reduction potential (mV) 720 900

Nip Pressure (psi) 40 75

The dye range speed was set to match the specific dye range set-up sheet by the operator.

The magnitude was controlled and maintained by ABB digital drive control system. The immersion

length was determined by multiplying speed and immersion time. The immersion time of each yarn

skein was measured with a stop watch. Immersion time was defined to be from liquor surface to nip

point at the squeeze rolls and was averaged from 10 different measurements each time data was

collected. The dye concentration was measured according to accepted industry methods. The %T

was measured and converted into g/l concentrations by using calibration equations. The %T



142

method is given in Appendix A-1-2a. The reduction potential and pH were measured by respective

probes.

If a traditional 3 level full factorial design of experiment was planned, this would result in 39

or 19683 trials to cover 3 levels on 9 parameters. As previously discussed, such an experiment isn'tpossible. But if it were possible, the levels would look like table 3-13. Here the yarn count, number

of dips, and nip pressure were removed. Also oxidation thread-up length was assumed to be

sufficient to result in complete oxidation and therefore inconsequential. The first values in table 3-

13 for each parameter were the target value and the numbers in ()'s were the acceptable ranges to

fall within that group. These were grouped for each yarn count and each dip for analysis.

Because every possible combination of parameters were not processed in production, a

certain prime data set was defined which covers an acceptable range of parameters. Specificallyyarn skeins were processed targeting the following parameters and response variables measured

accordingly. The percent range of span from minimum to maximum value was calculated. Dye bath

concentration appears to vary over a large range. Likewise, the immersion length and speed change

by 30%. The pH does not appear to vary a great deal. This was not unexpected given this particular

dye house does not utilize dye bath pH buffering systems like those discussed by Etters and others.

Table 3-13: Prime data set in the observational study

Parameter Low Value Middle Value High Value Range in Percent

Immersion Length (m) 8.6 11.4 33%

Speed (m/min) 29 (26.5-31) 32 (31-34.5) 35 (34.5-36.6) 37%

Dye Conc. (g/l) 1.1 (0.7-1.5) 1.9 (1.5-2.3) 2.7 (2.3-3.1) 342%

pH 11.3 (11-11.6) 11.8 (11.7-12) 12.3 (12-12.6) 18%

mV 740 (700-780) 820 (780-850) 880 (850-900) 27%



143

The prime data set was created by assigning all possible production variations to one of the

groups in table 3-13. Once all possible production variations had been assigned, it was time to

collect data from the observational study. The actual value for each parameter in the prime data set

was illustrated in figure 3-33. Across each parameter the three ranges were demarcated.

Figure 3-33: Range of observational study dye range set-up conditions and interactions.

26

28

30

32

34

3638

S p e e d m / m i n

1

2

3

I n d i g o

g m / l i t

11

12

13

B o x p H

700

800

900

B o x m V

8.63 11.37

Dwell

length m

26 2931333537

Speed m/min

1 2 3

Indigo

gm/lit

11 12 13

Box pH

Scatterplot Matrix

High value

Middle value

Low value

High value

Middle value

High value

High value

Middle value

Low value

Middle value

Low value

Low value

Scatterplot of Observational Study Dye Range Set-up Conditions and Interactions

g/l



144

Once all data was collected for the prime data set, ANOVA analysis was conducted to

determine significance of each parameter. Unlike traditional design of experiments, analysis of

observational studies incorporate the actual parameter value measured during the study instead of

the target value. An effects screening test was conducted and the standard error recorded for the

parameters at each response variable for 6.3/1 yarns after one dip of indigo. Then more data,

defined to be the replicated data set, was collected at the same dye range set-up conditions.

Although the dye range set-up conditions were replica of the prime data set, the actual measured

dye range variables were not the same. As each new data set was collected, the data was fed into

the effect screening test and ANOVA analysis was repeated. The new standard error was recorded.

This process was repeated for each replicated dye range condition until the standard error reached

a point of diminishing return. At this point, the addition of more data would not further improve

the model and the observational study was concluded.

Figure 3-34 demonstrates the diminishing improvement of standard error for dye bath

concentration parameter with the addition of replicates. "0" replicates on the x axis represents the

original prime data set. As each replicate data set was added, the new standard error was

calculated. In figure 3-34 the standard error of indigo dye bath concentration parameter affect on

%COWY, %IOWY, Integ, and Penetration level was monitored. Dye bath concentration was chosen

since it was the most statistically significant parameter on all response variables. The curves for

each response variable were a second order polynomial fit with projected trajectory of 5 imaginary

replicates. After 11 replicates the standard error of %IOWY, Integ, and Penetration Level appear to

reach their minimum value. In fact the last additional 6 data sets have a standard error average of

1.56e-4, 9.8e-1, and 1.66e-2 for %IOWY, Integ, and Penetration level respectively. The last four

replicate data sets had an average standard error of 2.82e-3 for %COWY with the last data set

having a value higher than the previous three data sets. Since the standard error was no longer

improving, the observational study was concluded. For completeness, this convergence test based

on parameter standard error was repeated after the official dye model was constructed and

redisplayed later.



145

Figure 3-34: Affect of additional replicated data sets on standard error of indigo dye bath concentration parameter and

four response variables after one dip of indigo.

Data analysis was conducted on all available data sets. After all data had been collected, the

data was then compared to Fick's law of diffusion to calculate the diffusion coefficients.

Additionally, cause and effect and the mechanism for dye pick-up were determined.

The final step in traditional design of experiments is simulation. Since true simulation isn't

possible, model predicted dye responses were compared to data sets from an independent dye

range. The simulation data sets were collected from a third indigo dye range from a different dye

house in a different country. Use of the third dye house guaranteed zero affect in developing the

model. The %COWY, %IOWY, penetration level, and final indigo shade from the third dye range

were compared to calculated values from the indigo dye models. The final simulation and validation

are shown in Chapter 5.

0

0.5

1

1.5

2

2.5

33.5

4

4.5

0 5 10 15 20 25

S t a n d a r d E r r o r o f I n d i g o

( g / l )

Number of Additional Replicates Added

Additional Replicates Affect on Standard Error

%COWY e-3 %IOWY e-4 Integ PL e-2



146

4 Data Analysis from the Observational Study

Yarn skeins were run and dye range set-up conditions were recorded as discussed in chapter

3. Also, response variables were measured and expressions calculated as detailed in chapter 3. The

entire data set is presented in Appendix section A-4-1 for reference. Data analysis consisted of

graphical and statistical techniques to evaluate and discuss general trends and specific relationships

between dye range set-up conditions and response variables. Once the effects of each parameter

were understood, empirical models were constructed to calculate %COWY, %IOWY, penetration

level, and Integ shade value. Last, dye theory model was constructed based on general dye and

diffusion theory.

4.1 Review of Main Parameter Affects on Response Variables Obtained from Observational Study

To determine the significance of each dye range set-up condition on the response variables,

first a graphical approach was employed. The left graph in figure 4-1 illustrates the impact number

of dips had on the %COWY. Clearly, by increasing the number of dips, the total %COWY was

increased. The variability within each individual dip was due to other parameter effects. The right

graph in figure 4-1 illustrates the effect of successive dips on %IOWY. While there is still a good deal

of variability in the %IOWY at each dip, the trend from dip to dip appears to be more linear in nature

when compared to %COWY relationship to dips.

Figure 4-1: Number of dips affect on %COWY and %IOWY for all data points.

%IOWY vs. Dip

Dip

1 2 3 4 5 6 7

0.000%

1.000%

2.000%

3.000%

4.000%

Graph Builder



speci

conc

mete

and 2

in %C

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%CO

Figure

and re

%IO

relati

To further

ic data sets

ntrations wi

rs/minute. T

.3 g/l at 11.9

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er rate. Las

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4-2: Build curv

duction potenti

Using the

Y build curv

onship for %I

explore the

re presente

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pH and 805

to 2 dips. Ad

, the spacin

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same data se

as a functio

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COWY and

. In figure 4

tely constan

ing was 12.0

V. All thre

ditional dips

between dy

higher %CO

r %COWY as a f

ts a similar r

n of number

ber of dips.

IOWY as th

2, 6.3/1 yarn

speed, pH,

pH and 789

e follow the

beyond 2 co

e bath conce

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unction of num

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of dips base

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e number of

was dyed in

nd mV. All t

mV with the

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tinued to in

ntrations wa

er concentra

ber of dips on

ist for %IO

on the sam

illustrate wit

dips increase

three differe

hree were 31

2.7 g/l at 11.

build curve

crease the %

as expected

tions resulte

.3/1 yarn coun

Y. Figure 4-

data points.

h increasing

d, a couple o

nt indigo dy

.1

8 pH and 800

ith large inc

OWY althou

with higher

in the lowe

at similar spee

illustrates t

Notice the l

number of di

147

f

bath

mV,

rease

gh at

dye

d, pH,

e

inear

ps



the %

This s

previ

exam

dips.

Figure

and re

dept

4-4 ill

point

versu

Integ

pene

IOWY linear

ame linear b

us data has

ples have be

Refer to Xin4

4-3: Build curv

duction potenti

Since the

of shade to

ustrates the

s. Even thou

s the numbe

and %IOWY

ration levels

increases.

ehavior is ex

been publish

n discussed

6 Integ vs dip

relationship fo

al.

IOWY incre

increase as

realationship

gh the %IOW

of dips is ju

nder equilib

from one di

lso the high

ibited by all

ed comparin

relating shad

s curve in se

r %IOWY as a f

sed with ea

ell. Howeve

between Int

Y builds in a l

tified when

rium sorptio

to the next.

r the dye ba

data sets fro

%IOWY and

e of the yarn

tion 1-1.

nction of num

h additional

r, the relatio

eg shade val

inear nature

onsideratio

dye conditi

It should be

th concentra

all dye ran

the effects

(K/S or Inte

er of dips on 6

dip of indigo

ship does n

e and numb

the non-lin

is given to n

ons as well a

noted the in

tion, the high

ge set-up co

f increasing

) to increasi

.3/1 yarn count

dye, one wo

t appear to

er of indigo d

ar nature of

on-linear rel

s the possibil

crease in dip

er the %IOW

ditions. Whi

dips, number

g numbers o

at similar spee

uld expect th

e linear. Fi

ips from all

Integ shade

tionship bet

ity for variab

s does not ac

148

Y.

le no

ous

f

d, pH,

e

ure

ata

ween

le

tually



149

cause the change in Integ shade. Instead, the change in Integ is caused by the increase in %IOWY

and it's distribution which is a result of the additional indigo box dip.

Figure 4-4: Integ shade value as a function of number of indigo dye box dips for all data points.

To further investigate Integ variation as it relates to number of dips, once again three

specific dye conditions were used. These specific dye conditions are graphed in figure 4-5. Clearly,

the Integ shade value builds in a non-linear fashion as the number of dips is increased. The depth of

shade also maintains the effect of indigo dye box concentration: the higher the dye concentration,

the darker the shade while lighter indigo dye bath concentrations resulted in lighter shades.

Integ vs. Dip

Dip

1 2 3 4 5 6 7

I n t e g

0

20

40

60

80

100

120

Graph Builder



Figure

potent

be no

non-li

curve

of dip

previ

dips

decre

unch

relati

with

4-5: Integ shad

ial.

Since %IO

n-linear func

near relatio

s in figure 4-

s. The pene

us relations

as increase

ase with red

nged. The d

onship betw

ach addition

e value as a fun

Y caused th

tion of numb

ship to %IO

. The other

ration level

ips, the pen

. As the nu

cing severit

ecreased ave

en Integ and

al dip due to

ction of numbe

e Integ shad

er of dips?

Y during eq

possibility w

s a function

etration leve

ber of dips

. From dip 5

rage penetr

dip as demo

additive pro

r of dips on 6.3

e and %IOW

s previously

ilibrium sor

s changes in

of all data po

l has a uniqu

as increase

through 7 t

tion level wi

strated in fig

cess of layeri

1 yarn count at

by dips was

shown in ch

tion. This c

penetration

ints is shown

and unexp

the penetra

e penetratio

th each dip,

ure 4-5. The

ng dye not b

similar speed,

linear, what

pter 3, the I

uld explain t

level as a fu

in figure 4-6

cted shape a

tion level co

n level remai

ould explain

penetration

the dip pro

pH, and reducti

caused Integ

teg shade h

he shape of

ction of num

. Unlike the

s the numbe

tinued to

ns relatively

the non-line

level decrea

ess itself.

150

on

to

s a

ber

r of

r

ed



151

Figure 4-6: Penetration level for all data points as a function of the number of dips.

When reviewing the penetration level as a function of the number of dips under the three

specific dye conditions, a similar relationship as shown in figure 4-6 exists. Figure 4-7 shows the

specific relationships. At dip #1 all three dye box concentrations have approximately the same

penetration level. After dip 2, the penetration level becomes separated by the dye box

concentration with higher concentration resulting in a lower penetration level. The decreased

penetration level signifies increased ring dyeing or decreased dye penetration into the yarn. This

effect is actually expected when consideration is given to how dye is added at each dip. The indigo

dye added at dip 4 is layered on top of the existing dye from dip 1, 2, and 3. And as additional dye is

added by more dips, the dye continues to be layered on. Thus the Integ shade value becomes

darker with each additional dip because the dye is applied in a ring dyed fashion by each dip. Notice

the greater the dye bath concentration, the lower the penetration level or more ring dyed the yarn.

Penetration level vs. Dip

Dip

1 2 3 4 5 6 7

P e n e t r a t i o n l e v e l

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Graph Builder



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153

Figure 4-8: %COWY for all data points as a function of dye bath concentration after one, three, and six dips.

As expected the %IOWY had a strong relationship to the dye bath concentration. Figure 4-9

illustrates the build curve of %IOWY as a function of dye concentration when separated by one,

three, and six dips. As shown in figure 4-3, as the number of dips increased the total amount of

%IOWY also increased. Additionally, the general trend was increased %IOWY as the dye bath

concentration was increased. However, this relationship wasn't linear over the entire range of dye

bath concentrations. The %IOWY build curve was fairly linear from low concentrations till

approximate 1.75 g/l. But increasing concentration from 1.75 g/l to 2.5 g/l does not result in

substantial change in %IOWY. Then, at 2.5 g/l continued increases in dye concentration does result

in increased %IOWY. This relationship was repeated for each number of dips although it is

accentuated by the higher number of dips. This relationship is best described as an indigo dye bath

concentration build plateau spanning 1.75 to 2.5 g/l.

%COWY vs. Average Indigo (gm/lit) by Dip

Average Indigo (gm/lit)

0.5 1 1.5 2 2.5 3 3.5 4

% C O W Y

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

14.00%Legend

1

3

6

1

3

6

Graph Builder

(g/l)

%COWY vs Average Indigo (g/l) by Dip



154

Figure 4-9: %IOWY for all data points as a function of dye bath concentration after one, three, and six dips.

Since there is a strong relationship between %IOWY and Integ shade value as well as %IOWYand dye bath concentration, Integ versus dye bath concentration at various number of dips should

have a similar shape as discussed from %IOWY versus dye bath concentration in figure 4-9. This is

confirmed in figure 4-10. The Integ shade value has a fairly linear relationship to dye bath

concentration until 1.75 g/l. At 1.75 g/l a plateau is reached where further increases in dye

concentration does not produce substantial increased depth of shade. Once the dye concentration

reaches 2.5 g/l, the Integ shade value resumes increasing in value with increased dye concentration.

While there was variation in data points on both figures 4-9 and 4-10, the plateau relationship is

graphically evident.

Measured %IOWY vs. Average Indigo (gm/lit) byDip


0.5 1 1.5 2 2.5 3 3.5 4

M e a s u r e

d % I O W Y

0.000%

0.500%

1.000%

1.500%

2.000%

2.500%

3.000%

3.500%

4.000%

4.500%Legend

1

3

6

1

3

6

Graph Builder

(g/l)

Measured %IOWY vs Average Indigo (g/l) by Dip



155

Figure 4-10: Integ shade value as a function of dye bath concentration at various numbers of dips.

To investigate penetration level as a function of dye bath concentration, figure 4-6 was

expanded to include the variation in dye bath concentration within each dip to produce figure 4-11.

In this graph, the penetration level is shown to vary by dye bath concentration after 1, 3, and 6 dips.

The mean value within each dip forms the same relationship with increasing dips as previously

discussed: increasing dips resulted in decreased penetration level. Additionally, the variation due to

dye concentration within each dip illustrates penetration level is dependent on dye concentration

and the number of dips. Notice a great deal of random variation in penetration level at any specific

dip and/or dye bath concentration indicates other parameters have an effect on penetration level.

Measured Integ vs. Average Indigo (gm/lit) by Dip


0.5 1 1.5 2 2.5 3 3.5 4

M e a s u r e d I n t e g

0

20

40

60

80

100

120Legend

1

3

6

1

3

6

Graph Builder

(g/l)

Measured Integ vs Average Indigo (g/l) by Dip



156

Figure 4-11: Penetration level for all data points as a function of dye bath concentration within each dip.

With the obvious main parameter effects accounted for, further investigation of secondary

parameters such as yarn count, speed, pH, mV, dwell length, and nip pressure become difficult to

visualize if the entire data set was incorporated in graphical form. To reduce the complexity, all of

the remaining parameter screenings and graphical analysis will be discussed after six dips of indigo.

Also, all graphs are generated with arrows that insect at 2.0 g/l dye bath concentrations and a single

figure incorporates all four response variables graphs to facilitate trend illustration and discussion.

Before reducing yarn count to a single value, the effect of yarn count on the response

variables was evaluated. To illustrate the effect of yarn count on %COWY, %IOWY, Integ, and

penetration level; figure 4-12 was constructed after six dips of indigo with various dye bath

concentrations. The overall general trend was increasing %COWY as the dye bath concentration

Penetration level vs. Average Indigo (gm/lit) by Dip


0.5 1 1.5 2 2.5 3 3.5 4


0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9Legend

1

3

6

1

3

6

Graph Builder

(g/l)

Penetration Level vs Average Indigo (g/l) by Dip



157

was increased. Furthermore, increasing the yarn count resulted in greater %COWY values at any

given dye bath concentration. The general relationship across all dye conditions is greater yarn

counts (ie finer yarns) have greater %COWY then lower yarn counts (ie courser yarns).

Given the %COWY dependence on yarn count, a similar relationship is expected for %IOWY.The second row of graphs in figure 4-12 illustrates the relationship of %IOWY as a function of dye

bath concentration after six dips for each yarn count. As expected, the general %IOWY curve had a

plateau from 1.75 g/l to 2.5 g/l within each yarn count. Furthermore, the higher yarn counts (finer

yarns) had greater %IOWY than the lower yarn counts (coarser yarns). More specifically the same

relationship for yarn count exists at every dip of indigo.

If the %COWY and %IOWY varies with different yarn counts, how does the resulting Integ

shade value vary? Well, in fact the Integ shade value doesn't vary at least not as much as one mightexpect. The third row of graphs in figure 4-12 shows the Integ values as the indigo dye bath

concentration was increased after six dips across all four yarn counts. The biggest trend was the

increased Integ as the dye bath concentration was increased within each yarn count. Although a

slight increase in Integ is exhibited as the yarn count is increased. Any significance with increasing

yarn count will need to be determined from a full ANOVA analysis.

If the %IOWY increased by yarn count and the Integ shade is relatively constant by yarn

count than the penetration level as the yarn count was increased is expected to increase. The

bottom row of graphs in figure 4-12 illustrates that very relationship for six dips as a function of dye

bath concentration. The penetration level clearly decreased as the dye bath concentration was

increased at a constant yarn count. The penetration level increased as the yarn count was increased

regardless of the dye bath concentration.



158

Figure 4-12: Illustrates %COWY, %IOWY, Integ, and penetration level varies with yarn count and dye concentration after

six dips.

Yarn Count Affect on %COWY, %IOWY, Integ, andPenetration Level

6.3 7.1 8 12

Yarn Count

Indigo gm/lit

0.5 1 1.5 2 2.5 3 3.5

% C O W Y

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

% I O W Y

0.50%

1.00%

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3.00%

3.50%

4.00%

I n t e g

30

40

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0.2

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0.5 1 1.5 2 2.5 3 3.5 0.5 1 1.5 2 2.5 3 3.5 0.5 1 1.5 2 2.5 3 3.5

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(g/l)



159

Now that yarn count effects had been investigated and to further reduce the complexity, all

of the remaining parameter screenings and graphical analysis were reduced to 6.3/1's yarn count

after six dips of indigo. All graphs will continue to be generated with arrows that insect at 2.0 g/l

dye bath concentrations and a single figure incorporates all four response variables graphs to

facilitate trend illustration and discussion.

This researcher hypothesized speed would have an impact in overall indigo dyeing process.

However, the top graphs in figure 4-13 indicates speed has very little affect on %COWY. Within each

speed range, the %COWY builds in a similar fashion as previously discussed with changes in dye bath

indigo concentration. Alas, there are no obvious curve shifts as the speed range is increased from

26.5-31 m/min to 31-34.75 m/min or to 34.75-36.6 m/min. The 2.0 g/l indigo dye bath

concentration arrow remains mostly flat as the speed was increased from the left most graph to

center graph and ending with the right most graph.

However, it is clear from graphs on second row in figure 4-13 that speed does have an

impact on %IOWY. The %IOWY build curves maintain characteristic shape as a function of indigo

dye bath concentration including the 1.75 g/l plateau. The 2.0 g/l concentration arrow shows a

decrease in %IOWY as the speed was increased. In fact, the average %IOWY shift is from ~2.25 % to

~1.5% IOWY when the speed was increased from 26.5 m/min to 36.5 m/min. Whether the

reduction is due to lower wet pick-up or less time for diffusion to occur, the trend is apparent.

The increasing speed also affected the Integ shade value. As the speed increased, the Integ

value decreased as seen by following the 2.0 g/l concentration arrow in third row of graphs of figure

4-13. At lower speed ranges the Integ value for 2.0 g/l is approximately 85. However, at the higher

speed levels the Integ value had dropped to below 70 given the same dye bath concentration.

Given speed affects on %IOWY and Integ, it is expected to have an impact on the

penetration level. The last row of graphs in figure 4-13 showed an increased speed causing an

increase in penetration level. This was due to the greater rate of drop in Integ value compared to

the drop in %IOWY as speed was increased. The Integ value was lower than expected given the

amount of indigo on weight of yarn. Therefore, the penetration level increased indicating more

penetration of the dye into the yarn structure at greater speeds.



160

Figure 4-13: Speed affect on %COWY, %IOWY, Integ, penetration level at various dye bath concentrations after six dips

of indigo on 6.3/1 yarn.

Speed Affect on %COWY, %IOWY, Integ, and Penetration Level

26.52 - 31.09 31.09 - 34.75 34.75 - 36.58

Speed

Indigo gm/lit

0.5 1 1.5 2 2.5 3 3.5

% C O W Y

2.00%3.00%

4.00%5.00%6.00%7.00%

8.00%9.00%

10.00%11.00%

12.00%

% I O W Y

0.50%

1.00%

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2.00%

2.50%

3.00%

3.50%

I n t e g

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161

Next the effect of pH was investigated. As previous research by Etters and others, pH

should play a major role in the %IOWY, Integ, and penetration level. Figure 4-14 was created based

on 6.3/1 yarn count after six dips of indigo dyeing. Four rows of graphs represent each of the

response variables. The pH range is broken down into three groups: Low with pH from 10.96 to

11.6, Middle range with pH from 11.61 to 11.86, and High with pH from 11.9 to 12.6. Across each

response variable graphs a 2.0 g/l constant dye bath concentration arrow was drawn.

Across the first row of graphs, as the pH of the dye bath was increased the %COWY actually

decreased. This relationship is a little surprising considering, with everything else constant, higher

pH should have more sodium hydroxide in the bath which should result in more sodium hydroxide

on weight of yarn and therefore higher %COWY. Perhaps other parameters or interactions are

causing this unexpected trend. Unlike pH's effect on %COWY, the %IOWY actually increased at

higher pH levels. While the increase in %IOWY was not overwhelming, the second row of graphs

gives a good indication that increased pH causes higher %IOWY. Furthermore, given the reduced

%COWY and the increased %IOWY, the fixation rate appears greater at higher pH levels.

The Integ shade value remained constant as the pH was increased as shown in third row of

graphs of figure 4-14. A constant Integ value coupled with increasing %IOWY should have a major

impact on penetration level. As expected, increasing pH caused a major shift toward increased

penetration level. The relationship is clearly illustrated in final row of graphs in figure 4-14. This

was caused by the increase in %IOWY while the Integ shade remained constant or actually become

lighter in shade. There the Integ value is not as great as one would expect given the %IOWY because

the dye is more penetrated into the yarn structure. This relationship was also supported by

research of Etters and others.



162

Figure 4-14: pH affect on %COWY, %IOWY, Integ, penetration level at various dye bath concentrations after six dips of

indigo on 6.3/1 yarn.

pH Affect on %COWY, %IOWY, Integ, and Penetration Level

10.96 - 11.6 11.6 - 11.86 11.86 - 12.588

Box pH

Indigo gm/lit

0.5 1 1.5 2 2.5 3 3.5

% C O W Y

2.00%3.00%

4.00%5.00%6.00%7.00%

8.00%9.00%

10.00%11.00%

12.00%

% I O W Y

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

3.50%

I n t e g

30

40

50

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100

P e n e

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163

The effects reduction potential had on response variables were far less pronounced

compare to any previous parameter. In fact, any effect may not be significant and must be validated

by a complete ANOVA analysis. Figure 4-15 indicates mV may have a non-linear effect on %COWY.

There are shifts to higher %COWY at the middle mV range compared to the lower and upper ranges.

The exact extent and significance of the effect can only be determined during complete ANOVA

analysis.

Increased reduction potential does appear to have a major and consistent role in the

%IOWY after six dips of indigo at various dye bath concentration levels. The line of constant dye

concentration is clearly trending lower as the reduction potential is increased as evident in second

of graphs in figure 4-15. This relationship is contradictory to traditional indigo dyeing theory since

lower mV means greater reduction potential. One would think greater reduction potential would

result in more indigo on weight of yarn not less. There are of course other potential causes for this

relationship such as effects from speed, pH, etc.

Reduction potential also has a slight non-linear effect on Integ shade values. The third row

of graphs in figure 4-15 indicates the shade becomes slightly darker as the reduction potential is

increased from low mV to mid-range mV along constant dye bath concentrations. Yet the Integ

shifts slightly lower as the reduction potential is further increased to the high mV range. Once again

the overall change in Integ values isn't great but the general trend does appear to exist.

Coupling %IOWY and Integ shade values to calculate penetration level reveals the overall

trend of decreasing penetration level as the reduction potential is increased. This trend is

demonstrated in the fourth row of figure 4-15. This is not surprising given the general trend of

increasing Integ and decreasing %IOWY as the reduction potential is increased. A darker shade with

less dye can only exist when a greater percentage of the dye is located at the outer surface, i.e.

more ring dyed.



164

Figure 4-15: Reduction potential affect on %COWY, %IOWY, Integ, and penetration level at various dye bath

concentrations after six dips of indigo on 6.3/1 yarn.

Reduction Potential Affect on %COWY, %IOWY, Integ, andPenetration Level

726 - 786 786 - 851 851 - 891

Box mV

Indigo gm/lit

0.5 1 1.5 2 2.5 3 3.5

% C O W Y

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

% I O W Y

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

3.50%

I n t e g

30

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5060

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(g/l)



165

The effect of dwell length on each response variable is displayed in figure 4-16 for the

relationship on 6.3/1 yarn after 6 dips of indigo. Increasing the dwell length from 8.6 meters to 11.4

meters causes the %COWY, %IOWY, and Integ shade values to decrease as demonstrated by arrows

of constant dye bath concentration in graphical rows 1, 2, and 3. This relationship is also

contradictory to traditional thinking. If the dwell length increased and everything else is constant,

the yarn would be exposed to the dye bath for a greater time. One would think greater time should

result in more pick-up or exchange of dye and other chemicals from the bath to the yarn. As rows 1,

2, and 3 from figure 4-16 demonstrates, this did not happen. Therefore another parameter or

interaction of parameters must be affecting the results.

The penetration level has a slight increase in value as the dwell length is increased in figure

4-16. This trend would be expected since everything else held constant greater dwell length would

result in greater time for the dye to penetrate into the yarn structure.



166

Figure 4-16: Dwell length affect on %COWY, %IOWY, Integ, and penetration level at various dye bath concentrations

after six dips of indigo on 6.3/1 yarn.

Dwell Length Affect on %COWY, %IOWY, Integ, andPenetration Level

8.63 11.37

Dwell length

Indigo gm/lit

0.5 1 1.5 2 2.5 3 3.5

% C O W Y

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

% I O W Y

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

3.50%

I n t e g

30

4050

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100

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167

Given the odd relationships uncovered while investigating dwell length, a detailed review of

dwell time is presented. Dwell time is a factor of speed and dwell length and presented in terms of

seconds. The dwell time was measured from dye liquor surface to entry nip point on the dye range.

The dwell time was summarized into three groups: 14 to 16.7 seconds, 16.7 to 19.6 seconds, and

19.6 to 25.7 seconds. Each group and corresponding response variables on 6.3/1 after 6 dips of

indigo are presented in figure 4-17.

Unfortunately, the effect of dwell time presents more surprising results. The first row of

graphs in figure 4-17 indicates %COWY decreases with increasing dwell time. This is unexpected

since typically increased dwell time allows for greater dye pick-up and therefore greater %COWY.

Likewise, the second row of graphs show %IOWY doesn't change with dwell time. This is also

surprising following the same logic as %COWY. Third row of graphs show Integ values generally

decrease with increasing dwell time. The behavior of these response variables is contradictory toconventional thinking under the influence of changing dwell time. There must be an underlying

effect from another parameter or interaction of parameters which should be revealed by a detailed

ANOVA analysis.

The last row of figure 4-17 indicates increasing penetration level with increasing dwell time.

This is expected. By increasing submerge time in the dye, the dye is expected to penetrate deeper

into the yarn structure. This causes great dye penetration or less ring dyeing as reflected in higher

penetration level values.



168

Figure 4-17: Dwell time affect on %COWY, %IOWY, Integ, and penetration level at various dye bath concentrations after

six dips of indigo on 6.3/1 yarn.

Dwell Time Affect on %COWY, %IOWY, Integ, andPenetration Level

14.03 - 16.7 16.7 - 19.6 19.6 - 25.7

Dwell time

Indigo gm/lit

0.5 1 1.5 2 2.5 3 3.5

% C O W Y

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

% I O W Y

0.50%

1.00%

1.50%

2.00%

2.50%

3.00%

3.50%

I n t e g

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(g/l)

(sec)



169

The effect of nip pressure on %COWY, %IOWY, Integ, and penetration level is examined in

figure 4-18. As the nip pressure is increased from the 40/45 psi range to the 50/75 psi range,

virtually no impact is detected on the %COWY, %IOWY, Integ, and penetration level.

Figure 4-18: Nip pressure affect on %COWY, %IOWY, Integ, and penetration level at various dye bath concentrations

after six dips of indigo on 6.3/1 yarn.

(g/l)



170

4.2 Empirical Dye Models Based on Dye Range Parameters and the Resulting Affect on Indigo Dye

Response Variables

Clearly manual calculation of the ANOVA analysis for all nine dye range set-up condition

affects and interactions on four response variables is mathematically daunting and moreimportantly unnecessary. Thanks to the advances of modern technology, the observational data

was analyzed using SAS JMP 8.0 statistical software package. As discussed in chapter 3.4, the initial

or "prime data" sets were analyzed using the statistical package on all four response variables. Once

a base line model was established, additional data points or "replicas" were added to each model.

Then the analysis was repeated to confirm statistically significant parameters remained important

and no new parameters became important. Also, the standard error after the addition of each

replica was recorded. The standard errors were tracked to determine convergence. The

observational study was concluded. The final response model generated. Following this procedure

the initial model, convergence check, and final model are presented next for dye range set-up

condition affects on %COWY, %IOWY, Integ shade, and penetration level.

4.2.1 %COWY Empirical Model Generation

Using the prime data set and SAS JMP 8.0 statistical software package the %COWY empirical

model was generated using the dye range set-up conditions as the input values. The overall

correlation of fit was determined to 0.91 with an F ratio of 374.2 as shown in table 4-1. The best

model fit was determined to involve the dye bath concentration and pH. Also, the second order

term of speed and interaction of speed and pH were also determined to be statistically significant as

indicated by the P-values. Because the second order term of speed was significant the first order

term was left in the model even though the P-value warrants removal. Also listed in table 4-1 are

the standard errors for each significant parameter.



171

Table 4-1: ANOVA analysis results from the prime data set on %COWY.

With the initial model for %COWY generated and the standard errors recorded, additional

replica data set were added one at a time. The actual parameter standard errors are listed in

appendix section A-4-2a for reference. To facilitate communication of convergence, the standard

errors for each parameter were normalized by the initial standard error from the prime data set.

Then the normalized parameter standard errors were averaged at each replica point to create a

single value. Figure 4-19 demonstrates the convergence test for the empirical model of %COWY as

each new averaged normalized standard error is added. At the 0 x-axis point the value is 1.0 since



172

this is the average normalized value to itself. All additional points are based on this starting point.

With the addition of the first three replica points the average normalized standard error

actually increased. However after 5 replica points were added to the model, the average

normalized standard error dropped below 1.0 and continued to decrease with each additional

replica set. After 11 replica data sets were added, the average normalized standard error was

approximately 0.90 or 10% less than the prime data set and remained virtually unchanged for the

balance of replica data sets. This signifies the observational study could have been concluded after

11 replica data sets based on %COWY analysis.

Figure 4-19: Convergence test for empirical %COWY model.

Now the final empirical %COWY model was generated based on all available data points.

The final R2 correlation coefficient was 0.88 with an F ratio of 380 as shown in table 4-2. For

completeness the final parameter estimates and standard errors are also shown. The final model

maintained the same statistically significant parameters as the prime data set model as

demonstrated in the effect tests. No new statistically significant terms surfaced.

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

0 5 10 15 20 25

A v e r a g e N o r m a l i z e d S t a n d a r d E r r o r

f o r a l l S i g n i f i c a n t P a r a m e t e r s


Convergence Test for Empirical %COWY Model



173

Table 4-2: ANOVA analysis for %COWY from the entire data set.



174

Using the parameter estimates from table 4-2, the final empirical model for %COWY was

created. The official equation is listed below as equation 4-1.

% =

⎣

−0.6590+ (0.03819∗ ) +ℎ()

⎣

1:0.02:0.16423:0.31264:0.42055:0.48626:0.54107:0.5830⎦

+ (2.8376 ∗

) + 0.8576 ∗ log ℎ( ) − (0.2874∗) − (6.5040 ∗ ( −33.1)) −

2.5018

∗ ( − 11.83) ∗ ( −33.1)⎦

Equation 4-1: Empirical model %COWY as a function of dye range set-up conditions.

To better illustrate the relationship between actual %COWY and the predicted value from

the empirical model the two values were plotted against each other in figure 4-20. There is

obviously a strong relationship with the predicted versus actual following a linear 1 to 1 relationship.

There are however a few points were the predicted %COWY is in the range of 4% to 6% but the

actual values are in the 8% to 12% range. However, overall the %COWY model performed well.



175

Figure 4-20: Comparison of actual versus predicted %COWY for the entire data set.

To investigate the effects of each parameter on %COWY and compare the results to

previous graphical analysis, the prediction profile was created. Figure 4-21 illustrates the calculated

%COWY as it varies by each dye range set-up condition. The graph in the first column shows an

increasing %COWY value as the yarn count is increased. This confirms the significance graphically

displayed in figure 4-12. Additionally, the influence of yarn count on %COWY has not been observed

in previously published experiments.

A c t u a l % C O W Y



176

Figure 4-21: %COWY prediction profile for dye range set-up condition affect on %COWY from the empirical model.

The graph in the second column from figure 4-21 confirms the number of dips has a non-

linear impact on the %COWY. The shape of this curve is very similar to the curve in figure 4-1 when

the %COWY versus dips was discussed. Also, the dye range speed was determined to be statistically

significant but by the second order term. As the middle column graph illustrates, as the speed is

increased the %COWY increases until a limit is reached at approximately 33 m/min. The original

graphical analysis did not detect this relationship. The graph in the fourth column identifies a strong

relationship between the dye bath indigo concentration and the %COWY. Logically, as the dye bath

concentration is increased the %COWY also increases. In the final coumn graph of figure 4-21, as

the pH of the dye bath is increased the %COWY decreases. Recall this same relationship was

detected in figure 4-14.

4.2.2 %IOWY Empirical Model Generation

The same process was repeated for the %IOWY using the prime data set as the initial

starting point for the ANOVA analysis. The R2 correlation coefficient was determined to be 0.97 with

an F ratio of 1585 as shown in table 4-3. This was determined to be the best possible model fit using

all dye range set-up conditions, second order terms, and interactions. The parameter estimates

listed in table 4-3 produce the initial standard errors for each significant parameter. Note the dye

bath pH was determined to be statistically insignificant with a P-value of 0.1449. However, this

% C O

W Y

0 . 0 8

6 3 7 1

[ 0 . 0

8 2 7 2 ,

0 . 0

9 0 1 8 ]

6 8 1 0

1 2

1 4 1 3 5 7

2 6

2 9

3 2

3 5 1 2 3

1 1

1 2

(g/l)

%COWY Prediction Profile for Dye Range Set-up Conditions



177

parameter was left in the model due to strong evidence in the graphical analysis section and

previously published material that pH should play a strong role in %IOWY.

Table 4-3: ANOVA analysis from the prime data set on %IOWY.

Next, each replica data set was introduced to the empirical model for %IOWY. After each

introduction, the new parameter standard errors were recorded. As with %COWY, the average

normalized standard error after introduction of each replica set was calculated. The convergence

trend is illustrated in figure 4-22 with the individual data posted in appendix section A-4-2b. As each



178

new replica data set is introduced, the average normalized standard error continues to decrease.

After 14 replica sets were included, the average normalized standard error remains fairly flat with

no major change in the values. After 16 replica sets the average normalized standard error is 0.85 or

15% less than the prime data set and point of diminishing returns indicated the observational study

was concluded.

Figure 4-22: Convergence test for the empirical %IOWY model.

The final empirical model for %IOWY as a function of dye range set-up conditions was

calculated based on the entire data set. During this analysis, no new single order, second order, or

interaction parameter effects were deemed statistically significant. Additionally, the effect of pH

was determined not to have become significant. The P-value of 0.3704 in table 4-4 indicates the

variation due to another parameter is just as likely as the affect of pH. For this reason, the pHparameter was removed from the model and the ANOVA analysis repeated.

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2

0 5 10 15 20 25 A v e r a g e N o r m a l i z e d S t a n d a r d E r r o r



Convergence Test for Empirical %IOWY Model



179

Table 4-4: Effects test from %IOWY ANOVA analysis for the entire data set with pH component.

After removing the pH parameter from the ANOVA analysis the R2 correlation coefficient

was determined to be 0.97 with an F ratio of 2597 from table 4-5. These two coefficients indicate

the model is a very strong fit to the data. Also listed under the parameter estimate section is the

final standard error for each parameter.



180

Table 4-5: ANOVA analysis for the %IOWY from the entire data set

Using the parameter estimates from table 4-5, the final %IOWY empirical model equation

was determined and listed as equation 4-2.



181

% = exp[−6.0772 + ℎ()

⎣

1:0.02:0.60573:1.03414:1.30315:1.5257

6:1.70627:1.8717⎦

+ 4.4823e ∗ −1.5847e ∗

+0.8713 ∗log ℎ ]

Equation 4-2: Empirical model %IOWY as a function of dye range set-up conditions.

To better illustrate the relationship between actual %IOWY and the predicted value from

the empirical model the two values were plotted against each other in figure 4-23. There is

obviously a strong relationship with the predicted versus actual following a linear 1 to 1 relationship.

Figure 4-23: Comparison of actual and predicted %IOWY from the final empirical model.

A c t u a l % I O W Y



182

A prediction profile graph was created for the empirical model %IOWY as a function of each

dye range set-up condition. As shown in figure 4-24, increasing yarn count causes the %IOWY to

increase. This relationship was observed during the graphical analysis section and hasn't been

documented by others. Just as demonstrated by other experiments (Xin46) and illustrated in the

graphical analysis section, increasing the number of dips causes the %IOWY to increase in a nearly

linear fashion. This relationship is highlighted in the second column graph of figure 4-24. The third

column graph shows increasing speed was determined to cause the %IOWY to decrease. This was

originally observed in the graphical analysis section and hasn't been documented by others. In the

final column of figure 4-24, increasing the indigo concentration in the dye bath causes the %IOWY to

increase. This relationship has been well documented in previous experiments.

Figure 4-24: Prediction profile for %IOWY and dye range set-up parameters.

M e a s u r e d

% I O W Y

0 . 0

1 9 9 3

[ 0 . 0

1 9 3 4 ,

0 . 0

2 0 5 4 ]

7 8 9 1 0 1 1 1 2 1 3 5 7 2 6 2 8 3 0 3 2 3 4 3 6 1 2 3

(g/l)

%IOWY Prediction Profile for Dye Range Set-up Conditions



183

4.2.3 Integ Empirical Model Generation

ANOVA analysis of the prime data set for dye range set-up conditions affect on Integ shade

are presented in table 4-6. The overall correlation coefficient R2 was 0.96 with an F ratio of 1049.

This was determined to be statistically significant. The initial parameter standard errors are listed inparameter estimates section of table 4-6. The P-value for each dye range set-up parameter is listed

in effect tests section. No other first or second order condition or interaction of conditions was

determined to be statistically significant.

Table 4-6: ANOVA analysis of Integ shade from the prime data set.



184

The convergence test for dye range set-up parameter affects on Integ shade value are

illustrated in figure 4-25. The individual parameter standard error for each replica set is

documented in the appendix section A-4-2c. Each additional replica set caused the average

normalized standard error to decrease. After 17 replica sets the average normalized standard error

reached the point of diminishing return at 0.816 or 18.4% less than the prime data set average

normalized standard error. As indicated by the overall trend line, additional replica sets would not

greatly reduce the standard error and the observational study was concluded.

Figure 4-25: Convergence test for empirical model Integ.

The final empirical Integ model based on dye range set-up parameters was generated. The

correlation coefficient R2 value of 0.96 and F ratio of 1610 from table 4-7 indicated the overall model

improved from the prime data set. The final parameter standard errors are displayed in the

parameter estimates section of table 4-7. During the ANOVA analysis other dye range set-up

condition first order, second order, and interaction effects were evaluated and determined to not

0.8

0.85

0.9

0.95

1

1.05

1.1

1.15

1.2




Convergence Test for Empirical Integ Model



185

become statistically significant. The final P-value for each parameter is listed in effect tests section

of table 4-7.

Table 4-7: ANOVA analysis for Integ from the entire data set.

The final Integ equation was determined based on the parameter estimates from table 4-7.

The empirical model Integ prediction equation based on dye range set-up conditions is listed in

equation 4-3.



186

Integ = exp[4.0128+ℎ()

⎣

1:0.02:0.67633:1.05114:1.27715:1.4299

6:1.53447:1.6367⎦

+ 1.0585e ∗ −8.6794e ∗

+0.7791 ∗log ℎ −0.1271∗]

Equation 4-3: Empirical model Integ as a function of dye range set-up conditions.

The comparison between actual Integ shade values and empirical model predicted are

shown in figure 4-26. Overall the model fit is fairly uniform. However, notice at the higher

predicted Integ values the relationship falls off the 1 to 1 line. Second, there is a group of data

points at 40, 80, 110, and 140 predicted Integ units completely off line with the actual values.

Figure 4-26: Comparison of actual and empirical model predicted Integ shade values.

A c t u a l I n t e g



187

The prediction profile for each dye range set-up condition effect on predicted Integ shade

value from the empirical model is shown in figure 4-27. Just as seen in the graphical analysis section

as the yarn count is increased the Integ value increased. Increasing depth of shade as a function of

yarn count has not been previously published. Just as Xin46 and Chong29 have demonstrated, as the

number of dips was increased the resulting Integ shade value also increased. As previously

discussed in the graphical section, increases in speed caused the Integ values to decrease. Again,

this hasn't been previously discussed in the literature. As the dye bath concentration was increased

the predicted Integ shade value also increased. This again is a well established relationship in

published literature and confirmed here. In the last column of figure 4-27, as the dye bath pH values

increase the Integ shade values decrease. This mirrors Etter's detailed experiments on pH sensitivity

of the resulting shade of the yarn.

Figure 4-27: Prediction profile for Integ shade values as a function of each dye range set-up conditions.

M e a s u r e d

I n t e g

8 4 . 1

9 7 9 8

[ 8 1 . 3

5 1 8 ,

8 7 . 1

4 3 7 ]

7 9 1 1 1 3 5 7

2 6

2 8

3 0

3 2

3 4

3 6 1 2 3

1 1

1 2

(g/l)

Integ Prediction Profile for Dye Range Set-up Conditions



188

4.2.4 Penetration Level Empirical Model Generation

The penetration level from the ANOVA analysis will be discussed. The empirical model from

the prime data set doesn't exhibit a strong correlation to the data as demonstrated by the R2

correlation coefficient of 0.48 but deemed significant due to F ratio of 32.6 and P-value for themodel less than 0.0001 as shown in table 4-8. Also, the parameter standard errors are shown in the

parameter estimate section. The effect tests determined the yarn count, dip, dye bath

concentration, pH, speed/pH interaction, and second order speed terms to be significant. Notice

the first order speed term has been left in the model due to interaction and second order effects.

No other dye range set-up parameter was determined to be significant.



189

Table 4-8: ANOVA analysis results from the prime data set and penetration level.

Following the previously discussed convergence test, the average normalized standard error

for each parameter and interaction was recorded after each replica data set was introduced. The

complete standard error values are recorded in appendix section A-4-2d. As shown in figure 4-28, as

each new replica set was introduced, the average normalized standard error decreased in value.

After 15 replica data sets were introduced, the average normalized standard error remains fairly



190

consistent and the point of diminishing return was determined to have been reached. The value of

the last three replica sets was 0.73 or 27% less than the prime data set average normalized standard

error. At this point the observational study was concluded.

Figure 4-28: Convergence test for empirical model penetration level.

The ANOVA analysis on all data sets for penetration level determined the speed and pH

interaction term to no longer be statistically significant as indicated by the P-value of 0.3853 in table

4-9. Therefore, this parameter interaction was removed from the final empirical model for

penetration level as a function of dye range set-up parameters and the analysis was repeated.

0.6

0.7

0.8

0.9

1

1.1

1.2


f o r a l l S i g n i f i

c a n t P a r a m e t e r s


Convergence Test for Empirical Penetration Level

Model



191

Table 4-9: Effect tests for all data points with speed and pH interaction

The final ANOVA analysis of penetration level as a function of all dye range set-up conditions

did not reveal any new first order, second order, or interaction terms. The final model correlation

coefficient was 0.51 with an F ratio of 62.5 as shown in table 4-10. While this isn't a strong

relationship it is deemed significant due to medium strength F ratio and model P-value much less

than 0.0001. The individual parameter final standard error is listed in parameter estimate section.

Note the speed first order term was determined to remain unimportant in the effect tests section

however the term was left in the model due to the significance of the second order speed term.



192

Table 4-10: Final empirical model ANOVA analysis for all data sets

The final penetration level prediction equation was determined based on the parameter

estimates from table 4-10. The empirical model prediction equation for penetration level as afunction of dye range set-up conditions is provided as equation 4-4.



193

Penetration Level = −0.4789+ℎ()

⎣

1:0.02:0.04333:0.0098

4:−0.03985:−0.0736

6:−0.10447:−0.1214⎦

+ 1.4097e ∗ −

8.6054e ∗ − 3.5665e ∗ Dye Bath +7.6393 ∗ + 9.3778 ∗ ( −

33.1)

Equation 4-4: Empirical model penetration level as a function of dye range set-up conditions.

The comparison between actual and predicted penetration level for all data points is

illustrated in figure 4-29. The poor correlation highlighted in the ANOVA analysis is graphically

apparent. However, the overall trend does follow the general 1 to 1 line. One possible reason for

this error lies in using the ANOVA analysis to calculate and model the penetration level directly. An

alternative method would be to use the calculated %IOWY and Integ shade values from the

prediction models. The Integ would be converted into %IOWY from equilibrium sorption then the

penetration level directly calculated. This may yield a better correlation and will be investigated

shortly.



194

Figure 4-29: Comparison between actual and predicted penetration level.

The dye range set-up parameter effects on the predicted penetration level will be discussed.

Figure 4-30 shows the prediction profile. As discussed and highlighted in the graphical analysis

section, increasing yarn count caused the penetration level to increase. This indicates finer yarns

are more penetrated than courser counts given everything else as a constant. This is an interesting

observation that hasn't been discussed by others. The same relationship for increasing dip is

exhibited in the empirical model for penetration level. Speed does affect the penetration level but

not in a linear fashion as discussed in the graphical analysis section. Instead, increasing the speed

from 26 m/min to 32 m/min caused the penetration level to decrease. After 32 m/min further

increases in speed have little effect on the penetration level. As discussed numerous times,

increasing the dye bath concentration caused the penetration level to decrease. In the last graph on

figure 4-30, the dye box pH has the same relationship as documented by many others in the

published experiments. Increasing the box pH caused the penetration level to increase or the yarns

become less ring dyed.

A c t u a l P e n e t r a t i o n

L e v e l



195

Figure 4-30: Prediction profile of empirical model penetration level as a function of dye range set-up parameters.

A c t u a l

P e n e t r a t i o n L e v e l

0 . 3 1 0

2 5 3

± 0 . 0 1

7 6 2 5

7 9 1 1 1 3 5 7

2 6

2 9

3 2

3 5 1 2 3

1 1

1 2

(g/l)

Penetration Level Prediction Profile for Dye Range Set-up Conditions



196

4.3 Theoretical Model for Indigo Dye Process

A theoretical dye model was constructed based on general dye theory summarized by Etters

and discussed in section 1.4.1 coupled with diffusional theory developed by Ficks. The primary

purpose for this investigation was to gain an understanding of the mechanisms that influence thegeneral trends discussed in section 4.1 and 4.2. Additionally, develop a rigorous mathematical

model of the indigo dye process that would be quantitatively extendable to all long chain rope

indigo dye ranges.

4.3.1 Derivation of Theoretical Dye Model

Following Etters's dye theory model, the approach is broken into two different components.

1. Dye movement and propagation on a macro scale into the yarn structure from the dye bath. 2.

Dye attraction and movement into the fibers on a micro scale. Both processes occur simultaneously

during the dipping process. After the yarns have been squeezed by the nip rollers, macro movement

within the yarn stops. However, dye attraction for the individual fibers may continue until all the

dye is oxidized. Using this approach, the theoretical model was broken down into three main

sections: the dip process where the yarns are actually submerged in the indigo dye bath, the nip

process where the excess dye liquor is squeezed from the yarns, and last the oxidation process

where the final fixed indigo (%IOWY) was determined.

Etters described four main paths that occur in the dip process. These are summarized

below. This dye model did incorporate these four dye paths in the dipping process. However, the

model was expanded to allow path 4 to continue beyond the nip process.

1. Diffusion of the dye in the external medium (usually water) toward the diffusional boundary layer

at the fiber surface.

2. Diffusion of dye through the diffusional boundary layer that exists at the fiber surface.

3. Adsorption of the dye onto the fiber surface.

4. Diffusion of dye into the fiber surface.

In addition to these four paths, the theoretical model compensated for wet pick-up from the

nip process, wash reduction of chemicals on weight of yarn, and the rate of oxidation. All combined

this would result in eight unknown coefficients to completing describe the indigo dyeing process:

the four previously discussed paths each with an unknown coefficient, the wet pick-up, wash



197

reduction, diffusion of oxygen through the yarn structure, and oxidation rate. The observational

study produced three known values for each yarn, dip, and dye range set-up. Specifically the three

known values were %COWY, %IOWY, and Integ shade. To overcome the deficiency in number of

known values, several assumptions were made.

First the diffusion of dye in the external medium and diffusion of dye through the boundary

layer were grouped together as one unknown coefficient called the effective yarn diffusion

coefficient, Dy. This coefficient controlled the dye bath concentration within the yarn structure that

was available to dye into the fiber. It was not the actual diffusion coefficient of indigo dye through

the dye bath. The influence of this parameter determined the effective dye bath concentration

within the yarn structure which affected the %COWY, %IOWY, and indigo distribution within the

yarn.

The diffusion coefficient for indigo dye in the water solution is not directly known.

However, a value can be assumed based on other equations and theoretical work. Ozisik59

presented a method that calculates the diffusion coefficient by use of equation 4-5.

= 7.4 ∗ ()/.

Equation 4-5: Ozisik diffusion coefficient calculation in external medium.

ε = Association factor for solvent, H20, = 2.6.

M = Molecular weight of solvent, H20, = 18.02.

T = Temperature in Kelvin = 293K.

μ = Viscosity of solvent = 1 cP (centipoise).

V = Molal volume of solute A as liquid at its normal boiling point = 165 cm3/g mol.

After performing the calculations the indigo dye diffusion coefficient in dye bath was determined to

be 6.934e-6 cm2/sec. While this value is not exact, it does provide a starting point for optimization

calculations that iteratively seek the effective yarn diffusion coefficient final value.

Second, the adsorption of dye onto the fiber surface and the diffusion of dye into the fiber

surface were grouped together to created the effective fiber diffusion coefficient, Df . The coefficient



198

controlled the total movement of dye into the fiber surface. It was not the actual fiber diffusion

coefficient. This coefficient regulated the amount of dye into the fiber which resulted in the final

%IOWY value.

Now the theoretical model had six unknown values and one more unknown value can beapproximated. The diffusion of oxygen, DOy, through air follows known classical diffusion process.

The mass percentage composition of dry air at sea level is approximately 75.5% nitrogen, 23.2%

oxygen, and 1.3% argon8. The corresponding mole fractions are 0.78 N2, 0.21 O2, and 0.0096 Ar at

one atmosphere pressure. The density of air at room temperature (20° C) and one atmosphere

pressure is 1.21 kg/m3 or g/l8. Therefore the initial concentration of oxygen in the air is 0.21 * 1.21

g/l = 0.2541 g/l. Since air is mostly composed of oxygen and nitrogen, the mixture can be modeled

as a binary system. The diffusion of oxygen through nitrogen at room temperature (20° C) and one

atmosphere pressure has been determined to be 0.219 cm2/sec60. This value was used during the

oxidation process.

In order to manipulate the remaining five unknown coefficients, calculations were expanded

to incorporate several dips of indigo across multiple yarn counts. The following relationships were

utilized to construct an iterative process to goal seek the optimum value for each unknown

coefficient.

1. The effective fiber diffusion coefficient, Df , was assumed constant regardless of yarn count and

only dependent on the specific dye range set-up and indigo dip analyzed.

2. The effective yarn diffusion coefficient, Dy, was assumed constant regardless of yarn count and

only dependent on the specific dye range set-up and indigo dip analyzed.

3. The wash reduction coefficient was constant regardless of yarn count and dips. The dip

assumption applied only to the interior dips not first or last dip since these nip pressures were

higher than the interior dips. This coefficient only depended on dye range set-up.

4. The wet pick-up coefficient was constant regardless of yarn count and dips. Constant wet pick-up

only applied to the interior dips for the same reason as wash reduction.

5. The oxidation rate was assumed constant for each yarn count and dip process. It only depended

on the dye range set-up parameters.

Using the above assumptions the following relationships were identified. The effective fiber

diffusion coefficient was governed by the final Integ shade of the yarn. By converting the Integ

shade into %IOWY from equilibrium sorption, the outside or visible surface indigo concentration was



199

determined. The concentration was fiber diffusion dependent. Therefore the goal seek algorithm

adjusted the fiber diffusion coefficient until the calculated %IOWY on the outside surface matched

the target value from the Integ conversion.

With the fiber diffusion coefficient identified the effective yarn diffusion coefficient wasregulated by the final calculated total %IOWY. The algorithm adjusted the yarn diffusion coefficient

while applying the appropriate fiber diffusion coefficient until the total calculated %IOWY matched

the target value from Pyrrolidinone extractions.

The wet pick-up coefficient controlled the final %COWY. Given the yarn diffusion

coefficient, the dye concentration distribution within the yarn was calculated. The wet pick-up

coefficient regulated the percentage of dye bath concentration that was allowed to move on to the

oxidation process. Excess dye bath concentration would either continue to diffuse into the fiber orwas oxidized by oxygen and formed the oxidized boundary layer. By calculating the oxidized

boundary layer the wet pick-up coefficient was determined by the algorithm by matching the value

to the targeted measured %COWY.

Once the fiber diffusion coefficient, yarn diffusion coefficient, and wet pick-up were

determined that matched the targeted %COWY, %IOWY, and Integ shade for each yarn count and

dip; the wash reduction value was adjusted until the wet pick-up coefficient was constant across all

interior dye baths. Then the oxidation rate was adjusted until the minimum standard deviation was

determined for fiber diffusion coefficient, yarn diffusion coefficient, and wet pick-up across all the

yarn counts. This method resulted in one fiber diffusion coefficient per dip, one yarn diffusion

coefficient per dip, one wash reduction value, one wet pick-up value, and one oxidation rate per

indigo dye range set-up across all yarn counts.

Once the individual dye theory coefficients are determined, a model for each coefficient was

constructed using the nine dye range set-up conditions. Using the dye theory coefficient equations,

the resulting %COWY, %IOWY, and Integ values would emerge from the model. Then the

penetration level was calculated based on the predicted %IOWY and Integ values. At the conclusion

the theoretical and empirical models will be compared to one another to identify agreements and

conflicts.



200

4.3.1.a The Dip Process

The dye theory model will incorporate dye bath concentration variation as it moves through

the yarn structure, effective diffusion coefficient encompassing the affinity of reduced indigo dye

molecules for the surface of cotton fibers and diffusion of indigo dye into the fiber surface, wet pick-up caused by the nip rollers, and last oxidation. Of course any discussion on diffusion will involve

Fick's first and second laws of diffusion which are presented in one dimensional form in equation 4-

6. The parameter D is referred as the diffusion coefficient and is written in terms of distance

squared per second (cm2/sec). The coefficient describes the rate at which a material diffuses

through a unit area.

= −

=

Equation 4-6: Fick's first and second law of diffusion.

When expanding Fick's laws to cylinders it is customary to neglect material transport along

the yarn length or z axis and assumes no differential material transport occurs around the

circumference of the yarn. The remaining direction is radial or along the yarn's radius. This was

considered the primary route for material transport and Fick's laws are rewritten into equation 4-7.

=

−(,)

Equation 4-7: Transient second order partial differential of mass diffusion in radial direction.

Here C is defined to represent the dye bath concentration in grams/liter, t is the time in seconds, r is

the radius in centimeters, Dy is the yarn diffusion coefficient in cm2/sec, and F(C,r) is the grams per

liter of indigo in the dye bath removed per time into the cotton fibers. This last term behaves



201

similar to heat generation term in classical heat transfer theory and is dependent on the dye bath

concentration and location within the yarn.

One of the simpler methods to solve classic transient second order partial diffusion

equations is to approximate the solution through finite difference methods. The introduction ofF(C,r) term to represent the rate of dye removal adds a twist but finite difference remains the

simplest method. First, the partial differential equation is transformed into a series of linear

algebraic equations by Crank-Nicholson's explicit finite difference method by assuming constant Dy.

The resulting expression is listed in equation 4-8.

∆ =

∗

∆ +

∆ +

∆ ∗

− 2

+

+

− 2

+ − [(,)] Equation 4-8: Crank-Nicholson explicit finite difference model for mass diffusion.

The superscript “j” was used to represent the current time while “j+1” equals next time step. The

subscript “i” represents the current node while “i-1” and “i+1” represents the previous and next

node respectively.

The dye removal term, F(C,r), was defined by the amount of dye that leaves the dye stream

and transfers to the cotton fiber per time. The amount of dye in grams leaving the dye bath at each

node is defined by the affinity of the dye molecule for cotton fiber surface. This dye will form a

boundary layer around the fibers as long as the affinity is faster than the diffusion of dye from the

surface into the fiber interior. Since the exact boundary layer thickness is unknown, the affinity of

dye for cotton fiber and subsequent diffusion from boundary layer into fiber was grouped together.

The resulting expression was the relative or effective fiber diffusion coefficient, Df .

By setting the amount of dye leaving the dye stream at each node equal to the amount of

dye transferred to the fiber, the F(C,r) term was defined. This relationship was modeled by

incorporating two different aspects. First, the maximum possible %IOWY was calculated based on



202

the equilibrium sorption experiments discussed in chapter 3.3, equation 4-11. Second, the fraction

of the maximum possible %IOWY was calculated based on Cranks2 theoretical analysis solution for

infinite dye bath conditions, equation 4-10. Incorporating these two expressions together in

equation 4-9 resulted in the final relationship of %IOWY at each node.

% = % ∗

Equation 4-9: Actual %IOWY based on maximum possible %IOWY and fractional relationship.

= 1 − ∑

≈ / ∆

/ − ∆ −

/ ∆ /

Equation 4-10: Crank's expression for the fractional relationship of dye pick-up.2

Where 's are the positive roots of ( ∗ ) = 0 and introduced Df to represent the fiber

diffusion coefficient, units of cm2/sec, into the fibers where α is the cotton fiber radius in

centimeters. The effective fiber radius of 0.0009 cm was used from Hudson56.

% = ∗()

Equation 4-11: Maximum %IOWY from equilibrium sorption experiments.

It follows that the grams of indigo removed from the dye stream were related to the %IOWY

at each node by converting the %IOWY into grams. Recognizing the %IOWY was actually grams of

indigo per gram of cotton, the grams of indigo was calculated by multiplying the %IOWY by the

number of grams of cotton at each node. Now the results from equation 4-9 was linked with the

F(C,r) term by equation 4-12. Since the fraction of maximum possible %IOWY was non-linearly

dependent on the step time, ∆t, the solution for dye stream concentration is no longer explicit in

nature. Therefore, the greatest time step that ensured stability must be deteremined.



203

(,) = ∗%

Equation 4-12: Functional relationship between indigo leaving the dye bath stream and dye diffused into the cotton

fiber.

The boundary conditions needed to solve the finite difference model consists of initial time

conditions, dye concentration conditions at the interior node, and dye conditions at the exterior

node. The initial boundary conditions at t<0 are listed in equation 4-13.

() = 0 ≤ < 0Equation 4-13: Initial dye distribution at t<0.

Obviously the dye concentration within the yarn is zero prior to the first indigo dye box. During

multiple dip applications, this assumes all indigo dye has been either extracted by the nip or fully

oxidized and therefore immobile for continued yarn or fiber diffusion.

Next the dye bath concentration at the outside node was defined by boundary condition in

equation 4-14.

() = ℎ = ≥ 0Equation 4-14: Dye bath concentration at the outside surface node.

This condition assumes dye stream concentration at the outside node is equal to dye bath

concentration and all other chemical additives as soon as yarn enters the dye bath and maintainedduring the entire dip process. Given the relatively rough yarn surface, due to irregular shape from

uneven yarn thickness and wrapper fibers, micro turbulent flow develops instead of conventional



204

laminar flow. The micro vortices produce localized mixing of the dye bath. This was assumed to

result in constant concentration of the dye bath at the outside or surface node.

Equation 4-15 exists due to symmetry about the center of the yarn where r = 0.

= 0 = 0 > 0

Equation 4-15: Boundary condition at the center of the yarn due to symmetry.

Prior to indigo dye box #1, the yarns are free of any indigo dye. Also the calculated %IOWY

distribution from a dip was used in additive nature for each subsequent dip. This will simulate the

additive nature of multiple dip indigo dyeing and expressed in equation 4-16.

% = ( ℎ) ℎ

Equation 4-16 Functional relationship of %IOWY at the surface related to Integ shade.

To determine the distribution of indigo dye within the yarn, the amount of indigo on the

surface was assumed to equal the corresponding amount of dye from uniformly dyed yarns. The

relationship developed in chapter 3.3 for Integ shade value will be utilized. Given the Integ shade

value, the corresponding %IOWY on the surface of the yarn was calculated by relationship in

equation 4-16 and utilizing expression in equation 4-17.

% = −2.6465 + 9.5386 ∗ + 1.3593 ∗ ( − 55.2088) +3.9090 ∗ ( − 55.2088) +2.4244 ∗ ( − 55.2088) +6.4303 ∗( − 55.2088)

% = % ∗

Equation 4-17: Relationship of surface %IOWY by Integ shade.



205

A finite difference nodal mesh was then constructed starting at the center of the yarn

(node=0) and progressing toward the exterior surface of the yarn (node=M) as shown in figure 4-31.

By applying the appropriate finite difference equations and/or boundary conditions, M numbers of

linear algebraic equations were developed. The experimenter has assumed uniform dye bath

conditions exist surrounding the individual fibers in each node during the time step under

consideration.

Each nodal equation was rearranged with all dye concentrations at time step j+1 on the left

hand side and j time steps on the right hand side and making substitutions for beta and lambda.

This resulted in the following equations for the center (equation 4-18), interior (equation 4-19), and

exterior (equation 4-20) nodes.

Node = 0, center where = and = :

0 1 2 m-1 m m+1 M-1 M

r

∆r∆r

∆r/2

nodes

C0

C1

C2

Cm

CM

Figure 4-31: Nodal mesh arrangement and nomenclature for finite difference method implementation.



206

( − − − ) +

(1 + 2 ) = (− − + − ) +

(1 − 2 ) − ( , )

(1 + 2 ) =

(1 − 2 ) − ( , )

Equation 4-18: Nodal equation for the center node.

(− −) +

( 1 + 2 ) + ( − ) =

( + ) + ( 1 − 2 ) +

(− + ) −(

, )

Equation 4-19: Nodal equation for the interior nodes.

Node = M - 1 where and = dye bath concentration:

(1 + 2 ) +

( − ) = (1 − 2 ) +

(− + ) + 2 ∗ ( + )− ( , )

Equation 4-20: Nodal equation for the exterior node.

All three nodal equations utilized a simplified expression for lambda and beta as detailed in equation

4-21.

= ∆∆ , β = ∆

∆

Equation 4-21: Expression for lambda and beta coefficients in the nodal equations.

Here the Dy coefficient is assumed to be a constant value, cm2/sec. Re-arranging and grouping the

following M simultaneous equations were written in matrix form, equation 4-22.



207

⎣

1 + 2 −2 0 0 … − 1 + 2 − − 0 …

0 … … … 0… 0 − 1 + 2 − − … 0 0 − 1 + 2 ⎦

⎣

⎢

…

⎦

⎥=

⎣

1 − 2 2 0 0 …− + 1 − 2 + 0 …

0 … … … 0… 0 − + 1 − 2 + … 0 0 − + 1 − 2⎦ ⎣

…

⎦

+

⎣

−( , )−(

, )…

−( , )

−( , ) + 2 ∗ ( + )⎦

Equation 4-22: Matrix example of all nodal equations in finite difference model.

To utilize the lambda and beta equations from equation 4-21, the effective yarn radius was

determined from Mogahzy's relationship for yarn count (English cotton count)57. Equation 4-22 was

the equation to calculate the effective yarn radius at a given open end spun yarn count. With the

effective yarn radius, the ∆r value was calculated by dividing the radius by the number of nodes

minus one.

() = ..

√

Equation 4-23: Mogahzy's relationship for open end yarn radius as a function of yarn count.57

Additionally the yarn porosity value was determined. This property was defined to be the

area of the fiber in a nodal shell per total area of yarn at that nodal shell. Nabovati58 reported

typical yarn porosity values in the range of 0.69 to 0.95. Given the 100% cotton yarns are dyed in a

zero tension state, the porosity value of 0.65 was assumed for all calculations since this was the

absolute low end of published values.

Solution for the future dye concentration within the yarn from the algebraic equations in 4-

22 was conducted by Guess-Jordan elimination method executed in purpose written software



208

program. The concentration gradient is in units of grams per liter and was governed by the diffusion

of dye through the yarn through coefficient Dy.

4.3.1.b The Nip Process

Before defining the parameters and equations in the oxidation process two more

parameters must be defined. The wash reduction is defined as the percent of unfixed oxidized dye

and other chemicals removed from the fiber surface resulting from previous dip of indigo. These

remaining chemicals were called the Oxidized Boundary Layer or OBL. It was calculated as shown in

equation 4-24 by subtracting the fixed indigo on weight of yarn from the unfixed chemicals after the

previous dip, converting the percent chemical on weight of yarn into grams of chemical, and

multiplying by the wash reduction coefficient. The wash reduction value will be zero during the first

dip of indigo since no previous dye exists.

() = ℎ ∗ (% − %) ∗ ()

Equation 4-24: Calculation of oxidized boundary layer as a function of wash reduction coefficient, and %COWY and

%IOWY from the previous dip.

Next, the wet pick-up caused by the squeeze of nip rolls after the dip process wasinvestigated. Wet pick-up is defined to cause a fraction of excess reduced dye bath liquor between

the fibers to be extracted. The excess reduced dye was called the Reduced Boundary Layer or RBL

and two forms must be tracked. The concentration of the RBL so future %IOWY calculations could

be determined and the number of grams of reduced dye for oxidation tracking. The concentration

of the RBL is simply the concentration of the dye bath at each node after the nip process, since

squeezing the yarns and reducing the quantity of excess dye doesn't change the concentration. This

is summarized in equation 4-25. Second, the quantity of reduced dye must be tracked. Here the

grams were calculated by multiplying the dye bath concentration by the available liter space

between the fibers at each node and then multiplying by the wet pick-up coefficient.



209

= ℎ(

)

() = ℎ ∗

∗

Equation 4-25: Determining the reduced boundary layer concentration and quantity after the nip process.

4.3.1.c The Oxidation Process

The movement and concentration of oxygen in the yarn structure was modeled exactly the

same as the dye bath liquor. The same nodal mesh was utilized. The difference was oxygen

concentration was determined at each time step instead of dye bath concentration. This was

expressed in grams of oxygen (O2) per liter. The equations and boundary conditions are listed in

equations 4-26 to 4-28.

∆ =

∗

∆ +

∆ + ∆ ∗

− 2 +

+ − 2

+

− [(,)] Equation 4-26: Explicit finite difference equation for oxygen distribution in the nodal mesh.

Here DOy was the oxygen diffusion coefficient.

(, ) = ∗

Equation 4-27: Rate of oxygen removal from the air stream.

Here Xi was defined to be the fraction of oxygen removed from the air stream.



210

= (%∗( ))

∗∗

∗∆

Equation 4-28: Fraction of oxygen removed from the air stream as a function of total reduced dye present.

The initial oxygen concentration is assumed zero at the start of the oxidation process. The

outside node oxygen concentration was set equal to the air concentration and maintained during

the entire oxidation process. Also like the dye bath concentration, oxygen concentration was

symmetrical about the center or core of the yarn.

() = 0 ≤ < 0() = = ≥ 0 = 0 = 0 > 0

Equation 4-29: Boundary conditions for solving finite difference equations.

The oxidation rate, OR, is an unknown coefficient defined to be the grams of reduced indigo

per gram of oxygen per second consumed during the oxidation process and has units of 1/sec. The

values of Xi can range from zero to one. A value greater than one means either the oxidation rate,

grams of reduced indigo, and/or time step were high compared to the grams of available oxygen. In

this situation all of the available oxygen was consumed by the reduced indigo but more wasn't

consumed than available. This assumption now makes the total finite difference model implicit

instead of full explicit since the Xi value was dependent on the ∆t value. Therefore, many more time

steps were used in the calculations to produce a stable solution.

After each oxidation rate time step the grams of oxygen and impact on reduced indigo are

tracked. First the grams of oxygen removed from the air stream were calculated based on reduced

boundary layer and the %IOWY that required oxidizing. Then the total change in grams per liter of



211

oxygen was calculated so the next time step calculation would impact air stream concentration

within the yarn structure. Next the quantity of reduced boundary layer components RBLgm (grams)

and RBL (g/l) were reduced by indigo diffused into the cotton fiber and the dye in the boundary

layer oxidized by oxygen. The diffusion of dye into the fiber utilized the same equations as

previously discussed during the dip process. This property allowed fiber diffusion which impacts

Integ shade and total %IOWY to continue beyond the dip process. The oxidized boundary layer was

increased by the addition of oxidized dye from the reduced boundary layer. Of course oxidation at

each node was complete after RBLgm equals zero and all dye in the %IOWY was oxidized. Equation

4-30 summarizes the expressions used to track the converting of reduce dye into oxidized state.

∆ = −% ∗ − ∗

∗ ∗ ∆

∆ = ∆

∆ = ∗ ∗

∗ ∆

% = % ∗

Equation 4-30: Equations used to track the convergence of reduced indigo dye into oxidized state.

Last the %COWY calculation must be defined. This value represents the unfixed indigo and

residual sodium hydroxide and sodium sulfate from the dyeing process that has not been washed off

the fiber surface. The measured value of this parameter will depend on three main constitutes.

1. The indigo dye, sodium hydroxide, and sodium dithionite concentration in the dye bath.

2. The net pick-up of chemicals during the dip and nip process.

3. The fixation rate of the dye.

The indigo dye concentration is a measured value based on empirical correlations discussed

during the %T measurements. On the other hand, the total alkalinity measurement doesn't directly

relate to just the sodium hydroxide concentration. Likewise, the mV reduction potential doesn't



212

directly measure only sodium dithionite concentration. As a result, only one component of item #1

is a direct measurement of concentration in the dye bath. Additionally, the actual wet pick-up of

chemicals during the dip and nip process was an unknown property which was approximated by the

wet pick-up coefficient. The fixation rate of indigo dye was unknown and the main property under

investigation. Due to these shortcomings an approximation was developed. The amount of residual

chemicals on weight of yarn will be a direct function of the amount of indigo on weight of yarn. This

functional relationship was developed by analyzing the indigo reduction/oxidation process.

The oxidation of reduced indigo, IR, produces the following chemical reactions.

+ + 0 + 2 + 2

2 + 2

Equation 4-31: Chemical reactions and intermediaries during the oxidation process.

From equation 4-31, for every mole of reduced indigo that is oxidized, 2 moles of sodium hydroxide

and 2 moles of sodium sulfate or Glauber salt were produced. By converting the mole fractions by

the molecular weight a relationship of grams of each chemical per gram of indigo was generated a

shown in equation 4-32.

∗ = 2 ∗ .

. = .

∗ = 2 ∗ .

. = .

Equation 4-32: Relationship for the grams of auxiliary chemicals per gram of indigo present.

Adding these two together and 1.0 for the grams of indigo itself resulted in a value of 2.3884 grams

of total chemicals per gram of indigo. The total %COWY at each node was calculated based on the



213

total indigo on weight of yarn from yarn diffusion, fiber diffusion, and wet pick-up reduction effect

during the nip process plus residual oxidized indigo dye in the oxidized boundary layer . This

expression is summarized in equation 4-33.

% = 2.3884∗[(% ∗ )+ + ]

Equation 4-33: Calculation for the %COWY based on total indigo amounts.

Equation 4-33 assumes the only residual chemicals on weight of yarn were derived from the

oxidation of reduced indigo and no other residual chemicals exist. This obviously isn't the situation

under real world dyeing conditions where excess sodium hydroxide and sodium dithionite are feed

to the dye range. However, it was directly related to the amount of indigo on weight of yarn and

varies linearly with indigo amount. Due to this assumption calculated values for the wet pick-up and

wash reduction will not be absolute numbers. Instead, the wet pick-up and/or wash reduction

coefficient may scale greater or less than reality to make the calculated %COWY match the

measured value. How these scale will depend on the actual concentration of sodium hydroxide and

sodium sulfate in the dye bath. Since the amount of these components is usually related to the

indigo concentration, it is expected wet pick-up and wash reduction coefficients will depend on

indigo dye bath concentration.



214

4.3.1.d Optimization of Wet Pick-up and Wash Reduction

Once the fiber diffusion, yarn diffusion, and wet pick-up coefficients were determined for

the individual yarn counts after each dip, nip, and oxidation process; the slope of the wet pick-up as

it changed across each dip of indigo was calculated. The wash reduction value, which was constant

across all dips, was adjusted until the slope of wet pick-up equaled zero. This resulted in a constant

wash reduction and wet pick-up coefficient value for each yarn count across the interior indigo dye

boxes.

4.3.1.e Optimization of Oxidation Rate

The oxidation rate was determined for all yarn counts at each indigo dye box and individual

dye range set-up. This was carried out by following the original dye coefficient assumptions.

Specifically, constant fiber diffusion, yarn diffusion, and wet pick-up regardless of yarn count. The

standard deviation for the fiber diffusion, yarn diffusion, and wet pick-up was calculated for a

specific indigo dip across the yarn counts. The goal was to determine the oxidation rate that

minimized the standard deviation for these coefficients. To facilitate the optimization the variation

in standard deviation as the oxidation rate changes was incorporated.

To establish an algorithm to goal seek the optimum oxidation rate, the behavior of oxidation

was investigated. All of the following calculations and relationships pertain to a 36.5 m/min, 2.5 g/l

dye bath concentration, 11.7 pH, 800 mV reduction potential, and 8.6 meter dwell length dye range

set-up and one indigo dip but the same relationships exists under all set-up conditions. The

optimum fiber diffusion coefficient was calculated for each yarn count at a given oxidation rate. The

results are illustrated in figure 4-32. At extremely fast oxidation rates the variation in fiber diffusion

coefficient across the yarn counts was great. As the oxidation rate decreased, the variation in fiber

diffusion decreased. Also note the overall fiber diffusion coefficient value decreased. At low

oxidation rates the fiber diffusion coefficients became approximately equal and independent of yarn

count. There are two properties of oxidation rate worth noting. At extremely high oxidation rates

the reduced indigo on the yarn after the nip process was flash oxidized. This means the indigo was

instantaneously oxidized. While at extremely low oxidation rates, the indigo was never oxidized in

the time allotted. Recall oxidation time was determined by oxidation thread-up length and dye



range

oxida

Figure

figur

decre

acros

was a

to de

speed. Bot

tion rate occ

4-32: Fiber diff

The same

4-33. Her

ased. As the

s the yarn co

t a maximu

rease and t

of these cas

rred betwe

sion coefficien

graph was cr

the yarn dif

oxidation ra

unts became

. Further re

e magnitude

es do not act

n 1.0 e-3 an

s for each yarn

eated for yar

usion coeffic

e was decre

greater. At

uctions in o

of the yarn

ually exist in

1.0 oxidatio

count as the o

n diffusion c

ients have a

sed from hi

.0 e-2 oxida

idation rate

iffusion coe

real world.

n rate units.

idation rate ch

efficients as

different beh

h values, th

ion rate unit

caused the v

ficient shifte

or this exam

anges.

a function o

avior as the

variation in

s the variatio

ariation bet

d lower.

ple the real

oxidation ra

xidation rat

yarn diffusio

n in yarn diff

een yarn co

215

te in

was

n

usion

nts



Figure

inves

varia

value

up at

Again

4-33: Yarn diffu

The variat

igated. As il

ion between

of wet pick-

low oxidatio

this pheno

sion coefficient

ion in calcula

lustrated in fi

yarn counts

p shifts high

rates were

enon doesn'

s for each yarn

ted wet pick-

gure 4-34, a

increased. A

er regardless

caused by la

t occur in th

count as a func

up values as

the oxidatio

t approximat

of yarn coun

k of indigo o

real world.

tion of oxidatio

a function of

n rate was d

ely 1.0 e-2 o

t. The shifts

xidation duri

n rate.

oxidation ra

creased fro

idation rate

in yarn diffu

ng the allott

e was

high values

units the me

ion and wet

d oxidation t

216

the

an

pick-

ime.



Figure

error

devia

Next,

coeffi

meas

been

relati

comb

comb

optim

the c

resul

4-34: Wet pick-

By incorp

in fiber diffu

tion for fiber

these stand

cient. Then,

urement rela

determined.

onship are di

ined normali

ined normali

um oxidatio

mbined nor

ing in consta

up variation wi

rating these

ion, yarn dif

diffusion, ya

rd deviation

the normaliz

tionship. W

The normali

splayed in fig

zed standard

zed standard

rate was 0.

alized stan

nt combined

hin yarn count

properties to

usion, and

n diffusion,

were norm

ed standard

en this valu

zed standard

ure 4-35. St

deviations

deviations b

64 oxidatio

ard deviatio

normalized

as a function

gether the o

et pick-up w

nd wet pick

lized by the

eviations w

reached a

deviations f

rting with a

ere high. As

egan to decr

rate units.

n to increase

tandard devi

f oxidation rat

ptimum oxid

as determine

up at each o

average stan

re combine

inimum the

r each dye c

extremely l

the oxidatio

ease. In this

urther incre

slightly in va

ations due t

.

ation rate th

d. First, the

xidation rate

dard deviatio

to produce

optimum oxi

oefficient an

w oxidation

n rate was in

particular ex

ases in oxida

lue with furt

instantaneo

t minimizes

standard

was calculat

n for each

a single error

dation rate h

the combin

rate the

reased the

mple, the

ion rate cau

er increases

usly fast indi

217

the

d.

ad

ed

ed

go



oxida

end o

stand

Figure

4.3.2

bath

coun

calcul

rate.

value

comb

tion. Due to

f the spectru

ard deviatio

4-35: Standard

Algorithm to

The opera

oncentratio

and dip. Fir

ated based o

Then the wa

s across all d

ined normali

the nature o

m with incre

was reache

deviations as a

Calculate th

tor would in

, etc and th

st the fiber di

n the yarn c

sh reduction

e dips and y

zed standard

the oxidatio

sing oxidati

.

function of oxi

Dye Coeffic

ut the specif

final target

ffusion coeff

unt and ass

coefficient a

arn counts.

deviation oc

n profile all

n rate until

ation rate.

ients

ic dye range

alues for %

icient, yarn d

med initial

d wet pick-

hen the oxid

curred at ea

xidation rat

he minimum

set-up condi

OWY, %IOW

iffusion coef

ash reductio

p were opti

ation rate w

h dip. After

optimizatio

combined n

ions such as

Y, and Integ

icient, and

n, wet pick-u

ized to mai

s adjusted u

all calculatio

began at th

ormalized

speed, indig

hade by yar

et pick-up w

p, and oxida

tain constan

ntil the mini

s and

218

e low

dye

as

ion

t

um



219

convergence were satisfied, the program would output the average fiber diffusion coefficient,

average yarn diffusion coefficient, and average oxidation rate by indigo dip and the overall wash

reduction and wet pick-up coefficient values. The actual c++ computer program is provided in

appendix section A-4-3a.

4.3.3 Spatial and Time Step Optimization

Before the program can be used to determine the indigo dyeing coefficient from the

experimental data, the stability of the program was ensured. With the introduction of time

dependent components in the dye bath and air stream calculation, the model was no longer explicit

in nature. Additionally, the nodal spacing would influence the dye coefficient values. An iterative

process was utilized to determine the optimum nodal mesh size and time step to ensure stability of

the dye and air stream and convergence for the dye coefficients. The initial value was 5 nodes and 1second time step. These two values were increased until both stability and convergence was

guarantee across both the lowest and highest yarn counts and several dye range set-up conditions.

The final optimum values were 21 nodes and 0.01 second time step.

4.3.4 Determination of Indigo Dyeing Coefficient Models

After the computer program was utilized to calculate the optimum fiber diffusion

coefficient, yarn diffusion coefficient, wash reduction, wet pick-up, and oxidation rate for each yarn

count processed through each dye range set-up; each dye coefficient was profiled to determine

relationship to the dye range set-up values. Since convergence of the observational study was

already established during the empirical model phase, all available data from the two separate

indigo dye ranges were utilized in the analysis. When evaluating each dye coefficient all first and

second order dye range step-up parameters and the respective interactions were considered. The

following models for fiber diffusion coefficient, yarn diffusion coefficient, wash reduction, wet pick-

up, and oxidation rate were based on only the dye range set-up parameters that were statistically

significant.



220

4.3.4.a Functional Relationship of Effective Fiber Diffusion Coefficient

A statistical analysis of all dye range set-up parameters and the effect on effective fiber

diffusion coefficient was conducted to develop the functional relationship. It was determined the

dye bath concentration and pH at each dip was statistically significant. This was not surprising andin fact desirable. Likewise, no significant effect was contributed by dye range speed, dwell time,

dwell length, or yarn count. As shown in table 4-11, the adjusted R2 value was 0.68 for the

relationship between individual fiber diffusion coefficients and the calculated values from the

model. While this is not a perfect fit the F ratio of 100.5 and P value much less than 0.0001 does

support a statistically significant correlation. The influence and significance of dye bath

concentration and pH at each dip was re-enforced by evaluating the parameter estimates and effect

tests of each. Table 4-11 shows the P value for the dip number, dye bath concentration and pH was

much less than 0.0001.



221

Table 4-11: ANOVA analysis results for fiber diffusion coefficient.

Graphically, the relationship between calculated fiber diffusion and the individual points is

shown in figure 4-36. The wide variation at higher values contributed to the relatively poor

correlation. However, a large cluster of relatively similar values existed at lower values. This

grouping caused the correlation to improve.



222

Figure 4-36: Comparison of model predicted and actual fiber diffusion coefficient.

The statistical analysis also produced the working equation for fiber diffusion coefficient.

Equation 4-34 allows the fiber diffusion coefficient to be calculated based on the dye bath

concentration, pH, and specific dip.

= exp (−27.3480+ℎ()

⎣

1:0.02:−0.39033:0.2868

4:0.057835:0.91806:1.08807:0.9494 ⎦

+ 0.77664 ∗ ℎ + 0.40316 ∗ )

Equation 4-34: Dye Theory model effective fiber diffusion equation.

The prediction profile was produced and presented in figure 4-37. In the predication profile

the calculated value of fiber diffusion is shown as each dye range parameter varies with the 95%

confidence intervals shown in dotted blue lines. The general trend was increasing fiber diffusion as

A c t u a l F i b e r D i f f u s i o n



223

the dye bath pH was increased. This relationship supports the concept of increased dye affinity at

higher pH values. The effect of increased dye bath concentration was not completely unexpected as

many substances diffusion rate is concentration dependent. Under these conditions, faster diffusion

occurred at higher dye bath concentrations.

The fiber diffusion coefficient was effectively constant for dip one and two. Clearly, as the

yarns process through increasing numbers of dye dips, the fiber diffusion coefficient increased.

After dip two, the effective fiber diffusion coefficient increased from greater affinity of dye for the

fiber surface or actual diffusion into the fiber interior. This effect was also seen in the general trend

analysis and the empirical model discussion sections. This effect results in the yarn not only getting

darker due to more indigo on the outside surface with increasing dips but in fact gets darker than

simply multiplying the first dip times 2, 3, or say 6. Etters has already discussed increasing fiber

diffusion as the number of dips increased could be related to ionic charging of the cotton fiber by

excess sodium hydroxide thus increasing the affinity. The ionization after each dip causes the dye to

be more attracted to the fiber in the subsequent dip.

Figure 4-37: Effective fiber diffusion functional relationship to dye range set-up conditions.

P r e d i c t e d F i b e r D i f f u

s i o n

2 . 2

0 9 e - 9

[ 1 . 8

9 e - 9 ,

2 . 5

8 e - 9

]

1 2 3 4 5 6 7 1 2 3 1 1

1 2

(g/l)

Effective Fiber Diffusion Coefficient Prediction Profile for Dye Range Set-up



224

4.3.4.b Functional Relationship of Yarn Diffusion Coefficient

The yarn diffusion coefficient was evaluated against all dye range set-up values. The dye

bath concentration, pH, and dwell time at each dip was determined to have the greatest statistical

effect. Once again this was not surprising. Concentration and pH effect on diffusional coefficientswas expected. As shown in table 4-12 the adjusted R2 value was 0.72 for the relationship between

individual yarn diffusion coefficients and the calculated values from the model. While this was not a

perfect fit the F ratio of 106.6 does support a statistically significant correlation. The influence and

significance of dye bath concentration, pH, and dwell time at each dip was re-enforced by evaluating

the parameter estimates and effect tests of each. Table 4-12 shows the P value for the dip number,

dye bath concentration, pH, and dwell time was much less than 0.0001. A strong correlation

coefficient, reasonable F ratio for the model, and extremely low P values indicated the model was

more likely to cause the variation in yarn diffusion coefficient values than happenstance.



225

Table 4-12: ANOVA analysis results for yarn diffusion coefficient.

Using the parameter estimates from table 4-12, the functional relationship between yarn

diffusion coefficient and dye range set-up parameters was determined. The specific mathematical

equation is given as equation 4-35 and the distribution of actual versus calculated yarn diffusion

coefficients is shown in figure 4-39. Like the fiber diffusion coefficient distribution, the separation

between the model and actual values becomes greater at higher values. Similarly, the large cluster

of values at lower actual yarn diffusion coefficients influenced the overall model correlation.



226

Figure 4-38: Comparison of model predicted and actual yarn diffusion coefficient.

= exp (−17.3700+ℎ()

⎣

1:0.02:−0.05163:−0.45494:−1.0327

5:−1.39276:−1.48307:−1.4538⎦

− 0.5033 ∗ ℎ + 0.5889 ∗ −

0.07367∗ )

Equation 4-35: Dye theory model prediction equation of effective yarn diffusion coefficient.

The prediction profile was created and presented in figure 4-39. As the number of dips

increased the yarn diffusion coefficient decreased. This could be due to increasing amounts of

residual chemicals (oxidized dye, sodium hydroxide, and/or gluber salt) from the previous dip

impeding the path of the dye bath stream. Strangely, as the dye bath concentration increased the

yarn diffusion decreased. This is opposite the traditional behavior for concentration dependent

diffusion. However, taken in context with residual chemicals impeding the path, this relationship

0

0.000001

0.000002

0.000003

0.000004

0.000005

0.000006

0.000007

0.000008

0.000009

0.00001

0.000011

A c t u a l Y a r n D i f f u s i o n

0 0.000001 0.000003 0.000005 0.000007 0.000009 0.000011

Predicted Yarn Diffusion Coefficient

Comparison of Actual Yarn Diffusion by Dye Theory Model



227

becomes understandable. As the dye bath concentration increases, the amount of residual

chemicals from the previous dip increases. Thus the dye stream path was further hindered resulting

in a slower diffusion process at greater numbers of dip.

Figure 4-39: Effective yarn diffusion functional relationship to dye range set-up conditions.

The effect of pH on yarn diffusion coefficient is also shown in figure 4-39. As the pH was

increased the diffusion coefficient also increased. A higher diffusion value means a greater dye bath

concentration was penetrating into the structure of the yarn. This resulted in more dye being

available for fiber transfer in the yarn interior. This coupled with a higher fiber diffusion coefficient

at higher pH values as demonstrated in section 4.3.4.a produced a more penetrated (or less ring

dyed) yarn cross section. This supports the concept of ring dyed yarns as a function of pH previously

discussed by numerous authors and summarized in chapter 1.

The effect of dwell time on yarn diffusion coefficient must be discussed. As the dwell time

was increased, the yarn diffusion coefficient actually decreased. At first glance this seemed counter-

intuitive. However, one must realize to increase the dwell time on a fixed dwell length dye range,

the speed must be reduced. As the speed was reduced the turbulent forces acting to push the dye

P r e d i c t e d Y a r n D i f f u s i o n

3 . 1

7 2 e - 6

[ 2 . 8

5 e - 6 ,

3 . 5

3 e - 6 ]

1 3 5 7 1 2 3 1 1

1 2

1 4

1 6

1 8

2 0

2 2

(g/l)

Effective Yarn Diffusion Coefficient Prediction Profile for Dye Range Set-up Conditions



228

bath into the yarn structure were reduced. Whether this was an actual phenomenon or the result of

assuming constant dye bath concentration at the outside node surface, it was reasonable for this

effect to be present.

4.3.4.c Functional Relationship of Wet Pick-up

In contrast to the fiber and yarn diffusion coefficient analysis, the wet pick-up relationship

to individual dye range set-up parameters was not very strong. This was primarily due to the fact

that wet pick-up was dye range specific and highly dependent on chemical exchange. The calculated

wet pick-up numbers were indirectly measurements of the individual dye range under certain

dyeing conditions. Also, it was influenced by the diffusion of dye into the yarn and fiber structure

since this was a wet on wet application. Technically speaking the pick-up would be 0% if the yarns

were squeezed at the same pressure by the entrance and exit nip running through water only dyebath. Any pick-up on the yarn in actual dyeing process was the result of dye and other chemicals

replacing the water in the yarn. With this in mind, the nip pressure, dye bath concentration, and

yarn diffusion coefficient were expected to have the greatest impact on wet pick-up. After detailed

statistical analysis these dye range set-up parameters were the only significant influences. The best

possible model resulted in an R2 correlation coefficient of 0.26 and F ratio of 43.0 as shown in table

4-13. While this certainly wasn't a great model fit to the data, the significance of dye bath

concentration and yarn diffusion coefficients were deemed statistically significant due to P values

much less than 0.0001 and 0.0061 for nip pressure as shown in the effect test section of table 4-13.

The lack of correlation was certainly due the error or variation surrounding each wet pick-up value.



229

Table 4-13: ANOVA analysis for wet pick-up coefficient.

The poor correlation was further demonstrated by plotting the actual versus calculated wet

pick-up values as shown in figure 4-40. While a general trend following the 1 to 1 center line was

apparent, much variation occurred off line. The overall average wet pick-up was 4.1% and no

significant difference was determined between the two dye ranges in the investigation. Using the

parameter estimates from table 4-13, the analysis produced the following mathematical expression

for the wet pick-up coefficient as a function of dye range set-up parameters, equation 4-36. This

researcher proposed the unexplained variation in wet pick-up could be due to errors in the yarn dye

measurement properties such as %COWY. These errors would certainly influence the wet pick-up

values as well as other coefficients. Hopefully, the error in calculated coefficients would later off set

each other and the final model would still produce reliable %COWY, %IOWY, and Integ values

compared to measured performance.



230

Figure 4-40: Comparison of model predicted and actual wet pick-up coefficient.

− = 7.9595 − 1.5981 ∗ −1.1134 ∗ ℎ −

3960.69∗

Equation 4-36: Dye theory model prediction equation of wet pick-up.

Figure 4-41 demonstrates the predicted wet pick-up as a function of dye range set-up

parameters. As the nip pressure was increased the resulting wet pick-up decreased. This is typical

of most textile processes involving squeeze rolls. As the dye bath concentration or yarn diffusion

coefficient increased, the wet pick-up decreased. As discussed during the definition of %COWY

calculation, wet pick-up was expected to vary as the dye bath concentration varied. One would

expect the resulting %COWY to increase if exposed to greater concentration or if the diffusion of

chemicals into the yarn structure increased. However, the wet pick-up decreased in order to

maintain the correct %COWY value as the dye concentration increased. In any case, the relationship

of dye bath concentration and yarn diffusion coefficient was determined to be significant.

A c t u a l

W e t P i c k - u p



231

Figure 4-41: Dye theory model wet pick-up functional relationship to dye range set-up conditions.

4.3.4.d Functional Relationship of Wash Reduction

The wash reduction or amount of chemical on weight of yarn from a previous dip removed

during a subsequent dip was determined to be related to the dye bath concentration, speed, dwell

time, and dye bath reduction potential. The correlation between actual and calculated was 0.45

with an F ratio of 60.0 as displayed in table 4-14. While the correlation wasn't great it was deemed

significant due to a P value much less than 0.0001. The overall average wash reduction value was

13.1%. Evaluation of the individual parameter effects is shown in table 4-14. Speed had a P value of

0.0015 while all other parameters were much less than 0.0001. This indicated all were statistically

significant.

W e t p i c k - u p

0 . 0

3 1 4 9 2

± 0 . 0

0 2 6 8

5

4 0

5 0

6 0

7 0 1 2 3 0

0 . 0

0 0 0 0 1

0 . 0

0 0 0 0 2

0 . 0

0 0 0 0 3

0 . 0

0 0 0 0 4

0 . 0

0 0 0 0 5

0 . 0

0 0 0 0 6

0 . 0

0 0 0 0 7

0 . 0

0 0 0 0 8

(g/l)

Wet Pick-up Coefficient Prediction Profile for Dye Range Set-up Conditions



232

Table 4-14: ANOVA analysis results for wash reduction coefficient

The plot of actual versus calculated wash reduction coefficient is shown in figure 4-42. The

values vary in order of magnitude from 0.01 to 0.3 with a mean value of 0.13. The overall trend

followed a 1 to 1 relationship. However, there are obvious issues with the correlation. When the

model predicted the wash reduction value to be 0.15, the actual value varied from 0.02 to 0.26. As

with wet pick-up this variation could be explained by error in measurements of yarn properties

which resulted in other dye coefficients skewing to match the results. It is hoped the averages will

balance out in the final model. The parameter estimates from table 4-14 produced the following

mathematical expression for the wash reduction coefficient as a function of dye range set-up

parameters, equation 4-37.



233

Figure 4-42: Comparison of model predicted and actual wash reduction.

ℎ = −0.1043 + 4.3698 ∗ − 1.7414 ∗ + 6.4822 ∗ −6.8279 ∗ ℎ(

)

Equation 4-37: Dye theory model prediction equation of wash reduction.

The effect of each parameter on wash reduction is shown in figure 4-43. As the speed

increased the wash reduction increased. This seems straight forward as greater speed should

facilitate more chemical removal. As the dwell time increased the wash reduction decreased. As

with yarn diffusion this seemed counter-intuitive but on fixed length dye ranges an increase in time

results from a decrease in speed. As the dye box reduction potential increased the wash reduction

also increased. This was possibly due to actual reduction of the oxidized dye thereby increasing the

mobility of the dye molecule. In the last column of figure 4-43, as dye bath concentration increased

the wash reduction decreased. This probably has more to do with an increase in chemicals to be

removed and less with the influence of the concentration on washing. However, dye bath

A c t u a l W a s h R e d u

c t i o n



234

concentration effect on wash reduction maybe related to the definition of %COWY as previously

discussed.

Figure 4-43: Dye theory model wash reduction functional relationship to dye range set-up conditions.

4.3.4.e Functional Relationship of Oxidation Rate

The last dye theory coefficient evaluated was oxidation rate. It was determined the speed,

oxidation time, and reduction potential at each dip were statistically significant. The other dye

parameters did not have a significant impact. The best correlation established was 0.51 with an F

ratio of 45.3 and P value much less than 0.0001 as shown in table 4-15. The parameter estimates

and effect tests are also displayed in table 4-15. While only dip had a P value much less than 0.0001,

the other parameters were statistically significant since P values were below 0.0272. While the

model fit did not possess an extremely strong correlation to the data, it was deemed the best model

possible.

W a s h %

0 . 1

1 0 5 8 1

± 0 . 0

0 6 7 9 6

2 7

2 9

3 1

3 3

3 5

3 7

1 4

1 5

1 6

1 7

1 8

1 9

2 0

2 1

8 0 0

9 0 0 1 2 3

(g/l)

Wash Reduction Coefficient Prediction Profile for Dye Range Set-up Conditions



235

Table 4-15: ANOVA analysis results for oxidation rate coefficient.

The plot of actual versus calculated oxidation rate is presented in figure 4-44. The values

ranged from 0.01 to 0.2 grams of reduced indigo that were oxidized per gram of oxygen per second.

Of course this wasn't necessarily the true or absolute oxidation rate; it was relative to other dye

range set-up conditions in this observational study under the current dye theory model. As the

actual oxidation rate increased in most cases the predicted values did not increase as rapidly.

However, the correlation at lower oxidation rates appears to be quite well. The analysis produced

the following mathematical expression for the oxidation rate coefficient as a function of dye range

set-up parameters, equation 4-38.



236

Figure 4-44: Comparison of model predicted and actual oxidation rate.

= exp (−10.4654+ℎ()

⎣

1:0.02:−0.46863:−0.69324:−0.98265:−0.68856:−1.34627:−1.3170⎦

+ 0.1263 ∗ +

6.8530 ∗ − 1.0179 ∗ )

Equation 4-38: Dye theory model prediction equation of oxidation rate.

The prediction profile which relates the calculated oxidation rate to the input variables is

shown in figure 4-45. As the dip number increased the oxidation rate decreased. This was probably

related to the increase of residual chemicals on weight of yarn as the number of dips increased. As

the speed increased the oxidation rate increased. This was probably due to increase air circulation

into and through the yarn structure thereby increasing the amount of available oxygen. Likewise, as

the oxidation time increased due to either slower speeds or increased thread-up length, the rate

increased. Interestingly as the reduction potential increased, the oxidation rate decreased. This of

A c t u a l O x i d i z a t i o n

R a t e



237

course makes sense. The interestingly part was that reduction potential wasn't used in any dye

theory model calculation and yet the effect surfaced here.

Figure 4-45: Dye theory model oxidation rate functional relationship to dye range set-up conditions.

4.3.5 Algorithm to Calculate the %COWY, %IOWY, and Integ Shade

The final program enters in the appropriate dye range set-up conditions: yarn count, dip

number, speed, dyeing dwell time, pH, dye bath concentration, nip pressure, and oxidation dwell

time. Then the corresponding values for indigo dyeing coefficients: fiber diffusion, yarn diffusion,

wet pick-up, wash reduction, and oxidation rate were calculated. The following logic was used to

calculate the %IOWY, %COWY, and Integ shade value. The actual computer program is referenced

in appendix section A-4-3b.

Enter dye range parametersCalculate dyeing coefficients and initialize all parameters

Start time loop for the dip process equal to total dwell time

Calculations:

Dye bath concentration within the yarn

Diffusion of dye into the fiber

P r e d i c t e d O x i d i z a t i o n R a t e

0 . 0

8 6 6 5 8

[ 0 . 0

7 6 0 6 ,

0 . 0

9 8 7 3 ]

1 3 5 7 2 7

2 9

3 1

3 3

3 5

3 7

6 0

7 0

7 0 0

8 0 0

9 0 0

Oxidation Rate Coefficient Prediction Profile for Dye Range Set-up Conditions



238

Close dip time loop

Adjust boundary layers due to wet pick-up and removal of previous oxidized dye

Start oxidation time loop equal to total oxidation time

Calculations:

Oxygen concentration within the yarn

Adjust reduced indigo available in yarn

1. Dye in boundary layer by amount of dye oxidized

2. Dye diffused into fiber

3. If no reduced boundary exists start to oxidize dye in the fiber

Increase oxidized boundary layer

Close oxidation time loop

Calculate total %IOWY by summing all %IOWY at each node

Calculate total %COWY by adding total %IOWY and summing oxidized boundary layer at each node

Convert %IOWY at the surface of the yarn into Integ shade value

Repeat for each additional dip



239

5 Empirical and Dye theory model simulation and validation

The final step in traditional experimental design is model simulation and validation. Under

this observational study, simulation was conducted by comparing calculated and measured %COWY,

%IOWY, and Integ shade values, from sources of data independent from the respective data setsused to create the models. First the models were compared to a third dye range located in Canada.

Again, none of the Canadian data was used in the creation of the empirical or dye theory models.

Second, the empirical and dye theory models were compared to actual production yarns. This will

validate the effectiveness of model results to actually predict production dye properties.

5.1 Simulation of Empirical and Dye Theory models on Third Independent Dye Range

Yarn skeins were processed on a third indigo long chain rope dye range following the same

methods and procedures previously discussed in Chapter 3. Due to curtailment of this production

facility all indigo shades were transferred to US operations so customers would have a seamless

transition. To make the transition as smooth as possible, US technicians with US laboratory

equipment went to the Canadian operation. By having the same person and the same equipment

perform indigo dye box testing, conditions such as grams of indigo per liter and reduction potential,

as much testing error was removed as possible. This effort resulted in five different dye range set-

ups with yarn skeins to be compared to empirical and dye theory models. The specific dye range

conditions for each dye range set-up are listed in table 5-1. The complete set of observational data

is listed in appendix section A-5-1 for detailed review.

Table 5-1: Canadian dye range set-up conditions used for simulation

Reference

Shade #

# of

Dips

Speed

(m/min)

Dwell

Time (sec)

Oxidation

Time (sec)

Dye Bath

(g/l)

Dye

pH

Dye

mV

Dye NaOH

(g/l)

443 1 to 6 29 20.1 73.6 1.26 12.2 813 2.58

418 1 to 6 32 18.2 66.7 1.66 11.8 814 3.29

402 1 to 6 28 20.8 76.3 1.99 12.2 841 3.53

471 1 to 6 32 18.2 66.7 2.09 12.1 838 3.42

401 1 to 6 28 20.8 76.3 2.21 12.1 820 3.72



240

5.1.1 Actual Versus Predicted %COWY

The individual dye range parameters were used to calculate %COWY from the empirical dye

model. The empirical model performed beautifully with a great correlation of R2 = 0.91 and deemed

highly significant with F ratio of 651 as shown in table 5-2. The predicted versus actual graph, figure5-1, does however show a slight issue. The slope of curve fit wasn’t 1.0. With a slope of 1.014, the

model over predicts the true %COWY by 1.4%. This isn’t a huge difference but it was real.

Figure 5-1: Empirical model predicted %COWY compared to actual measured values.

% C O W Y A c t u a l



242

Figure 5-2: Dye theory model predicted %COWY compared to actual measured values.

Table 5-3: ANOVA analysis results of dye theory model to actual measured %COWY

The empirical model obviously out performs the dye theory model in predicting the

%COWY. Not only does the empirical model predict the true value better but the error associated

with the prediction was about half that of the dye theory model. The flaw in the dye theory model

% C O W Y A c t u a l



243

was traced back to the basic assumptions used to generate the solution algorithm. By assuming

total chemical on weight of yarn was directly related to amount of indigo on weight yarn, the dye

theory model doesn't accurately predict the true %COWY. This wasn't a good start for the dye

theory model but there are many more comparisons to evaluate.

5.1.2 Actual Versus Predicted %IOWY

At the end of the day the most important property any model should predict well is %IOWY

and the resulting shade. The comparison of calculated %IOWY to actual measured %IOWY is

presented in figure 5-3 and table 5-4 for the empirical model. The empirical model matched up with

the actual values very well as indicated by the R2 of 0.94. Furthermore the model results were

deemed statistically significant following the overall model F ratio of 1077. However, like %COWY,

the predicted %IOWY over estimated the actual %IOWY by 1.2% since the slope is 1.012.

Figure 5-3: Empirical model predicted %IOWY compared to actual measured values.

% I O W Y A c t u a l



244

Table 5-4: ANOVA analysis results of empirical model to actual measured %IOWY

After a rough start in predicting %COWY, hopefully the dye model theory will redeem itself

in predicting the %IOWY. In fact, the dye theory model actually has a slightly better correlation

coefficient than the empirical model at 0.95 and an F ratio of 1112, see table 5-5. Both of these

indicate extremely good fit to the measured values. However, the slope of the fit is 0.94 which

indicates approximately 6% over estimation. While this was an extremely accurate data fit, the

overall performance wasn't as good as the empirical model but certainly redeemed itself from the

misstep on %COWY predication.



245

Figure 5-4: Dye theory model predicted %IOWY compared to actual measured values.

Table 5-5: ANOVA analysis results of dye theory model to actual measured %IOWY

% I O W Y A c t u a l



246

5.1.3 Actual Versus Predicted Integ Shade Value

The Integ shade values for the empirical model prediction versus actual are presented in

figure 5-5 and table 5-6. The overall correlation coefficient for the fit was R2 of 0.97 with an F ratio

of 2108. Both of these calculations indicate extremely strong empirical model fit to the actualmeasured values. The slope of the model fit was 1.084 which means the model underestimates the

actual Integ shade values by 8.4%.

Figure 5-5: Empirical model predicted Integ compared to actual measured values.

I n t e g A c t u a l



247

Table 5-6: ANOVA analysis results of empirical model to actual measured Integ

The dye theory model fit to actual measured Integ shade values is shown in figure 5-6. The

overall model fit correlation coefficient was R2 of 0.97 with an F ratio of 1823 as shown in table 5-7.

These values indicate an extremely strong correlation to the actual values and perform as well as

the empirical model. Unfortunately, the slope of the fit is 1.097 with an intercept of -5.8. These are

the result of the dye theory model over predicting the Integ shade at low values and slightly under

predicting at high values. However, the general trend is for comparable Integ prediction

performance to the empirical model.



248

Figure 5-6: Dye theory model predicted Integ compared to actual measured values.

Table 5-7: ANOVA analysis results of dye theory model to actual measured Integ




249

5.1.4 Actual Versus Predicted Penetration Level

By converting the measured Integ shade values into %IOWY on the surface of the yarn, the

actual penetration level was calculated. Comparison of the empirical model predicted penetration

level to actual penetration levels are presented in figure 5-7 and table 5-8. The overall modelcorrelation coefficient was R2 of 0.63 which isn’t extremely strong but deemed statistically

significant by the F ratio of 109 and P-value < 0.0001. The reason for poor correlation is due to the

great variation as evident by the wider range of the confidence intervals in figure 5-7. The mean

penetration level is 0.38 units. The slope of the data fit is 0.97 which is very close to a 1 to 1 ratio as

visibly evident. However, the intercept is -0.05 penetration units which is 1/8 of the mean value.

This causes the empirical model to over predict the level of penetration in the yarns. In other words

the empirical model predicts the yarns are less ring dyed or more penetrated than what actually

occurred.

Figure 5-7: Empirical model predicted penetration level compared to actual measured values.

P e n e t r a t i o n L e v e l A c t u a l



250

Table 5-8: ANOVA analysis results of empirical model to actual measured penetration level

The dye theory model has a similar issue with the predicted penetration level on the

Canadian dye range. Comparison of the dye theory model predicted penetration level to actual

values were summarized in the table 5-9 and figure 5-8. The overall model fit was slightly better

than the empirical model as indicated by R2 correlation coefficient of 0.67 and F ratio of 129.

However, the slope wasn't close 1 to 1. A slope of 0.81 coupled with an intercept of 0.04 indicates

the dye theory model also over estimates the level of penetration.



251

Figure 5-8: Dye theory model predicted penetration level compared to actual measured values.

Table 5-9: ANOVA analysis results of dye theory model to actual measured penetration level

0.2

0.3

0.4

0.5

0.6

P e n e t r a t i o n L e v e l A c t u a l

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6

Dye Theory Model Penetration Level Predicted

Linear Fit

Dye Theory Model Compared to Canadian Dye Range Actual Penetration Level



252

5.1.5 Summary of Dye Theory Model Compared with Empirical Model

It was expected that the empirical model would provide the best possible prediction of

%COWY, %IOWY, Integ, and penetration level. This was the purpose of the calculation, to provide a

baseline for comparing the dye theory model performance. Taken in this context, the dye theorymodel preformed reasonably well. While the dye theory model did not perform well in predicting

the %COWY, this property in fact has little to do with actual dyeing of yarns with indigo dye as all

residual chemicals are washed off during the final wash stage in the dye range. The most important

properties are %IOWY, Integ shade, and the resulting penetration level.

As shown, the dye theory model preformed very well compared to the empirical model in

predicting the %IOWY and Integ shade. The difference between the two models is approximately

5% in %IOWY prediction while the Integ shade predictions were almost identical. The relatively poorperformance of the dye theory model in penetration level prediction compared to empirical model

is disappointing but understandable. The empirical model directly calculates the penetration level

while the dye theory model penetration level was calculated based on predicted %IOWY and

converted Integ shade values. The difference between direct and indirect penetration level

calculations can certainly explain the difference in performance of the two models. This discrepancy

warrants further investigation.

Indigo build profiles were constructed for each Canadian dye range set-up for detailed

comparison of measured %IOWY and Integ shade versus the predicted values from both models.

Figure 5-9 shows the build profile of Integ shade as a function of %IOWY for the measured

observational skeins, empirical model, and dye theory model. Each individual point represents the

%IOWY and Integ shade after a particular dip of indigo. Clearly on this dye range set-up, both

models over predict the amount of %IOWY. The empirical model predicts the Integ shade values

fairly well while the dye theory model over predicts the Integ.

The really interesting observation is the location of the prediction profiles relative to the

observational skein data. Curves falling below the measured build profile indicate more penetration

or less ring dyeing. While any curves above the measured profile would indicate less penetration or

more ring dyeing. On this particular dye range set-up, the dye theory model prediction build curve



is act

pene

Figure

conce

simil

dye s

unde

profil

pene

and I

the In

same

ally closer t

ration level

5-9: Indigo buil

tration and 12.

By constru

r relationshi

t-up and fig

predict the

e better mat

ionrat than

teg values

teg. In this

degree.

the observa

han the emp

d profile for Ca

2 pH.

cting similar

developed.

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easured. In

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irical model.

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Figure 5-10

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he resulting I

rvational m

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This indicat

e set-up on 443

curves for th

was construc

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the empirica

l slightly ove

dels over est

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However, th

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etter predict

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mates the %I

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basically th

253

s the

pH

ghtly

re

OWY

ates



Figure

conce

Figure

conce

5-10: Indigo bu

tration and 11.

5-11: Indigo bu

tration and 12.

ild profile for C

8 pH.

ild profile for C

1 pH.

nadian dye ran

nadian dye ran

ge set-up on 4

ge set-up on 4

8 shade with 3

1 shade with 3

m/min, 1.66 g

m/min, 2.09 g

/l dye bath

/l dye bath

254



255

The superior performance of empirical model prediction of penetration level compared to

dye theory model results from the model's ability to calculate the penetration level independent of

the %IOWY and Integ shade values. The dye theory model penetration level is indirectly converted

from the predicted %IOWY and Integ values. This ability gives the empirical model a false sense of

conformity. The analysis of empirical model penetration level prediction is repeated but this time

the penetration level is calculated from the predicted %IOWY and Integ values. Figure 5-12 and

table 5-10 compares the empirical model predicted indirect penetration level to the actual

penetration level calculated from the measured %IOWY and Integ. Now the correlation coefficient

is R2 of 0.59 with an F ratio of 92.7. This is actually a slightly inferior fit to the data than the dye

theory model. More importantly, with a slope of 0.70 and intercept of 0.066 the shape of the fit

was worse than the dye theory model. Recall dye theory had a slope of 0.80 and intercept of 0.04.

Figure 5-12: Empirical model predicted indirect penetration level compared to actual measured values.

0.2

0.3

0.4

0.5

0.6

P e n e t r a t i o

n L e v e l A c t u a l

0.2 0.25 0.3 0.35 0.4 0.45 0.5 0.55 0.6 0.65

Empirical Model Indirect

Penetration Level Predicted

Linear Fit

Empirical Model Indirect Penetration Level Comparison on Canadian Dye Range



256

Table 5-10: ANOVA analysis results of empirical model indirect penetration level to actual measured penetration level

Considering the overall performance of the dye theory model compared to empirical model,

an acceptable level of performance was obtained. The dye theory model predicts the %IOWY and

Integ shade as well as the empirical model. While the empirical model direct penetration level does

perform better than the dye theory model, the calculated indirect penetration level of the empirical

model was actually worse than the dye theory model.

5.2 Simulation of Empirical and Dye Theory Models to Actual Production Yarn

The real measure of any indigo dye model is how well it predicts %IOWY and Integ shade

from actual production dyed yarns. To perform this comparison, actual production dyed yarns were

measured for %IOWY and Integ shade after processing through production scale indigo chain rope

dye ranges. Six production shades were selected and the particular dye range set-up conditions are

summarized in table 5-11. Five of the shades were pure indigo so %IOWY and Integ values were

measured. The 1169 shade was a black sulfur top so only the %IOWY was applicable. Three samples

were collected from each of the two prime USA production ranges to provide variation in dwelllength.



257

Table 5-11: Production Yarn Dye Range Set-up Conditions

Reference

Shade #

# of

Dips

Speed

(m/min)

Dwell

Time (sec)

Oxidation

Time (sec)

Dye Bath

(g/l)

Dye

pH

Dye

mV

Dwell

Length, m

1134 1 to 7 31.1 16.7 69.5 2.994 11.98 789 8.631157 1 to 6 32.9 15.9 65.7 2.497 12.41 847 8.63

1169 1 to 7 31.1 16.7 69.5 2.34 11.6 888 8.63

4223 1 to 2 32.9 20.7 67.5 2.07 12.49 907 11.37

1134 1 to 6 29.3 23.5 75.9 3.497 11.62 897 11.37

1110 1 to 2 32.9 20.7 69.5 0.733 12.23 813 11.37

The resulting %IOWY and Integ values are detailed in table 5-12. The actual %IOWY and

Integ values correspond to the actual production yarn count were measured. Columns five and six

list the results predicted by the empirical model. Columns seven and eight list the predicted results

from the dye theory model.

Table 5-12: Measured, Empirical Model, and Dye Theory Model %IOWY and Integ values

Reference

Shade #

Production

Yarn Count

Actual

%IOWY

Actual

Integ

Empirical

%IOWY

Empirical

Integ

Dye Theory

%IOWY

Dye Theory

Integ

1134 7.75 3.01% 85.4 3.21% 112.7 3.02% 92.2

1157 6.55 1.89% 77.3 2.34% 91.3 1.88% 76.21169 9.75 2.56% N/A 2.79% N/A 2.55% N/A

4223 6.3 0.55% 33 0.64% 32.37 0.55% 33.2

1134 7.75 3.39% 101.1 3.28% 128.7 3.39% 107.7

1110 12 0.30% 12.1 0.33% 15.53 0.31% 14.2

One will notice the dye theory %IOWY in column seven of table 5-12 matches the measured

actual %IOWY from column three. This was an intentional result due to adjustments in the yarn

porosity value during the prediction model calculation phase. Unlike the empirical model, the dyetheory model was porosity dependent. The original value of 0.65 was selected as discussed in

section 4.3.1.a since observational yarn skeins were in non-tension state. But what value should be

used for yarns under tension when submerged in a dye bath? Instead of guessing at a value, this



258

researched decided to find the porosity value that would match the target %IOWY. This would allow

the predicted Integ values to be calculated and the final porosity value would be analyzed. Given

this assumption the dye theory model predicted %IOWY will match the production yarn actual

value.

The results of the empirical model predicted %IOWY are presented in figure 5-13 and table

5-13. The model predicts the %IOWY extremely well as the correlation coefficient of 0.97 and F

ratio of 180 indicates. This is visually evident in the graph of predicted versus actual with all points

falling extremely close to the center line and well within the 95% confidence intervals demarcated

by the dotted lines. Furthermore, the slope of 0.98 and intercept of -0.10% confirms the empirical

model performed exceptional well at predicting the %IOWY on actual production scale dyed yarns.

Figure 5-13: Empirical model predicted %IOWY compared to actual measured values from production yarns.

%

I O W Y A c t u a l



259

Table 5-13: ANOVA analysis results of empirical model to actual measured production yarn %IOWY

As previously discussed the dye theory model %IOWY value was calculated by adjusting the

porosity value used in the model. These results are listed in table 5-14. To match the actual %IOWY

from production yarns the porosity value ranged from 0.92 to 0.995. Two interesting points to

make: the porosity values weren't constant and the porosity values were much higher than

expected. One possible cause for porosity variation will be presented shortly. For the higher values,

this could be explained by the high tension of the yarns in a wet state during the dyeing process or

the need for lower porosity value than 0.65 during the model construction phase. Either way the

porosity values were below the theoretical limit of 1.0.

Table 5-14: Calculated porosity value to fit Dye theory model %IOWY to production yarn results

Reference

Shade #

Production

Yarn Count

Actual

%IOWY

Actual

Integ

Dye Theory

%IOWY

Dye Theory

Integ

Porosity

Value

1134 7.75 3.01% 85.4 3.02% 92.2 0.964

1157 6.55 1.89% 77.3 1.88% 76.2 0.98

1169 9.75 2.56% N/A 2.55% N/A 0.968

4223 6.3 0.55% 33 0.55% 33.2 0.9925

1134 7.75 3.39% 101.1 3.39% 107.7 0.92

1110 12 0.30% 12.1 0.31% 14.2 0.995



260

For completeness, the resulting model fit of dye theory model %IOWY to actual measured

production yarns is presented in figure 5-14 and table 5-15. Of course there were no surprises.

Basically there was a perfect model fit to the data.

Figure 5-14: Dye theory model predicted %IOWY compared to actual measured values from production yarns.

%

I O W Y A c t u a l



261

Table 5-15: ANOVA analysis results of dye theory model to actual measured production yarn %IOWY

Next the empirical model predicted Integ values were compared to the measured values

from production yarns. The ANOVA analysis results are presented in table 5-16 and than graphically

displayed in figure 5-15. The empirical model had an extremely strong model fit to the measured

data as indicated by a correlation coefficient of 0.98 and F ratio of 254. Graphically, the model fit

demonstrates the strong correlation with most points falling near the center line and well within the

95% confidence intervals.

Unfortunately, the parameter estimates tell a different story. The slope of the fit is 0.75

with an intercept of 4.7 Integ units. As a result, the empirical model performs reasonably well at

predicting Integ values at lower depths of shade. But as the actual depth increases (higher Integ),

the predicted values over estimate the real values. As a result, at 85.4 measured Integ the empirical

model predicts 112.7 Integ and at 101.1 measured units the model predicts 128.7 units. These two

points average to 30% over estimate of Integ at darker shades by the empirical model.



262

Figure 5-15: Empirical model predicted Integ compared to actual measured values from production yarns.

Table 5-16: ANOVA analysis results of empirical model to actual measured production yarn Integ

In contrast, the dye theory model performed much better at predicting the Integ shade of

production dyed yarns. The model fit analysis results are presented in table 5-17 and figure 5-16.




263

The correlation coefficient is 0.99 with an F ratio of 498. This indicated an extremely strong

correlation that was statistically significant. Even better, the slope of the fit was 0.94 and intercept

was 0.64. As a result, the dye theory model predicted Integ virtually falls on the 1 to 1 curve to

actual Integ values and the 95% confidence intervals are extremely tight with the root mean square

error of the fit at 3.36 compared to 4.69 for the empirical model.

Figure 5-16: Dye theory model predicted Integ compared to actual measured values from production yarns.

I n t e g A c t u

a l



264

Table 5-17: ANOVA analysis results of dye theory model to actual measured production yarn Integ

The superior performance of the dye theory model compared to empirical model resulted

from the ability to compensate for yarn porosity. While this may seem like an unfair advantage for

the dye theory model, it illustrates the importance of building models based on theory instead of

pure statistical analysis. Simply by adjusting the space between fibers in the yarn cross section, the

dye theory model could accurately predict the %IOWY and Integ shade while maintaining the

established relationships of the underlying dye coefficients such as fiber and yarn diffusion.

So what is the actual production yarn porosity value? After a complete ANOVA statistical

analysis only one parameter showed correlation to changes in required porosity value: dye range

speed. Regardless of yarn count, dwell length, dye concentration, and/or pH; only the dye range

speed correlated well with the changes in required porosity value. The ANOVA analysis results are

shown in table 5-18 and graphically displayed in figure 5-17. The correlation coefficient R2 was 0.90

and F ratio was 47.4. While this isn't the strongest correlation it was deemed to be statistically

significant due to P values of 0.0023.



265

Figure 5-17: Functional relationship between theoretical porosity value and dye range speed.

Table 5-18: ANOVA analysis results of dye theory model calculated porosity value to dye range speed

The relationship between yarn porosity and dye range speed makes sense under the context

of tension. Production yarn under tension will have a high porosity value than observerational

skeins under no tension. Additionally, as the dye range speed was increased, the tension the yarn

was exposed to would increase as well. The higher tension at faster speeds would result in slightly

T h e o r e t i c a l P o r o s i t y



266

higher porosity values as the individual fibers are packed closer together. While care should be

exercised not to base definitive conclusions from 6 data points, the evidence and rational behind the

relationship was compelling.



267

6 Summary of Results, Discussions, and Recommendations

During this endeavor several important learning's have been detailed and this researcher

will present each item with highlights and discussions on key components. Before any observational

data was gathered, a rigorous experimental design was conducted to determine the optimum

method for preparing 100% cotton yarn skeins in the laboratory. The optimum laboratory

procedure involved cooking the yarn skeins at 100° C temperature with 12.7 g/l of 50% sodium

hydroxide for 30 minutes. Following this method ensured the most consistent yarn preparation

from day to day. While this research was conducted on 100% cotton open end spun yarns, similar

methods more than likely applies to knitted or woven substrates. Hopefully, future studies will

repeat the analysis on several substrates so a common preparation method can be established.

Today, most published articles provide a detailed description of the preparation method utilized butthere are too many variations, study to study. Variations in preparation potentially can skew

measured results and absolute values do not translate from one experiment to another. If industry

adopted a common preparation method, research from many experiments could be grouped

together for greater understanding instead of each being treated as a standalone data set.

Following the practice of Etters, laboratory experiments were conducted under equilibrium

sorption conditions. There were two primary reasons for conducting these experiments. Under

equilibrium sorption conditions, a mathematical expression was developed that relates indigo dye

bath concentration to the maximum %IOWY. A relationship was developed that expressed %IOWY

in terms of indigo dye bath concentration at specific dye bath pH levels. It was determined the

profile of pH dependence followed the monophenolate ionic form of the indigo dye molecule as

purposed by Etters and summarized in equation 6-1.

ℎ =

..

= 0.016492 ∗ ℎ + 0.003465 = −0.244296 ∗ ℎ + 0.816158

% = ∗

Equation 6-1: Equations to calculate %IOWY as a function of dye bath concentration and pH under equilibrium sorption

conditions.



268

Second, equilibrium sorption conditions were used to develop a mathematical expression

for %IOWY located at the surface of the yarn to the Integ shade value. The reverse expression was

also developed. With these two equations the approximate %IOWY at the surface from non-

uniformly dyed yarns were calculated based on the measured Integ shade value as summarized in

equation 6-2. This resulted in the ability to quantitatively express the penetration level of non-

uniformly dyed yarns. Combining the two primary conclusions from the equilibrium sorption

experiments provided the base relationships needed to develop a theoretical dye model.

% = −0.02646 + (9.5386 ∗ ) + (1.3593 ∗ ( − 55.2088)) +

(3.909 ∗ ( − 55.2088)) + (2.4244 ∗ ( − 55.2088)) + (6.4303 ∗

( − 55.2088))

Penetration Level =%M

%

Equation 6-2: Expressions to relate penetration level of non-uniformly dyed yarns.

An extensive observational study was conducted on production scale indigo chain rope dye

ranges. During this study various dye range set-up parameters were recorded: yarn count, dip,

speed, dwell length, dwell time, oxidation time, nip pressure, dye bath indigo concentration, dye

bath pH, dye bath reduction potential, and dye bath total alkalinity. After processing each yarn

skein the %COWY, %IOWY, and Integ shade values were measured. The results from the

observational study provided the basis for general trend analysis, empirical dye modeling, and

theoretical dye modeling.

The general trends confirm many previously published conclusions but also indentified

several new relationships never before discussed. Measurement and analysis has never been

conducted on the %COWY after each dip of indigo. At first glance this value may seem trivial since

the property never shows up at the doff end of the indigo dye range. However, the residual

chemicals washed off during the wash section have monetary value. A better understanding of the

dye range set-up parameters that cause %COWY to increased while not improving either the %IOWY



269

or the Integ shade value; may result in reducing variable cost associated with each yard of fabric and

reduce effluent chemicals that require processing before releasing to the environment.

It was determined that finer yarns have a greater %COWY and the relationship is fairly linear

in nature. Likewise, adding more dips of indigo increased the %COWY but the relationship wasn'tlinear as each additional dip resulted in a smaller change in %COWY. Increasing the speed from 26

m/min to 33 m/min resulted in an increase in %COWY. At approximately 33 m/min the relationship

peaked and %COWY deceased at higher speeds. Unsurprisingly, increasing the dye bath indigo

concentration resulted in greater %COWY. Last, increasing pH actually decreased the %COWY. It

would appear that operating the indigo dye range with high number of dips, relatively fast speeds,

high pH values, and coarse yarns would reduce the residual %COWY. Of course these changes may

change the %IOWY and Integ shade values on established production shades but when developing a

new production shade with new dye range set-up conditions these trends should be kept in mind.

Many results have been published relating %IOWY to various parameters. Results from the

graphical and ANOVA analysis for %IOWY confirm many of these relationships. Specifically,

increased number of dips and increased dye bath concentration both resulted in increased %IOWY.

However, contrary to previously published results, dye bath pH was determined to be statistically

insignificant. This, of course, could be related to the limited dye bath pH range over which the

observational study was conducted. Also, the graphical analysis indicated an increase in pH caused

an increase in %IOWY. Both of these conclusions contradict conventional wisdom and should be

confirmed with additional production scale indigo dye range analysis preferably at far lower pH

ranges. In addition to previously published dye range set-up parameters this observational study

included many parameters never investigated before. It was determined that finer yarns have

increased %IOWY compared to courser counts. Also, the dye range speed was determined to have a

significant impact and increased speeds resulted in decreased %IOWY.

Besides %IOWY many published experiments discuss the relationship of indigo shade to dye

range set-up conditions. In most cases, the discussions are based on corrected K/S values at a

specific wavelength. In this study, shade was expressed in terms of Integ values which proved to be

continuous and unique, although not linear, over a wide range of %IOWY values. The general trend

and ANOVA analysis results from the observational study confirms all published trends. Specifically,



270

increased %IOWY, increased number of dips, increased dye bath concentration, and decreased dye

bath pH caused the Integ shade values to increase. Additionally, new relationships were uncovered

from the analysis of observational data. Finer yarns produced higher Integ values than courser

counts. Increasing the dye range speed resulted in a decreased Integ value; and increasing the dwell

time caused the Integ values to slightly decrease.

The last response variable evaluated from the observational study was penetration level. As

mentioned before, penetration level was a calculated parameter dependent on the Integ shade,

%IOWY, and derived expression relating Integ and %IOWY from equilibrium sorption. Finer yarn

counts were observed to have higher penetration levels than courser counts. This relationship

mirrors real world experiences since finer yarn counts are more penetrated or less ring dyed than

coarser counts. While finer yarns do have slightly higher Integ values at a given dye range set-up,

the change in %IOWY was much greater at finer counts. As the number of dips of indigo increased

the penetration level decreased. This was due to the additive nature of indigo dyeing with each

additional dip layered on top of the previous dip. As speed was increased, the penetration level was

observed to decrease non-linearly until approximately 33 m/min. Further increases in speed

resulted in slightly higher penetration levels. Although the impact of speed on penetration trends

hasn't been published, this relationship mirrors real world experience. An increase in the dye bath

concentration was determined to cause the penetration level to decrease. Also, increased dye bath

pH was linked to increased penetration levels. This observational study confirmed many pH related

experiments conducted by Etters.

Based on the observational study results an empirical dye model was created to link dye

range set-up conditions with the resulting %COWY, %IOWY, Integ, and penetration level. The

empirical model proved to perform well at predicting the response variables. When compared to a

third independent dye range, the empirical model performed well. The correlation coefficients,

slope, and intercept relating the predicted to actual values are listed in table 6-1.



271

Table 6-1: Empirical model performance review

Response Correlation Coef, R2 Slope Intercept

%COWY 0.91 1.014 -0.000

%IOWY 0.94 1.012 -0.001

Integ 0.97 1.084 -1.344

Penetration Level 0.59 0.680 0.066

The empirical model was compared to actual production yarns from full scale indigo chain

rope dye equipment. Surprising the %IOWY was predicted with exceptional level of accuracy.

Unfortunately, that level of performance was not carried over to the Integ shade prediction. The

empirical model correlated well with measured values but over predicted the actual value. At the

higher Integ levels the differences between actual and empirical model prediction approached 30%.

As a result, the penetration level wasn't predicted well either.

A second indigo dye model was also created based on general dye and diffusion theory. In

the dye theory model, dye coefficients such as fiber diffusion, yarn diffusion, wet pick-up, wash

reduction, and oxidation rate were calculated based on the dye range set-up conditions. Then, using

these dye coefficients the dye theory model calculated the resulting %COWY, %IOWY, Integ, and

indirectly penetration level.

Just like the empirical model, the dye theory model was compared to a third independent

indigo dye range. The resulting comparison demonstrated poorer correlation in predicting %COWY

then the empirical model. However, the dye theory model performed as well as the empirical

model at predicting the %IOWY and Integ. Further, the dye model actually outperformed the

empirical model at predicting penetration level. The correlation coefficients, slopes, and intercepts

from the dye theory model predicted compared to actual values are listed in table 6-2.

Table 6-2: Dye theory model performance review

Response Correlation Coef, R2

Slope Intercept%COWY 0.74 0.764 0.007

%IOWY 0.95 0.943 -0.001

Integ 0.97 1.097 -5.764

Penetration Level 0.67 0.806 0.041



272

The dye theory model was compared to actual full scale production dyed cotton yarns. By

adjusting the yarn porosity value used in the calculations to match the actual %IOWY, an excellent

correlation was established for the Integ shade values. The resulting correlation coefficient for

predicted and actual Integ was R2 of 0.99 with a slope of 0.945 and intercept of 0.643.

The outperformance of the dye theory model compared to the empirical model was due to

the ability to compensate for yarn porosity changes between the observational data collection state,

non-tension, and production state, high tension. Furthermore, potential porosity dependence on

dye range speed was introduced. While six data points were certainly not enough evidence to

present a compelling argument, the strong correlation does warrant further investigation.

Recommendations

1. Expansion of the equilibrium sorption experiments would add more insight in the behavior and

dependence of indigo dye uptake at various dye bath indigo concentrations and pH levels.

Additional data points at lower pH levels are required to confirm the mathematical relationships

presented. Specifically, higher dye bath indigo concentrations at much lower pH levels are required.

While the current study coupled with Etters' previously published results offers a compelling

argument, more data points are required to provide statistically strong support.

2. Additional observational studies need to be conducted from other full scale production chain

rope indigo dye ranges. By adding more data points to the dye theory model, confidence intervals

would be increased and observed general trends clarified. Specifically, a wider range of dye bath pH

levels must be explored which incorporates pH buffering systems. The inability to reproduce

published %IOWY and pH relationship must be further explored. Additionally, the speed and dwell

time effect on response variables needs a greater variety in the range of values. These can only be

achieved by varying the thread-up dwell length.

3. Refinement of the dye theory model nodal mesh would provide more insight in physico-

chemical effects during the indigo dye process. Making changes in the finite difference nodal mesh

which models the fiber and yarn structural characteristics would provide better prediction of dye



273

bath movement within the yarn structure and thereby better prediction of %IOWY, Integ shade, and

indigo distribution or penetration level. Furthermore, it may be possible to decouple the yarn and

fiber diffusion coefficients back into four elements instead of two. This would allow description of

dye affinity or adsorption for the fiber surface and diffusion into the fiber interior. As well as

understanding the difference between dye movement through the dye bath medium and boundary

layer surrounding the individual fibers.

4. Incorporate additional production scale dyed yarn data points to expand dye theory model

prediction and explore the effects of porosity value relating zero and production state tension.

The current dye theory model preformed well at predicting the production yarn %IOWY and Integ

shade. Additional data points are required to confirm the relationship. The relationship between

dye range speed and actual yarn porosity presented is extremely enticing. However more data

points are required from many different indigo chain rope dye ranges to confirm the relationship

presented.

5. Combine current presented information and recommendations to create a commercial quality

indigo dye prediction program. An accurate indigo dye prediction program would greatly assist the

manufacturing quality control engineer. By coupling the prediction software with end item shade

analysis and production history, the production engineer would know how current production

conditions will affect the end item. This would allow for intelligent dye range adjustments to be

made to control %IOWY and indigo distribution. Additionally, the indigo dye prediction software

would assist dye range equipment manufactures. By understanding the dye range mechanical

affects on %IOWY, Integ, and penetration level; certain fixed dye range mechanical properties could

be tailored to a customer's requirements. Finally, the indigo dye prediction software would greatly

assist an indigo dye house when developing new production shades. The ability to predict %IOWY,

Integ, and indigo distribution without the need for trials would reduce development time and costs.



274

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279

APPENDIX



280

Section A-1-2a: Spectrophotometric method to measure indigo dye bath concentration by %T.

Spectronic 21

1. Position sensitivity control to "M" (medium).

2. Adjust wavelength/Nanometer control to read "660".3. Set dial on face of Spectonic 21 to "Transmittance".

Method

1. Zeroing the machine

2. Fill the test tube with clear water.

3. Place test tube in opening.

4. Line up number on test tube with notch located to the right of the opening. Digital indicator

should zero to 100.0

Test

1. Add approximately 300-400 mls of water to a clean 500 ml volumetric flask.

2. Add a magnetic strring bar and place the flask on a magnestir with rapid agition.

3. Pipet 1 ml of dye box liquor into the swirling water, being careful to wipe any excess from the

outside of the pipet.

4. Agitiate for four minutes or until the Indigo is completely oxidized - bright blue.

5. Remove the magentic bar.

6. Dilute to volume with water and mix until uniform (500 ml).

7. Pour the solution into a test tube.

8. Place in Spectronic 21, making sure numbers are aligned with notch.

9. Read results.

Equation calculation for oz/gal of 20% indigo

= (−% ∗ 0.0373) + 3.628

Equation A-1-1: oz/gal of 20% indigo related by %T by Spectrophotometric method.



281

Section A-1-2b: Total alkalinity titration method.

1. Pipette 10 ml of liquor into a 250 ml beaker.

2. Add 100 ml of distilled water to the beaker.

3. Place the beaker on the mag stirrer and place a magnet in the liquor.

4. Begin stirring at a brisk level so that the level on the wall never exceeds the 150 ml mark.

5. Place the electrodes of a properly calibrated pH meter into the beaker.

6. Begin adding 0.05N Hcl acid at no more than 1 drop every 2 seconds to allow the pH meter

enough time to equilibrate after each addition. After the pH has dropped below 9.0, add not more

than 1 drop every 4 seconds.

7. Titrate to a pH of 8.28.

8. Calculate the g/l of total alkalinity by equation A-1-2.

/ = 0.2 ∗

Equation A-1-2: Calculation of total alkalinity by titration method.



282

Section A-2: Nothing.

Section A-3-1: % Reflectance values of mock dyed 100% cotton yarns used to calculate K/S.

Table A-3-1: % Reflectance values of mock dyed 100% cotton yarns used to calculate K/S.

Wavelength, nm 6.3/1 7.1./1 8.0/1 12.0/1

400 44.2175 46.26 47.10667 47.13

420 47.125 49.46 50.15667 50.27

440 50.29 52.83 53.35333 53.62571

460 52.9825 55.63333 55.94 56.39143

480 55.79 58.49 58.58 59.23714

500 58.2225 60.99333 60.86 61.71857

520 60.575 63.3 62.97 64.02857

540 62.86 65.51 65.02333 66.29143

560 65.1375 67.65333 67.02 68.53429

580 67.11 69.50667 68.81 70.49857

600 68.8975 71.16667 70.41667 72.25

620 70.5625 72.68 71.89 73.85429

640 72.2425 74.21667 73.34667 75.40429

660 73.93 75.83667 74.83 76.87286

680 75.7825 77.7 76.61667 78.47857

700 77.22 79.19 78.06333 79.75429

Section A-3-2: Nothing.



283

Section A-3-3: Balance of data from equilibrium sorption experiment.

Table A-3-3: %IOWY and Integ shade data from equilibrium sorption experiment

Yarn Count Dye Bath g/l Dye Bath pH %IOWY Integ Shade Stock Mix

7.1 0.641 12.25 1.10% 32.7 1

7.1 0.17663 12.8 0.29% 7.4 47.1 1.2287 12.8 1.16% 30.9 6

7.1 0.01577 13.17 0.02% 1.2 3

7.1 0.03494 13.3 0.04% 2.2 6

7.1 0.49612 13.19 0.51% 14.0 5

7.1 1.99985 13.21 1.48% 36.9 3

7.1 3.8843 13.24 2.29% 51.0 5

7.1 6.3355 13.1 3.28% 64.0 4

7.1 9.61464 13.31 4.10% 68.7 3

7.1 14.0149 13.2 5.33% 76.3 6

7.1 19.2293 13.43 6.04% 78.5 5

7.1 29.95 13.2 8.51% 91.0 4

8 2.548 11.2 2.98% 61.8 8

8 0.17663 12.8 0.29% 7.1 4

8 1.2287 12.8 1.17% 30.2 6

8 2.564 12.9 2.02% 47.5 7

8 0.01577 13.17 0.03% 1.2 3

8 0.03494 13.3 0.08% 2.3 6

8 0.49612 13.19 0.50% 14.1 5

8 1.99985 13.21 1.41% 35.9 3

8 3.8843 13.24 2.29% 48.3 5

8 6.3355 13.1 3.32% 63.2 4

8 9.61464 13.31 3.93% 67.9 3

8 14.0149 13.2 5.15% 75.4 6

8 19.2293 13.43 5.60% 78.7 5

8 20.191 13.3 6.67% 80.0 8

8 29.95 13.2 8.44% 89.8 4

12 0.641 12.25 1.09% 34.5 112 1.602 12.72 1.61% 45.6 1

12 0.17663 12.8 0.30% 7.8 4

12 1.2287 12.8 1.25% 31.4 6

12 2.564 12.9 2.06% 50.5 8

12 0.01577 13.17 0.02% 1.2 3

12 0.03494 13.3 0.06% 2.8 6

12 0.49612 13.19 0.50% 13.8 5

12 1.99985 13.21 1.46% 36.0 3

12 3.8843 13.24 2.31% 49.7 5

12 4.487 13.14 2.85% 59.3 7

12 6.3355 13.1 3.25% 60.7 4

12 9.61464 13.31 4.31% 68.7 3

12 14.0149 13.2 5.04% 75.6 612 19.2293 13.43 5.86% 75.8 5

12 29.95 13.2 8.53% 87.5 4



284

Section A-4-1: Observational Study Raw Data -Dye Range Parameters

Table A-4-1: Prime and replica raw data set

Shade

ID

Speed(m/min)

Dwell

Time(sec)

OxidationTime (sec)

Dye Bath

(gpl

100%Indigo)

DyeBath pH

Dye

Bath(mV)

Dye Bath

Alkalinity(gpl)

Dwell

Length(m)

OxidationLength (m)

Nip

Pressures(psi)

1160 36.6 14.1 59.1 0.891 11.66 745 3.16 8.63 36.03 70

Yarn Skein Response VariablesYarn

Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

7.1 1 only 1 6.9561 7.0521 6.9425 1.380% 0.128% 0.182% 6.198167 0.70

7.1 1 --> 2 2 7.0316 7.1811 7.0267 2.126% 0.263% 0.471% 13.73814 0.56

7.1 1 --> 3 3 7.0931 7.3064 7.101 3.007% 0.437% 0.802% 21.46723 0.54

7.1 1 --> 4 4 6.9405 7.119 6.9549 2.572% 0.526% 1.141% 28.84153 0.46

% Reflectance Readings

Wave-

length

(nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7

400 22.78 15.15 11.40 9.33

420 28.23 19.75 15.23 12.70

440 27.56 18.64 14.14 11.63

460 25.10 16.23 12.06 9.78

480 23.09 14.31 10.38 8.25

500 21.16 12.69 9.07 7.08

520 18.82 10.87 7.49 5.71

540 15.90 8.77 5.95 4.48

560 14.25 7.64 5.07 3.80

580 12.60 6.48 4.26 3.20

600 10.82 5.40 3.56 2.69

620 9.44 4.60 3.07 2.35

640 7.96 3.83 2.62 2.05

660 7.03 3.51 2.49 1.95

680 9.24 4.58 3.15 2.46

700 18.45 10.63 7.54 5.78



286

Table A-4-1: Continued

Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)

1160 36.576 14.1 59.1 0.764 11.91 762 2.5 8.63 36.03 70Yarn Skein Response Variables

Yarn

Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 I only 1 7.9045 7.5992 7.7051 7.5822 1.394% 0.150% 0.216% 7.2 0.69

6.3 1--2 2 7.616 7.3223 7.4879 7.3162 2.262% 0.281% 0.477% 13.9 0.59

6.3 1--3 3 7.7551 7.4518 7.6594 7.4602 2.786% 0.458% 0.802% 21.5 0.57

6.3 1--4 4 7.781 7.476 7.6616 7.4896 2.483% 0.523% 1.086% 27.7 0.48


Wave-

length


400 21.20 14.84 11.38 9.63

420 26.48 19.48 15.24 13.13

440 25.80 18.52 14.16 12.05

460 23.39 16.21 12.09 10.15

480 21.37 14.29 10.39 8.56

500 19.50 12.69 9.10 7.38

520 17.20 10.83 7.49 5.94

540 14.40 8.73 5.98 4.67

560 12.78 7.56 5.06 3.95

580 11.18 6.40 4.25 3.32

600 9.49 5.29 3.54 2.78

620 8.20 4.50 3.04 2.42

640 6.89 3.75 2.61 2.10

660 6.08 3.42 2.44 1.98

680 8.16 4.50 3.14 2.52

700 16.86 10.59 7.47 5.95



289


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1160 36.576 14.1 59.1 0.764 11.91 762 2.5 8.63 36.03 60.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

12 1 only 1 3.856 3.7189 3.8039 3.7106 2.286% 0.204% 0.240% 7.8 0.85

12 1--2 2 4.0024 3.8631 3.9669 3.8586 2.687% 0.377% 0.552% 15.7 0.68

12 1--3 3 4.0023 3.8535 3.9861 3.861 3.441% 0.560% 0.887% 23.4 0.63

12 1--4 4 3.9139 3.7728 3.8844 3.791 2.958% 0.725% 1.267% 31.5 0.57


Wave-

length


400 20.23 13.84 10.78 8.69

420 25.34 18.15 14.46 11.72

440 24.56 17.15 13.43 10.70

460 22.16 14.91 11.45 9.00

480 20.19 13.09 9.81 7.54

500 18.39 11.61 8.58 6.47

520 16.21 9.88 7.02 5.22

540 13.58 7.95 5.57 4.12

560 12.07 6.85 4.72 3.49

580 10.54 5.76 3.94 2.95

600 8.97 4.76 3.27 2.49

620 7.78 4.06 2.81 2.19

640 6.57 3.39 2.40 1.94

660 5.86 3.12 2.23 1.85

680 7.77 4.09 2.91 2.33

700 15.83 9.63 7.01 5.31



290


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1162 31.0896 16.7 69.5 1.066 11.76 743 3.42 8.63 36.03 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

7.1 1 only 1 6.9125 6.6961 6.8589 6.6845 2.431% 0.153% 0.226% 7.4 0.68

7.1 1--2 2 6.9989 6.7661 6.9954 6.7766 3.389% 0.357% 0.716% 19.5 0.50

7.1 1--3 3 6.9641 6.7352 7.0001 6.7439 3.933% 0.527% 1.171% 29.5 0.45

7.1 1--4 4 6.9822 6.7466 7.0094 6.7845 3.895% 0.645% 1.534% 37.0 0.42

7.1 1--5 5 6.9435 6.7046 6.9901 6.7499 4.258% 0.849% 2.028% 46.7 0.42

7.1 1--6 6 6.9078 6.6907 6.9952 6.7343 4.551% 0.998% 2.361% 53.0 0.42

7.1 1--7 7 6.915 6.6881 6.9739 6.7501 4.273% 1.138% 2.680% 57.4 0.42


Wave-

length


400 20.08 11.74 8.92 7.52 6.23 5.56 5.03

420 25.40 15.80 12.30 10.38 8.43 7.34 6.60

440 24.71 14.73 11.21 9.30 7.39 6.39 5.72

460 22.34 12.59 9.32 7.67 6.01 5.15 4.61

480 20.36 10.85 7.79 6.28 4.86 4.14 3.71

500 18.59 9.55 6.68 5.34 4.11 3.50 3.15

520 16.44 7.96 5.41 4.28 3.29 2.82 2.55

540 13.85 6.41 4.28 3.39 2.62 2.27 2.06

560 12.41 5.51 3.67 2.92 2.28 1.99 1.83

580 11.05 4.69 3.13 2.50 2.00 1.78 1.66

600 9.52 3.94 2.68 2.18 1.79 1.63 1.55

620 8.28 3.40 2.36 1.96 1.66 1.54 1.49

640 7.03 2.94 2.14 1.84 1.63 1.55 1.51

660 6.24 2.81 2.10 1.85 1.69 1.64 1.62

680 8.00 3.52 2.62 2.26 2.02 1.93 1.87

700 15.81 7.88 5.60 4.64 3.82 3.45 3.18



291


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1162 31.0896 16.7 69.5 1.066 11.76 743 3.42 8.63 36.03 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

8 1 only 1 6.0851 5.8856 6.0242 5.8739 2.355% 0.167% 0.235% 7.7 0.71

8 1--2 2 6.0246 5.8307 6.0216 5.8278 3.274% 0.355% 0.651% 18.0 0.54

8 1--3 3 6.0942 5.9039 6.1043 5.9017 3.394% 0.531% 1.048% 26.9 0.51

8 1--4 4 6.0591 5.8724 6.1037 5.8845 3.939% 0.735% 1.598% 38.2 0.46

8 1--5 5 6.1861 5.988 6.2333 6.0167 4.097% 0.926% 2.054% 47.2 0.45

8 1--6 6 6.0467 5.8509 6.11 5.884 4.428% 1.022% 2.237% 50.7 0.46

8 1--7 7 6.0202 5.8246 6.1046 5.8788 4.807% 1.196% 2.665% 57.2 0.45


Wave-

length


400 19.57 12.31 9.46 7.18 6.16 5.75 5.13

420 24.81 16.60 12.96 9.88 8.29 7.63 6.74

440 24.19 15.60 11.93 8.89 7.32 6.68 5.87

460 21.93 13.44 10.04 7.35 5.98 5.41 4.73

480 20.02 11.64 8.48 6.03 4.86 4.38 3.81

500 18.29 10.28 7.34 5.14 4.12 3.72 3.23

520 16.19 8.65 5.96 4.13 3.31 3.00 2.61

540 13.60 6.95 4.73 3.28 2.63 2.41 2.10

560 12.17 5.97 4.05 2.83 2.27 2.09 1.86

580 10.80 5.06 3.44 2.44 1.99 1.87 1.66

600 9.27 4.22 2.92 2.13 1.77 1.69 1.53

620 8.06 3.62 2.55 1.91 1.62 1.58 1.45

640 6.81 3.08 2.26 1.79 1.58 1.56 1.45

660 6.06 2.87 2.19 1.82 1.61 1.63 1.51

680 7.81 3.66 2.75 2.22 1.95 1.93 1.76

700 15.62 8.51 6.09 4.51 3.80 3.53 3.17



292


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath

pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1162 31.0896 16.7 69.5 1.129 11.7 747 3.62 8.63 36.03 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 7.9444 7.6489 7.801 7.6285 1.989% 0.171% 0.204% 6.8 0.84

6.3 1--2 2 7.6963 7.3949 7.6295 7.4014 3.172% 0.366% 0.671% 18.5 0.55

6.3 1--3 3 7.696 7.4129 7.6787 7.4273 3.586% 0.588% 1.374% 33.7 0.43

6.3 1--4 4 7.6995 7.3936 7.651 7.4227 3.481% 0.718% 1.629% 38.9 0.44

6.3 1--5 5 7.7576 7.4609 7.758 7.5016 3.982% 0.955% 2.133% 48.7 0.45

6.3 1--5 5 7.5935 7.3037 7.6196 7.3553 4.325% 0.950% 2.088% 47.8 0.45

6.3 1--7 7 7.7599 7.4576 7.7748 7.5221 4.253% 1.311% 2.919% 60.0 0.45


Wave-

length


400 20.29 12.05 7.97 7.15 5.94 6.02 4.74

420 25.62 16.25 10.97 9.91 8.01 8.19 6.23

440 25.26 15.27 10.04 8.90 7.07 7.20 5.41

460 23.17 13.13 8.40 7.35 5.78 5.85 4.37

480 21.34 11.35 6.95 6.00 4.67 4.71 3.52

500 19.62 9.99 5.94 5.10 3.94 3.98 2.98

520 17.47 8.38 4.78 4.10 3.17 3.20 2.42

540 14.78 6.75 3.77 3.23 2.53 2.56 1.98

560 13.25 5.79 3.22 2.77 2.19 2.21 1.75

580 11.80 4.91 2.74 2.38 1.92 1.95 1.59

600 10.15 4.11 2.35 2.07 1.71 1.76 1.50

620 8.84 3.54 2.08 1.87 1.60 1.62 1.43

640 7.51 3.05 1.91 1.77 1.58 1.60 1.49

660 6.60 2.86 1.89 1.78 1.61 1.66 1.58

680 8.53 3.63 2.36 2.19 1.93 1.97 1.83

700 16.88 8.28 5.09 4.48 3.68 3.69 3.08



293


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath

pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1162 31.0896 16.7 69.5 1.129 11.7 747 3.62 8.63 36.03 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

12 1 only 1 3.7295 3.6009 3.7002 3.5896 2.758% 0.221% 0.290% 9.2 0.76

12 1--2 2 3.997 3.8643 4.0212 3.8692 4.060% 0.456% 0.801% 21.4 0.57

12 1--3 3 3.9658 3.8243 4.0051 3.8387 4.728% 0.723% 1.375% 33.7 0.53

12 1--4 4 3.8058 3.6712 3.8291 3.6938 4.301% 0.939% 1.867% 43.6 0.50

12 1--5 5 3.9635 3.8259 4.021 3.8633 5.099% 1.219% 2.274% 51.4 0.54

12 1--6 6 3.955 3.8093 4.044 3.8612 6.161% 1.547% 3.116% 61.9 0.50

12 1--7 7 3.933 3.7989 3.9968 3.8481 5.209% 1.711% 3.613% 65.7 0.47


Wave-

length


400 17.75 11.06 8.21 6.61 5.78 4.69 4.34

420 22.65 14.93 11.24 9.02 7.71 6.05 5.57

440 22.01 13.97 10.23 8.04 6.76 5.25 4.81

460 19.84 11.98 8.51 6.63 5.50 4.25 3.87

480 17.97 10.28 7.02 5.40 4.44 3.43 3.12

500 16.32 9.02 5.99 4.58 3.74 2.90 2.65

520 14.35 7.47 4.82 3.67 3.01 2.37 2.16

540 11.99 5.98 3.80 2.91 2.40 1.93 1.79

560 10.65 5.11 3.24 2.48 2.08 1.71 1.61

580 9.37 4.30 2.75 2.15 1.83 1.56 1.48

600 7.99 3.58 2.34 1.87 1.64 1.45 1.41

620 6.88 3.07 2.07 1.69 1.52 1.39 1.37

640 5.81 2.62 1.89 1.59 1.49 1.43 1.43

660 5.22 2.48 1.84 1.63 1.56 1.54 1.54

680 6.78 3.22 2.35 1.98 1.85 1.78 1.78

700 13.96 7.52 5.09 4.07 3.51 3.02 2.87



294


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath

pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)T3675 34.75 14.7 62.2 1.932 11.5 836 4.82 8.63 36.03 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 8.209646 7.9091 8.2466 7.9158 4.267% 0.385% 0.861% 22.8 0.45

6.3 1--2 2 8.15951 7.8608 8.3462 7.8953 6.175% 0.631% 1.739% 41.0 0.36

6.3 1--2 2 8.167399 7.8684 8.2713 7.8062 5.120% 0.653% 1.748% 41.2 0.37

6.3 1--4 4 8.174977 7.8757 8.4725 7.9623 7.578% 1.222% 4.299% 70.1 0.28

6.3 1--5 5 8.167399 7.8684 8.5453 7.9757 8.603% 1.495% 5.891% 78.7 0.25

6.3 1--6 6 8.23736 7.9358 8.5928 8.0797 8.279% 1.741% 7.325% 85.3 0.24


Wave-

length


400 11.09 7.17 7.10 4.09 3.44 3.00

420 15.07 9.91 9.83 5.28 4.34 3.72

440 13.96 8.85 8.81 4.58 3.74 3.21

460 11.80 7.27 7.24 3.70 3.05 2.62

480 10.10 5.93 5.91 3.00 2.48 2.15

500 8.82 5.02 5.01 2.55 2.14 1.88

520 7.21 4.00 3.99 2.08 1.78 1.59

540 5.72 3.14 3.13 1.71 1.51 1.40

560 4.81 2.65 2.64 1.53 1.38 1.30

580 4.00 2.26 2.26 1.39 1.29 1.23

600 3.29 1.93 1.91 1.30 1.22 1.19

620 2.82 1.72 1.72 1.26 1.20 1.17

640 2.42 1.57 1.57 1.25 1.22 1.21

660 2.32 1.56 1.56 1.34 1.33 1.31

680 3.07 1.98 1.96 1.58 1.54 1.53

700 7.25 4.20 4.20 2.61 2.32 2.13



295


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath

pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)T3675 34.75 14.7 62.2 1.932 11.5 836 4.82 8.63 36.03 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

7.1 1 only 1 7.0445 6.8512 7.1585 6.8528 4.485% 0.359% 0.811% 21.7 0.44

7.1 1--2 2 7.07 6.8743 7.3384 6.9061 6.751% 0.691% 1.824% 42.7 0.38

7.1 1--3 3 7.2324 7.0316 7.5021 7.0851 6.691% 1.001% 2.701% 57.7 0.37

7.1 1--4 4 7.1538 6.9599 7.4319 7.0392 6.782% 1.476% 4.598% 71.8 0.32

7.1 1--5 5 7.1736 6.9814 7.5533 7.08 8.192% 1.773% 6.253% 80.4 0.28

7.1 1--6 6 7.1894 6.9918 7.5306 7.1185 7.706% 2.153% 7.877% 87.6 0.27


Wave-

length


400 11.62 6.97 5.30 3.99 3.40 2.93

420 15.70 9.58 6.97 5.10 4.33 3.64

440 14.54 8.52 6.11 4.41 3.73 3.13

460 12.32 6.97 4.95 3.57 3.03 2.55

480 10.56 5.69 3.99 2.90 2.46 2.08

500 9.25 4.82 3.37 2.47 2.11 1.83

520 7.61 3.84 2.70 2.02 1.75 1.55

540 6.04 3.01 2.15 1.67 1.48 1.36

560 5.08 2.55 1.85 1.50 1.34 1.27

580 4.22 2.18 1.64 1.37 1.26 1.21

600 3.46 1.86 1.46 1.28 1.19 1.16

620 2.94 1.67 1.37 1.24 1.17 1.15

640 2.51 1.55 1.34 1.25 1.19 1.18

660 2.39 1.56 1.39 1.34 1.29 1.28

680 3.18 1.97 1.66 1.57 1.50 1.49

700 7.55 4.09 3.14 2.55 2.28 2.08



296


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath

pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)T3675 34.75 14.7 62.2 1.932 11.5 836 4.82 8.63 36.03 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

12 1 only 1 6.1357 5.9461 6.2804 5.9571 5.622% 0.487% 0.841% 22.3 0.58

12 1--2 2 6.146 5.9627 6.4084 5.9993 7.475% 0.897% 1.768% 41.6 0.51

12 1--3 3 5.7399 5.5191 5.9891 5.579 8.516% 1.467% 2.980% 60.6 0.49

12 1--4 4 5.9484 5.9925 6.4706 6.086 7.978% 1.698% 4.228% 69.6 0.40

12 1--5 5 5.82 5.5935 6.2417 5.7228 11.588% 2.189% 7.207% 84.8 0.30

12 1--6 6 6.1973 6.0232 6.5289 6.1572 8.396% 2.463% 8.470% 90.0 0.29


Wave-

length


400 11.27 7.11 5.05 4.15 3.17 2.87

420 15.17 9.67 6.54 5.26 3.89 3.49

440 13.98 8.62 5.72 4.56 3.35 3.00

460 11.83 7.08 4.62 3.69 2.74 2.46

480 10.12 5.77 3.73 2.99 2.23 2.01

500 8.87 4.90 3.14 2.54 1.92 1.76

520 7.28 3.91 2.54 2.07 1.61 1.51

540 5.81 3.09 2.03 1.73 1.40 1.33

560 4.92 2.62 1.76 1.54 1.29 1.24

580 4.10 2.24 1.57 1.41 1.22 1.19

600 3.39 1.91 1.41 1.31 1.17 1.14

620 2.92 1.72 1.34 1.28 1.17 1.13

640 2.51 1.60 1.30 1.28 1.20 1.15

660 2.42 1.61 1.37 1.38 1.32 1.29

680 3.18 2.00 1.63 1.61 1.52 1.50

700 7.29 4.18 3.02 2.61 2.22 2.10



297


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)4257 31.09 16.7 69.5 2.084 11.62 847 4.71 8.63 36.03 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 8.3432 8.0041 8.3513 7.9669 4.338% 0.416% 0.951% 24.8 0.44

6.3 1--2 2 8.3076 7.9612 8.4339 7.9705 5.938% 0.652% 1.796% 42.2 0.36

6.3 1--3 3 7.7893 7.4662 7.9978 7.4984 7.120% 0.936% 2.622% 56.7 0.36

6.3 1--4 4 7.9303 7.5905 8.1786 7.6566 7.748% 1.383% 4.261% 69.8 0.32

6.3 1--5 5 8.3555 8.0023 8.6951 8.0934 8.658% 1.759% 5.960% 79.0 0.30

6.3 1--6 6 7.6623 7.3511 7.9466 7.4567 8.101% 2.089% 7.179% 84.6 0.29


Wave-

length


400 10.36 6.97 5.21 4.03 3.34 2.96

420 14.01 9.50 6.77 5.11 4.11 3.55

440 12.96 8.50 5.95 4.44 3.56 3.07

460 10.95 6.98 4.83 3.61 2.91 2.52

480 9.32 5.71 3.92 2.95 2.40 2.09

500 8.12 4.83 3.32 2.52 2.08 1.84

520 6.62 3.87 2.69 2.06 1.75 1.58

540 5.25 3.05 2.17 1.71 1.51 1.41

560 4.43 2.60 1.88 1.54 1.39 1.33

580 3.68 2.21 1.68 1.41 1.30 1.26

600 3.05 1.90 1.51 1.32 1.25 1.23

620 2.66 1.66 1.43 1.29 1.25 1.25

640 2.34 1.59 1.40 1.30 1.26 1.27

660 2.27 1.59 1.45 1.38 1.36 1.38

680 2.95 1.97 1.70 1.59 1.55 1.56

700 6.82 4.15 3.15 2.61 2.31 2.15



298


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath

pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1169 31.09 16.7 69.5 2.34 11.6 888 6.27 8.63 36.03 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 8.8602 8.6341 9.0951 8.6456 5.339% 0.339% 0.775% 20.8 0.44

6.3 1--2 2 8.1011 7.8951 8.4853 7.9318 7.476% 0.702% 1.773% 41.7 0.40

6.3 1--3 3 8.4191 8.2117 8.8716 8.2815 8.036% 1.108% 2.698% 57.6 0.41

6.3 1--4 4 8.6023 8.3729 9.0466 8.4835 8.046% 1.430% 4.058% 68.6 0.35

6.3 1--5 5 8.3565 8.1541 8.8352 8.2801 8.353% 1.808% 5.701% 77.7 0.32

6.3 1--6 6 8.3364 8.1265 8.9261 8.2935 9.839% 2.126% 6.905% 83.4 0.31

6.3 1--7 7 8.1278 7.9263 8.6595 8.0976 9.250% 2.474% 8.728% 91.0 0.28


Wave-

length


400 11.93 7.15 5.24 4.23 3.48 3.08 2.72

420 15.97 9.80 6.91 5.43 4.41 3.79 3.30

440 14.83 8.72 6.03 4.71 3.81 3.26 2.84

460 12.58 7.14 4.86 3.78 3.08 2.65 2.33

480 10.80 5.82 3.92 3.06 2.51 2.18 1.92

500 9.47 4.93 3.31 2.60 2.17 1.90 1.70

520 7.82 3.93 2.67 2.12 1.78 1.61 1.46

540 6.23 3.09 2.14 1.75 1.52 1.41 1.30

560 5.25 2.61 1.85 1.56 1.39 1.32 1.23

580 4.34 2.21 1.64 1.42 1.30 1.26 1.18

600 3.57 1.89 1.47 1.32 1.24 1.22 1.16

620 3.05 1.70 1.40 1.29 1.23 1.22 1.17

640 2.61 1.57 1.37 1.29 1.26 1.28 1.24

660 2.51 1.60 1.42 1.39 1.35 1.41 1.39

680 3.31 2.00 1.70 1.62 1.55 1.60 1.59

700 7.97 4.26 3.16 2.71 2.37 2.25 2.13



299


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1134 31.09 16.7 69.5 2.314 11.89 805 5.17 8.63 36.03 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 7.598 7.2978 7.632 7.274 4.579% 0.358% 0.669% 18.4 0.54

6.3 1--2 2 7.7048 7.4103 7.8917 7.3868 6.496% 0.757% 1.685% 40.0 0.45

6.3 1--3 3 7.7848 7.4763 7.9975 7.4662 6.971% 1.245% 2.699% 57.6 0.46

6.3 1--4 4 7.6821 7.3905 7.9348 7.4245 7.365% 1.500% 3.958% 67.9 0.38

6.3 1--5 5 7.7462 7.4572 8.0651 7.5261 8.152% 1.859% 5.370% 76.0 0.35

6.3 1--6 6 7.727 7.4248 8.1051 7.53 9.163% 2.177% 6.677% 82.4 0.33


Wave-

length


400 12.64 7.21 5.16 4.15 3.55 3.15

420 17.04 9.96 6.78 5.35 4.43 3.87

440 15.90 8.92 5.89 4.64 3.83 3.32

460 13.59 7.33 4.83 3.76 3.12 2.71

480 11.76 5.99 3.92 3.06 2.54 2.23

500 10.34 5.10 3.32 2.62 2.22 1.96

520 8.63 4.07 2.68 2.14 1.83 1.65

540 6.90 3.21 2.14 1.77 1.56 1.44

560 5.88 2.73 1.87 1.58 1.43 1.34

580 4.92 2.34 1.65 1.44 1.34 1.27

600 4.05 1.99 1.49 1.35 1.27 1.23

620 3.43 1.76 1.38 1.29 1.25 1.21

640 2.90 1.63 1.35 1.29 1.29 1.26

660 2.72 1.61 1.38 1.36 1.38 1.36

680 3.54 2.01 1.62 1.57 1.57 1.55

700 8.45 4.23 3.07 2.62 2.38 2.22



300


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1134 31.09 16.7 69.5 2.314 11.89 805 5.17 8.63 36.03 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

7.1 1 only 1 6.8377 6.6735 7.0041 6.647 4.954% 0.396% 0.699% 19.1 0.57

7.1 1--2 2 6.9015 6.6689 7.1094 6.6723 6.605% 0.766% 1.742% 41.1 0.44

7.1 1--3 3 6.6829 6.5137 7.0283 6.5492 7.900% 1.260% 2.647% 57.0 0.48

7.1 1--4 4 6.9189 6.6779 7.1999 6.7504 7.817% 1.477% 4.112% 68.9 0.36

7.1 1--5 5 6.8978 6.7207 7.3111 6.8215 8.785% 1.833% 6.694% 82.5 0.27

7.1 1--6 6 7.0832 6.8714 7.5302 7.0116 9.588% 2.150% 7.551% 86.2 0.28

7.1 1--7 7 6.92 6.7401 7.4097 6.9168 9.935% 2.644% 10.504% 97.4 0.25


Wave-

length


400 12.45 7.19 5.41 4.22 3.32 3.06 2.57

420 16.76 9.88 7.09 5.40 4.11 3.77 3.00

440 15.61 8.81 6.19 4.67 3.53 3.22 2.57

460 13.30 7.22 5.00 3.78 2.87 2.63 2.13

480 11.45 5.89 4.03 3.06 2.32 2.13 1.75

500 10.08 4.99 3.41 2.61 2.02 1.88 1.57

520 8.40 4.00 2.74 2.14 1.69 1.58 1.37

540 6.71 3.13 2.18 1.74 1.43 1.37 1.23

560 5.69 2.66 1.88 1.55 1.32 1.28 1.17

580 4.77 2.27 1.66 1.42 1.25 1.22 1.13

600 3.92 1.94 1.49 1.32 1.19 1.17 1.11

620 3.33 1.71 1.37 1.26 1.16 1.16 1.11

640 2.81 1.58 1.32 1.27 1.19 1.20 1.17

660 2.65 1.57 1.36 1.34 1.29 1.31 1.29

680 3.47 1.98 1.63 1.57 1.48 1.49 1.48

700 8.17 4.20 3.11 2.64 2.22 2.14 1.96



301


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1134 31.09 16.7 69.5 2.314 11.89 805 5.17 8.63 36.03 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

8 1 only 1 6.111 5.8975 6.2071 5.8698 5.250% 0.439% 0.705% 19.3 0.62

8 1--2 2 6.0613 5.8551 6.2451 5.8486 6.661% 0.863% 1.680% 39.9 0.51

8 1--3 3 6.0564 5.8397 6.2566 5.8536 7.139% 1.299% 2.390% 53.5 0.54

8 1--4 4 6.0814 5.8677 6.3564 5.9073 8.329% 1.593% 3.537% 65.2 0.45

8 1--5 5 5.9915 5.7855 6.2681 5.8422 8.342% 2.013% 5.328% 75.8 0.38

8 1--6 6 6.1051 5.8809 6.443 5.9587 9.558% 2.336% 6.044% 79.4 0.39

8 1--7 7 5.4855 5.2819 5.7895 5.3765 9.610% 2.802% 8.573% 90.4 0.33


Wave-

length


400 12.11 7.09 5.52 4.43 3.63 3.36 2.81

420 16.32 9.72 7.25 5.69 4.53 4.14 3.39

440 15.16 8.69 6.35 4.94 3.89 3.56 2.90

460 12.89 7.15 5.15 3.98 3.15 2.89 2.37

480 11.09 5.85 4.17 3.22 2.55 2.36 1.93

500 9.75 4.99 3.54 2.75 2.23 2.07 1.71

520 8.16 4.03 2.87 2.26 1.85 1.73 1.48

540 6.55 3.18 2.30 1.84 1.57 1.48 1.31

560 5.61 2.74 2.01 1.65 1.44 1.38 1.24

580 4.75 2.35 1.78 1.50 1.34 1.30 1.19

600 3.96 2.03 1.59 1.38 1.27 1.26 1.16

620 3.39 1.81 1.48 1.33 1.24 1.23 1.17

640 2.89 1.69 1.45 1.33 1.27 1.28 1.21

660 2.75 1.69 1.49 1.41 1.36 1.38 1.34

680 3.49 2.11 1.76 1.64 1.57 1.56 1.54

700 7.93 4.26 3.26 2.79 2.41 2.32 2.09



302


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1134 31.09 16.7 69.5 2.314 11.89 805 5.17 8.63 39.40 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

12 1 only 1 3.8875 3.7511 3.9984 3.7398 6.593% 0.511% 0.811% 20.5 0.63

12 1--2 2 3.9071 3.7686 4.0917 3.7811 8.573% 0.929% 1.554% 41.3 0.60

12 1--3 3 4.0031 3.861 4.2138 3.8945 9.138% 1.364% 2.938% 58.4 0.46

12 1--4? 4 3.9513 3.8107 4.162 3.8586 9.219% 1.941% 4.454% 70.7 0.44

12 1--5? 5 4.1207 3.9709 4.398 4.047 10.756% 2.348% 5.787% 78.7 0.41

12 1--6 6 3.8214 3.6823 4.1031 3.7702 11.428% 2.947% 8.498% 90.2 0.35

12 1--7 7 3.9128 3.771 4.186 3.8829 11.005% 3.366% 10.167% 95.3 0.33


Wave-

length


400 11.69 7.10 5.10 4.05 3.48 2.90 2.60

420 15.76 9.72 6.66 5.15 4.31 3.54 3.08

440 14.58 8.61 5.81 4.44 3.71 3.02 2.63

460 12.37 7.03 4.71 3.58 3.01 2.46 2.17

480 10.61 5.72 3.80 2.91 2.44 1.99 1.77

500 9.32 4.85 3.23 2.49 2.13 1.76 1.59

520 7.76 3.90 2.62 2.04 1.76 1.49 1.38

540 6.22 3.07 2.10 1.69 1.50 1.30 1.25

560 5.32 2.63 1.84 1.54 1.39 1.24 1.20

580 4.49 2.26 1.63 1.40 1.30 1.17 1.15

600 3.73 1.95 1.48 1.31 1.23 1.14 1.14

620 3.19 1.74 1.39 1.27 1.22 1.13 1.14

640 2.73 1.63 1.37 1.28 1.25 1.18 1.21

660 2.58 1.63 1.43 1.35 1.36 1.30 1.34

680 3.34 2.02 1.68 1.55 1.58 1.50 1.53

700 7.54 4.14 3.08 2.57 2.39 2.10 2.00



303


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)t3688 32.92 15.8 65.7 2.417 11.82 867 4.93 8.63 39.40 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

7.1 1 only 1 7.1993 6.9937 7.2912 7.0139 4.254% 0.402% 0.857% 22.6 0.47

7.1 1--2 2 7.214 7.0135 7.4253 7.0657 5.872% 0.766% 1.776% 44.9 0.43

7.1 1--3 3 7.2494 7.0394 7.4845 7.1113 6.323% 1.060% 2.900% 58.0 0.37

7.1 1--4 4 7.1546 6.9528 7.5403 7.0535 8.450% 1.501% 5.082% 74.7 0.30

7.1 1--5 5 7.1444 6.9383 7.4825 7.0733 7.843% 1.825% 6.725% 83.3 0.27

7.1 1--6 6 7.1714 6.9694 7.486 7.1378 7.412% 2.167% 8.503% 90.2 0.25

7.1 1--6,6 7 7.1765 6.9675 7.5829 7.1726 8.832% 2.572% 11.771% 99.3 0.22


Wave-

length


400 11.30 6.64 5.27 3.80 3.21 2.80 2.40

420 15.28 9.01 6.91 4.80 3.97 3.34 2.83

440 14.10 8.00 6.05 4.15 3.42 2.87 2.44

460 11.93 6.57 4.90 3.36 2.79 2.38 2.05

480 10.17 5.33 3.94 2.71 2.26 1.94 1.69

500 8.89 4.53 3.34 2.34 1.98 1.73 1.53

520 7.27 3.61 2.67 1.89 1.65 1.47 1.34

540 5.76 2.85 2.14 1.59 1.43 1.32 1.22

560 4.86 2.41 1.84 1.43 1.32 1.25 1.16

580 4.04 2.08 1.63 1.33 1.24 1.19 1.12

600 3.32 1.80 1.46 1.26 1.19 1.16 1.11

620 2.85 1.62 1.37 1.23 1.17 1.17 1.11

640 2.45 1.52 1.33 1.25 1.21 1.22 1.15

660 2.32 1.53 1.36 1.33 1.29 1.34 1.26

680 3.05 1.90 1.63 1.53 1.48 1.55 1.44

700 7.29 3.89 3.07 2.45 2.18 2.10 1.88



304


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1156 36.58 14.1 59.1 2.572 11.72 797 5.55 8.63 39.40 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 7.556 7.2736 7.583 7.2751 4.25% 0.333% 0.773% 18.7 0.43

6.3 1--2 2 7.4803 7.2056 7.651 7.2164 6.18% 0.639% 1.381% 38.2 0.46

6.3 1--3 3 7.6443 7.3585 7.8813 7.3934 7.10% 0.961% 2.715% 56.2 0.35

6.3 1--4 4 7.8569 7.5632 8.1077 7.6298 7.20% 1.262% 3.559% 63.9 0.35

6.3 1--5 5 7.5259 7.2366 7.8535 7.3429 8.52% 1.795% 5.705% 78.3 0.31

6.3 1--6 6 7.7609 7.4636 8.1188 7.5897 8.78% 2.090% 6.706% 83.2 0.31

6.3 1--7 7 7.7295 7.4312 8.0923 7.6072 8.90% 2.432% 8.581% 90.5 0.28


Wave-

length


400 12.60 7.55 5.36 4.57 3.46 3.11 2.66

420 16.95 10.42 7.09 5.96 4.35 3.84 3.19

440 15.82 9.38 6.21 5.17 3.74 3.28 2.73

460 13.54 7.73 5.03 4.15 3.02 2.66 2.26

480 11.68 6.31 4.05 3.35 2.44 2.14 1.84

500 10.26 5.36 3.41 2.83 2.10 1.87 1.63

520 8.57 4.30 2.76 2.32 1.76 1.60 1.44

540 6.85 3.38 2.21 1.89 1.50 1.41 1.31

560 5.79 2.86 1.90 1.66 1.38 1.32 1.24

580 4.82 2.43 1.67 1.50 1.29 1.25 1.21

600 3.95 2.06 1.50 1.39 1.25 1.23 1.20

620 3.36 1.82 1.41 1.33 1.24 1.24 1.24

640 2.85 1.68 1.39 1.36 1.30 1.32 1.35

660 2.70 1.65 1.42 1.42 1.43 1.47 1.52

680 3.56 2.11 1.72 1.69 1.66 1.71 1.76

700 8.59 4.57 3.24 2.92 2.46 2.37 2.24



305


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1156 36.58 14.1 59.1 2.572 11.72 797 5.55 8.63 39.40 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

7.1 1 only 1 6.9734 6.7622 7.0402 6.7304 4.11% 0.318% 0.744% 17.4 0.43

7.1 1--2 2 7.0212 6.7926 7.1906 6.8108 5.86% 0.591% 1.365% 37.8 0.43

7.1 1--3 3 6.8123 6.5915 7.086 6.6331 7.50% 0.987% 2.524% 54.2 0.39

7.1 1--4 4 6.9715 6.7395 7.2619 6.824 7.75% 1.423% 4.099% 68.1 0.35

7.1 1--5 5 6.9565 6.7298 7.3058 6.8297 8.56% 1.724% 5.340% 76.3 0.32

7.1 1--6 6 6.9443 6.7022 7.3574 6.8302 9.78% 2.231% 6.720% 83.3 0.33

7.1 1--7 7 6.8847 6.6635 7.2592 6.8068 8.94% 2.496% 7.807% 87.8 0.32


Wave-

length


400 13.21 7.64 5.59 4.24 3.59 3.13 2.82

420 17.66 10.55 7.38 5.42 4.50 3.81 3.39

440 16.52 9.51 6.47 4.69 3.85 3.26 2.88

460 14.16 7.84 5.24 3.79 3.11 2.65 2.37

480 12.27 6.40 4.23 3.06 2.50 2.14 1.93

500 10.81 5.44 3.57 2.58 2.15 1.87 1.69

520 9.11 4.35 2.87 2.11 1.79 1.59 1.48

540 7.31 3.42 2.30 1.75 1.53 1.39 1.34

560 6.22 2.90 1.97 1.56 1.41 1.32 1.28

580 5.20 2.45 1.74 1.44 1.33 1.26 1.24

600 4.28 2.08 1.55 1.34 1.28 1.24 1.23

620 3.61 1.83 1.44 1.30 1.27 1.25 1.25

640 3.06 1.67 1.41 1.33 1.34 1.34 1.37

660 2.88 1.66 1.47 1.42 1.47 1.50 1.56

680 3.79 2.10 1.79 1.66 1.69 1.71 1.82

700 9.00 4.60 3.40 2.77 2.53 2.35 2.35



306


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1156 36.58 14.1 59.1 2.572 11.72 797 5.55 8.63 39.40 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

7.1 2 only 1 6.983 6.7611 7.0953 6.7585 4.94% 0.399% 0.812% 20.5 0.49

7.1 2,2 2 6.8036 6.5773 6.9899 6.5918 6.27% 0.728% 1.443% 39.4 0.50

7.1 2,2-3 3 7.0364 6.7992 7.3311 6.8485 7.82% 1.129% 2.753% 56.6 0.41

7.1 2,2-4 4 6.9084 6.6972 7.2414 6.7656 8.13% 1.515% 3.770% 65.6 0.40

7.1 2,2-5 5 7.0571 6.8152 7.4134 6.9268 8.78% 1.980% 5.695% 78.2 0.35


Wave-

length


400 11.87 7.40 5.40 4.41 3.51

420 15.95 10.19 7.11 5.69 4.36

440 14.82 9.12 6.18 4.89 3.73

460 12.62 7.49 4.98 3.92 3.01

480 10.86 6.11 4.01 3.15 2.43

500 9.52 5.18 3.38 2.67 2.09

520 7.89 4.15 2.72 2.18 1.75

540 6.30 3.27 2.19 1.81 1.50

560 5.33 2.77 1.89 1.62 1.38

580 4.44 2.35 1.68 1.48 1.30

600 3.65 2.01 1.50 1.40 1.25

620 3.12 1.79 1.40 1.34 1.24

640 2.67 1.67 1.37 1.39 1.31

660 2.55 1.66 1.41 1.50 1.45

680 3.35 2.12 1.71 1.76 1.68

700 7.92 4.47 3.21 2.90 2.48



307


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1156 36.58 14.1 59.1 2.572 11.72 797 5.55 8.63 39.40 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

8 1 only 1 6.0265 5.8348 6.1145 5.8318 4.79% 0.369% 0.771% 18.6 0.48

8 1--2 2 6.0783 5.8852 6.2864 5.9 6.82% 0.729% 1.337% 37.3 0.55

8 1--3 3 5.9853 5.7931 6.2608 5.8401 8.07% 1.154% 2.445% 53.3 0.47

8 1--4 4 6.09 5.8885 6.3461 5.96 7.77% 1.532% 3.925% 66.8 0.39

8 1--5 5 6.0606 5.8632 6.3572 5.9571 8.43% 1.927% 5.307% 76.1 0.36

8 1--6 6 6.0638 5.8725 6.4474 5.9869 9.79% 2.310% 6.765% 83.5 0.34

8 1--7 7 6.0695 5.8727 6.4365 6.0203 9.60% 2.687% 8.083% 88.8 0.33


Wave-

length


400 12.86 7.76 5.69 4.39 3.66 3.17 2.83

420 17.19 10.61 7.52 5.65 4.60 3.89 3.37

440 15.96 9.55 6.56 4.88 3.93 3.30 2.87

460 13.60 7.88 5.32 3.93 3.17 2.66 2.35

480 11.74 6.46 4.30 3.18 2.57 2.16 1.91

500 10.31 5.49 3.63 2.70 2.21 1.88 1.70

520 8.63 4.40 2.91 2.20 1.82 1.58 1.46

540 6.91 3.46 2.33 1.80 1.55 1.40 1.33

560 5.85 2.93 2.01 1.60 1.42 1.32 1.27

580 4.87 2.48 1.76 1.45 1.32 1.25 1.21

600 4.00 2.11 1.58 1.35 1.27 1.23 1.22

620 3.39 1.87 1.46 1.28 1.24 1.22 1.22

640 2.87 1.73 1.43 1.30 1.29 1.30 1.33

660 2.70 1.70 1.48 1.38 1.42 1.46 1.51

680 3.58 2.18 1.78 1.63 1.65 1.70 1.75

700 8.55 4.72 3.43 2.80 2.53 2.37 2.26



309


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1156 36.58 14.1 59.1 2.572 11.72 797 5.55 8.63 39.40 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

12 1 only 1 3.9582 3.8257 4.0678 3.8273 6.33% 0.472% 0.812% 20.6 0.58

12 1--2 2 3.9604 3.8242 4.1419 3.8493 8.31% 0.882% 1.542% 41.1 0.57

12 1--3 3 3.9143 3.7782 4.148 3.8214 9.79% 1.407% 2.839% 57.4 0.50

12 1--4 4 3.8219 3.688 4.0574 3.7553 10.02% 1.860% 4.625% 71.8 0.40

12 1--5 5 3.8788 3.7391 4.1079 3.8222 9.86% 2.278% 6.089% 80.3 0.37

12 1--6 6 3.8516 3.7129 4.1444 3.8153 11.62% 2.747% 8.421% 90.0 0.33

12 1--7 7 3.9529 3.8151 4.2469 3.9385 11.32% 3.149% 9.766% 94.2 0.32


Wave-

length


400 11.88 7.26 5.34 4.05 3.43 2.90 2.64

420 15.83 9.93 6.96 5.12 4.23 3.53 3.13

440 14.66 8.84 6.07 4.40 3.62 2.99 2.65

460 12.47 7.23 4.91 3.55 2.93 2.43 2.18

480 10.74 5.90 3.96 2.87 2.37 1.97 1.78

500 9.44 5.02 3.34 2.43 2.05 1.72 1.57

520 7.82 4.00 2.68 1.98 1.70 1.46 1.36

540 6.28 3.15 2.16 1.65 1.46 1.30 1.25

560 5.33 2.66 1.86 1.48 1.35 1.23 1.19

580 4.45 2.26 1.65 1.36 1.27 1.17 1.16

600 3.68 1.94 1.49 1.29 1.23 1.17 1.17

620 3.13 1.70 1.38 1.26 1.21 1.16 1.19

640 2.70 1.57 1.36 1.31 1.29 1.26 1.29

660 2.60 1.57 1.43 1.42 1.40 1.42 1.48

680 3.44 2.00 1.73 1.64 1.63 1.64 1.69

700 7.93 4.30 3.22 2.64 2.41 2.22 2.17



310


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1157 32.92 15.9 65.7 2.497 12.41 847 3.67 8.63 39.40 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 8.142 7.9097 8.2668 7.933 4.51% 0.389% 0.829% 21.4 0.47

6.3 1--2 2 8.1133 7.8832 8.3604 7.9382 6.05% 0.620% 1.543% 41.2 0.40

6.3 1--3 3 8.1656 7.9386 8.458 8.0229 6.54% 0.961% 3.340% 62.1 0.29

6.3 1--4 4 8.0574 7.8317 8.3743 7.9624 6.93% 1.433% 4.997% 74.2 0.29

6.3 1--5 5 8.0475 7.8235 8.4644 7.9766 8.19% 1.799% 7.223% 85.5 0.25

6.3 1--6 6 8.1859 7.9489 8.5703 8.1472 7.82% 2.163% 8.439% 90.0 0.26

6.3 1--6,6 7 7.9508 7.719432 8.3508 7.937 8.18% 2.453% 9.925% 94.6 0.25


Wave-

length


400 11.83 7.30 4.93 3.87 3.17 2.83 2.55

420 15.90 10.00 6.42 4.88 3.90 3.39 3.00

440 14.64 8.87 5.57 4.19 3.33 2.89 2.56

460 12.40 7.26 4.51 3.39 2.71 2.37 2.12

480 10.61 5.91 3.64 2.75 2.20 1.93 1.76

500 9.29 5.02 3.09 2.37 1.92 1.72 1.58

520 7.64 3.99 2.48 1.93 1.59 1.47 1.38

540 6.09 3.14 1.99 1.62 1.38 1.32 1.26

560 5.11 2.65 1.72 1.45 1.27 1.24 1.21

580 4.24 2.24 1.52 1.33 1.20 1.18 1.17

600 3.49 1.92 1.38 1.25 1.16 1.17 1.17

620 2.98 1.70 1.30 1.21 1.16 1.18 1.18

640 2.57 1.60 1.30 1.26 1.24 1.28 1.29

660 2.45 1.59 1.34 1.36 1.35 1.43 1.45

680 3.20 2.01 1.58 1.57 1.58 1.62 1.66

700 7.71 4.28 2.95 2.54 2.28 2.16 2.07



311


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1157 32.92 15.9 65.7 2.497 12.41 847 3.67 8.63 39.40 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

7.1 1 only 1 7.1734 6.9485 7.2544 6.9731 4.40% 0.434% 0.882% 23.7 0.49

7.1 1--2 2 7.4045 7.1267 7.5365 7.1713 5.75% 0.768% 1.674% 43.3 0.46

7.1 1--3 3 7.4093 7.2019 7.6543 7.2853 6.28% 1.143% 3.005% 59.0 0.38

7.1 1--4 4 7.421 7.2128 7.7295 7.3259 7.16% 1.550% 4.910% 73.7 0.32

7.1 1--5 5 7.4693 7.2597 7.8361 7.4102 7.94% 1.943% 6.729% 83.3 0.29

7.1 1--6 6 7.1638 6.9308 7.4922 7.0949 8.10% 2.331% 7.859% 88.0 0.30

7.1 1--6,6 7 7.3332 7.1254 7.7125 7.3283 8.24% 2.702% 9.470% 93.3 0.29


Wave-

length


400 11.16 7.05 5.30 3.93 3.28 2.90 2.57

420 15.05 9.55 6.86 4.91 3.99 3.44 2.95

440 13.78 8.42 5.95 4.22 3.42 2.92 2.52

460 11.56 6.89 4.80 3.41 2.79 2.40 2.10

480 9.85 5.60 3.87 2.77 2.28 1.98 1.75

500 8.60 4.75 3.28 2.39 1.98 1.75 1.59

520 6.99 3.77 2.62 1.93 1.64 1.50 1.38

540 5.54 2.98 2.09 1.62 1.42 1.35 1.28

560 4.66 2.52 1.82 1.46 1.32 1.27 1.23

580 3.84 2.13 1.59 1.34 1.23 1.22 1.20

600 3.17 1.85 1.45 1.27 1.19 1.21 1.21

620 2.69 1.63 1.33 1.22 1.16 1.21 1.22

640 2.34 1.56 1.34 1.27 1.23 1.30 1.34

660 2.24 1.56 1.38 1.36 1.33 1.45 1.54

680 2.96 1.94 1.64 1.55 1.51 1.64 1.77

700 7.06 4.08 3.09 2.50 2.22 2.16 2.18



312


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1157 32.92 15.9 65.7 2.497 12.41 847 3.67 8.63 39.40 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

8 1 only 1 9.5909 9.3454 9.7845 9.3589 4.70% 0.405% 0.852% 22.4 0.48

8 1--2 2 9.8043 9.5337 10.0859 9.6053 5.79% 0.731% 1.610% 42.3 0.45

8 1--3 3 9.5334 9.2729 9.8587 9.3787 6.32% 1.176% 3.190% 60.7 0.37

8 1--4 4 9.4579 9.1968 9.8563 9.3389 7.17% 1.553% 5.139% 75.1 0.30

8 1--5 5 9.736 9.4737 10.2325 9.6579 8.01% 1.877% 6.661% 83.0 0.28

8 1--6 6 9.6276 9.3484 10.0819 9.5725 7.85% 2.304% 9.218% 92.5 0.25

8 1--6,6 7 9.6693 9.4075 10.1896 9.6689 8.31% 2.705% 10.476% 96.1 0.26


Wave-

length


400 11.41 7.09 5.03 3.84 3.28 2.77 2.48

420 15.32 9.77 6.59 4.89 4.09 3.35 2.93

440 14.10 8.65 5.71 4.19 3.48 2.85 2.49

460 11.91 7.08 4.61 3.38 2.83 2.34 2.08

480 10.20 5.75 3.72 2.74 2.28 1.90 1.71

500 8.93 4.89 3.16 2.36 2.00 1.69 1.54

520 7.34 3.89 2.55 1.92 1.65 1.44 1.35

540 5.84 3.07 2.03 1.60 1.43 1.28 1.24

560 4.91 2.58 1.76 1.44 1.31 1.20 1.19

580 4.06 2.19 1.56 1.31 1.23 1.15 1.16

600 3.35 1.87 1.41 1.24 1.19 1.13 1.16

620 2.86 1.67 1.32 1.19 1.17 1.13 1.17

640 2.49 1.57 1.32 1.22 1.23 1.22 1.29

660 2.40 1.58 1.36 1.30 1.34 1.35 1.46

680 3.16 2.01 1.61 1.51 1.53 1.56 1.67

700 7.42 4.21 2.99 2.46 2.26 2.09 2.07



313


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)X3254 27.43 18.9 78.8 2.614 12.29 778 2.85 8.63 39.40 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 7.0863 6.8354 7.0327 6.832 2.89% 0.457% 0.861% 22.8 0.53

6.3 1--2 2 7.0547 6.7858 7.0644 6.8202 4.11% 0.888% 1.643% 42.8 0.54

6.3 1--3 3 7.1753 6.9132 7.2362 6.973 4.67% 1.367% 2.886% 57.9 0.47

6.3 1--5 5 7.2079 6.9466 7.3506 7.0718 5.82% 2.223% 6.482% 82.2 0.34


Wave-

length


400 10.98 6.81 5.15 3.19

420 14.90 9.23 6.65 3.82

440 13.81 8.16 5.78 3.26

460 11.67 6.64 4.65 2.64

480 9.97 5.41 3.76 2.17

500 8.73 4.59 3.18 1.87

520 7.14 3.68 2.58 1.60

540 5.68 2.92 2.08 1.40

560 4.79 2.50 1.82 1.32

580 4.00 2.17 1.64 1.28

600 3.30 1.89 1.50 1.26

620 2.84 1.74 1.45 1.30

640 2.45 1.67 1.46 1.41

660 2.35 1.74 1.57 1.60

680 3.06 2.11 1.87 1.81

700 7.14 4.11 3.24 2.46



314


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1156 36.58 14.1 59.1 2.716 11.94 836 6.06 8.63 39.40 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

7.1 1 only 1 7.0846 6.8944 7.2006 6.9102 4.44% 0.395% 0.825% 21.1 0.48

7.1 1--2 2 7.2738 7.0726 7.5669 7.1244 6.99% 0.764% 1.694% 43.6 0.45

7.1 1--3 3 7.2817 7.0866 7.684 7.1666 8.43% 1.146% 3.115% 60.1 0.37

7.1 1--4 4 7.2632 7.0713 7.6334 7.1794 7.95% 1.439% 4.487% 70.9 0.32

7.1 1--5 5 7.2981 7.0959 7.7082 7.2403 8.63% 1.977% 7.020% 84.6 0.28

7.1 1--6 6 7.2366 7.0459 7.7565 7.2116 10.09% 2.212% 8.471% 90.1 0.26

7.1 1--7 7 7.3062 7.1145 7.7676 7.3076 9.18% 2.571% 10.845% 97.1 0.24


Wave-

length


400 11.54 6.73 5.02 4.06 3.11 2.80 2.50

420 15.49 9.16 6.50 5.14 3.80 3.38 2.95

440 14.41 8.16 5.71 4.45 3.26 2.91 2.52

460 12.27 6.71 4.62 3.58 2.65 2.37 2.08

480 10.57 5.49 3.74 2.90 2.16 1.93 1.71

500 9.27 4.65 3.17 2.47 1.87 1.70 1.53

520 7.65 3.70 2.54 2.00 1.56 1.44 1.32

540 6.13 2.93 2.04 1.67 1.37 1.30 1.22

560 5.18 2.49 1.77 1.50 1.29 1.23 1.17

580 4.31 2.13 1.58 1.38 1.23 1.18 1.13

600 3.57 1.84 1.43 1.31 1.21 1.17 1.14

620 3.07 1.68 1.38 1.29 1.23 1.22 1.18

640 2.62 1.57 1.34 1.30 1.30 1.28 1.26

660 2.54 1.60 1.41 1.44 1.46 1.46 1.46

680 3.31 1.98 1.68 1.66 1.66 1.66 1.70

700 7.75 4.10 3.07 2.67 2.31 2.19 2.12



315


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1156 36.58 14.1 59.1 2.716 11.94 836 6.06 8.63 39.40 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

8 1 only 1 9.157 8.8285 9.285 8.8582 5.17% 0.448% 0.828% 21.3 0.54

8 1--2 2 9.2187 8.8819 9.5447 8.9483 7.46% 0.822% 1.590% 42.0 0.52

8 1--3 3 9.2091 8.8697 9.6067 8.9843 8.31% 1.262% 2.837% 57.4 0.44

8 1--4 4 9.1593 8.8267 9.5991 8.9816 8.75% 1.690% 5.299% 76.0 0.32

8 1--5 5 9.1617 8.8393 9.74 9.0191 10.19% 1.936% 6.485% 82.2 0.30

8 1--6 6 12.3627 11.9224 13.1881 12.2615 10.62% 2.426% 9.334% 92.9 0.26


Wave-

length


400 11.71 6.98 5.19 3.66 3.18 2.64

420 15.68 9.49 6.71 4.56 3.88 3.16

440 14.53 8.46 5.89 3.95 3.35 2.72

460 12.33 6.97 4.79 3.22 2.73 2.25

480 10.59 5.70 3.89 2.62 2.24 1.85

500 9.25 4.84 3.29 2.25 1.94 1.64

520 7.63 3.86 2.65 1.84 1.63 1.42

540 6.09 3.05 2.14 1.55 1.42 1.28

560 5.14 2.58 1.86 1.41 1.32 1.21

580 4.28 2.22 1.65 1.31 1.26 1.16

600 3.54 1.91 1.49 1.25 1.23 1.15

620 3.04 1.73 1.43 1.25 1.26 1.19

640 2.59 1.61 1.41 1.28 1.33 1.24

660 2.48 1.60 1.47 1.40 1.50 1.39

680 3.27 2.02 1.75 1.62 1.71 1.60

700 7.84 4.25 3.22 2.54 2.40 2.11



316


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1156 36.58 14.1 59.1 2.716 11.94 836 6.06 8.63 39.40 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

12 1 only 1 6.2957 6.1185 6.4358 6.1379 5.19% 0.472% 0.790% 19.5 0.60

12 1--2 2 6.231 6.0586 6.515 6.1125 7.53% 0.919% 1.669% 43.2 0.55

12 1--3 3 6.2971 6.1169 6.6442 6.201 8.62% 1.331% 2.966% 58.7 0.45

12 1--4 4 6.2537 6.0728 6.6664 6.1909 9.77% 1.812% 4.964% 74.0 0.37

12 1--5 5 6.1908 6.0126 6.7291 6.1594 11.92% 2.260% 6.244% 81.1 0.36

12 1--6 6 6.2478 6.0675 6.7356 6.2375 11.01% 2.587% 8.617% 90.6 0.30

12 1--7 7 6.3074 6.1333 6.7564 6.3226 10.16% 2.970% 9.696% 94.0 0.31


Wave-

length


400 12.42 6.85 5.13 3.83 3.33 2.80 2.59

420 16.73 9.30 6.73 4.84 4.12 3.39 3.09

440 15.50 8.24 5.86 4.17 3.53 2.90 2.64

460 13.18 6.75 4.74 3.36 2.85 2.37 2.16

480 11.32 5.51 3.83 2.72 2.31 1.92 1.77

500 9.93 4.67 3.23 2.32 2.00 1.69 1.46

520 8.24 3.73 2.60 1.89 1.66 1.44 1.37

540 6.58 2.96 2.09 1.59 1.44 1.29 1.25

560 5.57 2.51 1.81 1.44 1.33 1.22 1.21

580 4.65 2.15 1.61 1.33 1.25 1.17 1.16

600 3.83 1.86 1.45 1.27 1.22 1.16 1.18

620 3.28 1.70 1.40 1.27 1.25 1.20 1.22

640 2.79 1.58 1.38 1.32 1.33 1.29 1.33

660 2.63 1.60 1.46 1.45 1.50 1.47 1.53

680 3.47 2.02 1.76 1.69 1.74 1.69 1.77

700 8.32 4.14 3.18 2.60 2.46 2.21 2.18



317


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1134 31.09 16.7 69.5 2.994 11.98 789 6.6 8.63 39.40 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 8.7563 8.5312 9.0642 8.5625 6.25% 0.445% 0.892% 24.2 0.50

6.3 1--2 2 8.3909 8.1668 8.8673 8.242 8.58% 0.863% 2.160% 50.0 0.40

6.3 1--3 3 8.2301 8.0143 8.7259 8.1204 8.88% 1.317% 3.666% 64.8 0.36

6.3 1--4 4 8.3198 8.0998 8.8964 8.2629 9.83% 1.798% 6.038% 80.0 0.30

6.3 1--5 5 8.0571 7.858 8.6747 8.0267 10.39% 2.166% 7.865% 88.0 0.28

6.3 1--6 6 8.182 7.9761 8.9362 8.1966 12.04% 2.681% 10.103% 95.1 0.27

6.3 1--7 7 9.2415 9.0051 9.9958 9.2982 11.00% 3.014% 13.358% 102.6 0.23


Wave-

length


400 10.91 6.13 4.65 3.48 3.01 2.60 2.31

420 14.81 8.22 6.02 4.34 3.67 3.06 2.64

440 13.56 7.19 5.20 3.71 3.12 2.60 2.25

460 11.35 5.81 4.18 2.99 2.53 2.14 1.86

480 9.64 4.69 3.37 2.43 2.06 1.75 1.56

500 8.39 3.96 2.85 2.08 1.79 1.55 1.40

520 6.82 3.17 2.31 1.73 1.52 1.37 1.25

540 5.40 2.52 1.88 1.48 1.35 1.24 1.17

560 4.52 2.15 1.64 1.35 1.26 1.19 1.14

580 3.75 1.86 1.47 1.25 1.18 1.14 1.11

600 3.10 1.63 1.35 1.20 1.15 1.15 1.11

620 2.67 1.51 1.30 1.20 1.16 1.19 1.15

640 2.34 1.47 1.31 1.27 1.25 1.29 1.28

660 2.26 1.52 1.39 1.40 1.40 1.48 1.48

680 2.96 1.87 1.64 1.63 1.61 1.72 1.72

700 6.97 3.64 2.88 2.44 2.22 2.18 2.04



318


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1134 31.09 16.7 69.5 2.994 11.98 789 6.6 8.63 39.40 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

8 1 only 1 8.741 8.4602 9.0905 8.4991 7.45% 0.577% 0.897% 24.4 0.64

8 1--2 2 8.6098 8.3352 9.1162 8.4211 9.37% 1.143% 1.853% 46.0 0.62

8 1--3 3 8.1409 7.8845 8.6864 7.9923 10.17% 1.534% 3.590% 64.2 0.43

8 1--4 4 8.4871 8.2161 9.1 8.3712 10.76% 1.972% 5.054% 74.6 0.39

8 1--5 5 7.8553 7.6096 8.4208 7.8006 10.66% 2.480% 7.095% 84.9 0.35

8 1--6 6 7.8736 7.622 8.638 7.8505 13.33% 2.947% 8.436% 90.0 0.35

8 1--7 7 8.6011 8.3298 9.3674 8.6612 12.46% 3.533% 10.628% 96.5 0.33


Wave-

length


400 10.75 6.43 4.59 3.76 2.99 2.71 2.38

420 14.54 8.55 5.87 4.68 3.57 3.16 2.66

440 13.32 7.52 5.07 4.00 3.05 2.69 2.28

460 11.14 6.13 4.07 3.22 2.50 2.22 1.91

480 9.44 4.97 3.27 2.60 2.05 1.82 1.59

500 8.21 4.22 2.78 2.25 1.81 1.63 1.45

520 6.69 3.39 2.27 1.85 1.55 1.43 1.31

540 5.33 2.72 1.86 1.57 1.38 1.31 1.24

560 4.49 2.34 1.66 1.44 1.30 1.26 1.22

580 3.74 2.04 1.51 1.35 1.27 1.23 1.20

600 3.11 1.79 1.40 1.29 1.25 1.23 1.24

620 2.67 1.64 1.33 1.26 1.24 1.25 1.27

640 2.36 1.63 1.40 1.35 1.37 1.40 1.45

660 2.29 1.67 1.52 1.49 1.53 1.60 1.70

680 2.96 2.01 1.75 1.68 1.71 1.81 1.94

700 6.84 3.89 2.97 2.58 2.33 2.29 2.26



319


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1134 31.09 16.7 69.5 3.133 12.54 801 6.16 8.63 39.40 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 7.3185 7.2391 7.5081 7.033 3.72% 0.470% 0.936% 26.0 0.50

6.3 1--2 2 7.1757 7.0941 7.4719 6.8659 5.33% 0.991% 2.121% 49.5 0.47

6.3 1--3 3 7.3111 7.2613 7.7102 7.0736 6.18% 1.586% 4.255% 69.3 0.37

6.3 1--4 4 7.216 7.1484 7.6962 7.0295 7.66% 2.035% 5.226% 75.6 0.39

6.3 1--5 5 7.097 6.9895 7.6214 6.9277 9.04% 2.699% 7.838% 87.9 0.34

6.3 1--6 6 7.2095 7.1868 7.8637 7.1291 9.42% 3.322% 10.718% 96.7 0.31

6.3 1--7 7 7.1665 7.1341 7.7023 7.0573 7.96% 3.632% 12.695% 101.3 0.29


Wave-

length


400 10.10 6.10 4.17 3.58 2.89 2.49 2.31

420 13.66 8.11 5.30 4.45 3.48 2.89 2.62

440 12.55 7.13 4.58 3.83 2.96 2.47 2.25

460 10.54 5.80 3.70 3.11 2.42 2.04 1.88

480 8.93 4.70 2.99 2.52 1.97 1.67 1.56

500 7.77 3.98 2.55 2.19 1.74 1.51 1.43

520 6.32 3.20 2.09 1.82 1.50 1.33 1.28

540 4.99 2.54 1.71 1.55 1.33 1.21 1.17

560 4.21 2.16 1.53 1.42 1.26 1.17 1.15

580 3.51 1.88 1.41 1.34 1.21 1.15 1.13

600 2.92 1.66 1.32 1.29 1.20 1.16 1.14

620 2.54 1.53 1.29 1.29 1.22 1.22 1.18

640 2.25 1.49 1.35 1.38 1.34 1.35 1.32

660 2.22 1.57 1.49 1.53 1.53 1.59 1.56

680 2.92 1.94 1.79 1.80 1.78 1.88 1.84

700 6.56 3.73 2.87 2.63 2.34 2.27 2.17



320


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1134 31.09 16.7 69.5 3.133 12.54 801 6.16 8.63 39.40 70.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

12 1 only 1 3.4995 3.4726 3.667 3.3694 5.60% 0.686% 0.987% 27.9 0.70

12 1--2 2 3.6025 3.5409 3.8154 3.4882 7.75% 1.339% 2.448% 53.4 0.55

12 1--3 3 3.6048 3.5595 3.8785 3.4992 8.96% 2.061% 4.629% 71.9 0.45

12 1--4 4 3.5576 3.5402 3.888 3.495 9.82% 2.679% 6.662% 83.0 0.40

12 1--5 5 3.564 3.5048 3.939 3.5345 12.39% 3.338% 9.695% 94.0 0.34

12 1--6 6 3.6194 3.5478 4.0037 3.5965 12.85% 3.916% 13.240% 102.3 0.30

12 1--7 7 3.6135 3.5623 4.0011 3.637 12.32% 4.354% 15.926% 107.1 0.27


Wave-

length


400 9.78 5.82 4.11 3.27 2.72 2.37 2.18

420 13.10 7.57 5.18 3.98 3.22 2.73 2.48

440 11.94 6.63 4.47 3.41 2.75 2.34 2.12

460 10.02 5.41 3.61 2.78 2.26 1.95 1.76

480 8.47 4.38 2.93 2.26 1.85 1.61 1.47

500 7.33 3.72 2.50 1.95 1.62 1.44 1.33

520 5.95 2.99 2.03 1.63 1.40 1.28 1.20

540 4.70 2.37 1.66 1.40 1.24 1.15 1.10

560 3.96 2.02 1.48 1.30 1.18 1.11 1.09

580 3.29 1.76 1.36 1.24 1.15 1.09 1.08

600 2.74 1.55 1.26 1.20 1.14 1.10 1.09

620 2.37 1.42 1.23 1.21 1.15 1.12 1.14

640 2.12 1.40 1.26 1.29 1.26 1.24 1.28

660 2.10 1.47 1.39 1.48 1.45 1.45 1.53

680 2.80 1.83 1.65 1.73 1.68 1.71 1.78

700 6.25 3.52 2.71 2.45 2.20 2.10 2.11



321


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)t3735 34.75 19.6 63.9 0.761 11.08 722 2.13 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 8.2806 7.9396 8.0993 7.9339 2.01% 0.137% 0.443% 8.2 0.31

6.3 1--2 2 8.1831 7.8587 8.00842 7.8595 1.91% 0.305% 0.765% 18.4 0.40

6.3 1--3 3 8.3069 7.9597 8.2823 7.9829 4.05% 0.577% 1.141% 32.7 0.51

6.3 1--4 4 8.236 7.9002 8.2137 7.934 3.97% 0.666% 1.539% 41.1 0.43

6.3 1--5 5 8.2356 7.8895 8.2191 7.936 4.18% 0.902% 2.312% 51.8 0.39

6.3 1--5,4 6 8.3191 7.9783 8.3805 8.0502 5.04% 1.167% 3.321% 61.9 0.35

6.3

1--5,4-

5 7 8.1713 7.8316 8.2105 7.9057 4.84% 1.358% 3.884% 66.5 0.35


Wave-

length


400 19.61 12.55 8.22 7.02 5.70 4.65 4.19

420 24.45 16.56 11.00 9.45 7.36 5.83 5.17

440 23.74 15.60 10.09 8.43 6.49 5.10 4.50

460 21.48 13.50 8.51 6.98 5.33 4.19 3.69

480 19.57 11.75 7.13 5.73 4.36 3.44 3.03

500 17.81 10.36 6.12 4.87 3.68 2.92 2.59

520 15.66 8.68 4.95 3.89 2.98 2.38 2.12

540 13.09 6.96 3.94 3.09 2.39 1.94 1.78

560 11.54 5.91 3.35 2.63 2.07 1.72 1.61

580 10.00 4.94 2.84 2.27 1.82 1.56 1.49

600 8.47 4.08 2.42 1.97 1.64 1.45 1.41

620 7.31 3.48 2.14 1.77 1.52 1.40 1.38

640 6.17 2.94 1.95 1.67 1.50 1.40 1.42

660 5.53 2.72 1.90 1.66 1.53 1.48 1.51

680 7.38 3.52 2.37 2.01 1.81 1.69 1.72

700 15.35 8.50 5.11 4.15 3.42 2.92 2.75



322


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1110 32.92 20.7 67.5 0.733 12.23 813 2.79 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

7.1 1 only 1 6.9391 6.6999 6.8035 6.6768 1.55% 0.134% 0.370% 6.9 0.36

7.1 1--2 2 6.9948 6.782 6.8888 6.7635 1.57% 0.220% 0.627% 12.9 0.35

7.1 1--2,1 3 6.854 6.62 6.746 6.6079 1.90% 0.365% 0.763% 18.3 0.48

7.1

1--2,1-

2 4 6.9343 6.7022 6.8375 6.6915 2.02% 0.446% 0.875% 23.5 0.51


Wave-

length


400 21.96 15.92 13.01 11.02

420 27.54 20.86 17.54 15.13

440 26.78 19.76 16.36 13.96

460 24.19 17.16 13.95 11.73

480 22.11 15.10 12.03 9.95

500 20.18 13.42 10.54 8.65

520 17.70 11.42 8.74 6.98

540 14.85 9.23 6.97 5.50

560 13.22 8.03 5.91 4.65

580 11.58 6.85 4.96 3.91

600 9.85 5.67 4.09 3.23

620 8.50 4.78 3.45 2.76

640 7.15 3.96 2.87 2.34

660 6.37 3.63 2.66 2.20

680 8.53 4.79 3.47 2.84

700 17.48 11.10 8.54 6.88



323


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1110 32.92 20.7 67.5 0.733 12.23 813 2.79 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

8 1 only 1 6.1777 5.9717 6.0737 5.9531 1.71% 0.131% 0.284% 5.5 0.46

8 1--2 2 6.0447 5.8247 5.939 5.8135 1.96% 0.245% 0.572% 11.3 0.43

8 1--2,1 3 6.1363 5.9296 6.0544 5.9254 2.10% 0.369% 0.726% 16.6 0.51

8

1--2,1-

2 4 6.1302 5.9119 6.0437 5.9109 2.23% 0.455% 0.864% 23.0 0.53


Wave-

length


400 24.57 17.14 13.71 11.23

420 30.34 22.27 18.38 15.33

440 29.79 21.15 17.21 14.13

460 27.25 18.48 14.73 11.86

480 25.14 16.37 12.75 10.07

500 23.14 14.60 11.21 8.74

520 20.53 12.55 9.40 7.10

540 17.40 10.23 7.52 5.61

560 15.57 8.96 6.44 4.76

580 13.73 7.74 5.43 3.99

600 11.74 6.45 4.48 3.31

620 10.20 5.46 3.80 2.82

640 8.62 4.53 3.15 2.39

660 7.62 4.10 2.91 2.22

680 10.19 5.39 3.76 2.88

700 20.21 12.11 9.10 6.97



324


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1110 32.92 20.7 67.5 0.733 12.23 813 2.79 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

12 1 only 1 3.9485 3.8069 3.8929 3.802 2.26% 0.171% 0.375% 7.0 0.46

12 1--2 2 3.9064 3.7635 3.8499 3.7621 2.30% 0.305% 0.630% 13.0 0.48

12 1--2,1 3 3.9594 3.8156 3.9091 3.819 2.45% 0.417% 0.756% 17.9 0.55

12

1--2,1-

2 4 4.0246 3.8837 3.9877 3.8952 2.68% 0.583% 0.930% 25.8 0.63

12

1--2,1-

2,1 5 3.9455 3.805 3.9101 3.8191 2.76% 0.670% 1.041% 29.8 0.64

12

1-2,1-

2,1-2 6 3.8618 3.7262 3.8285 3.747 2.75% 0.821% 1.271% 35.9 0.65

12

1-2,1-

2,1-2,1 7 3.8127 3.6766 3.7908 3.6985 3.11% 0.964% 1.530% 40.9 0.63


Wave-

length


400 22.20 15.94 13.27 10.41 9.36 8.07 7.25

420 27.85 20.82 17.82 14.23 12.93 11.16 10.02

440 26.95 19.65 16.59 12.98 11.74 10.04 8.89

460 24.22 17.04 14.11 10.82 9.71 8.26 7.26

480 22.01 14.98 12.14 9.10 8.09 6.73 5.87

500 20.02 13.30 10.63 7.86 6.90 5.71 4.97

520 17.58 11.34 8.85 6.33 5.52 4.54 3.94

540 14.72 9.18 7.06 5.00 4.34 3.57 3.11

560 13.10 7.99 6.01 4.24 3.67 3.04 2.65

580 11.46 6.80 5.06 3.57 3.10 2.59 2.28

600 9.75 5.64 4.17 2.97 2.61 2.21 1.96

620 8.42 4.78 3.52 2.57 2.25 1.93 1.74

640 7.08 3.96 2.94 2.20 1.97 1.73 1.59

660 6.33 3.63 2.72 2.10 1.89 1.68 1.57

680 8.44 4.78 3.53 2.70 2.41 2.10 1.93

700 17.23 11.05 8.60 6.28 5.48 4.58 4.01



325


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)t3706 34.75 19.6 63.9 0.94 11.48 861 2.22 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 8.2635 7.95 8.1871 7.9431 2.98% 0.163% 0.497% 9.4 0.33

6.3 1--2 2 8.3017 7.9697 8.2575 7.9723 3.61% 0.305% 0.776% 18.9 0.39

6.3 1--3 3 8.2384 7.918 8.2369 7.9335 4.03% 0.501% 1.046% 29.9 0.48

6.3 1--4 4 8.2754 7.9427 8.3124 7.969 4.65% 0.598% 1.507% 40.5 0.40

6.3 1--5 5 8.3279 7.9936 8.4145 8.028 5.27% 0.716% 1.936% 47.1 0.37

6.3 1--6 6 8.302 7.9718 8.3508 8.0209 4.75% 0.913% 2.765% 56.7 0.33

6.3 1--6,6 7 8.3061 7.9788 8.3878 8.0325 5.13% 1.102% 3.588% 64.2 0.31


Wave-

length


400 18.24 12.35 8.81 7.18 6.28 5.20 4.51

420 22.94 16.34 11.88 9.81 8.46 6.78 5.82

440 22.23 15.39 10.97 8.81 7.53 5.97 5.10

460 19.94 13.27 9.27 7.29 6.17 4.89 4.15

480 18.07 11.51 7.82 5.98 5.04 3.98 3.40

500 16.35 10.16 6.75 5.08 4.27 3.38 2.89

520 14.30 8.48 5.46 4.05 3.41 2.73 2.35

540 11.86 6.81 4.33 3.18 2.70 2.19 1.91

560 10.43 5.78 3.68 2.70 2.30 1.90 1.68

580 9.01 4.82 3.11 2.30 1.99 1.69 1.52

600 7.60 3.98 2.62 1.97 1.74 1.52 1.39

620 6.50 3.38 2.29 1.75 1.58 1.41 1.31

640 5.44 2.83 2.01 1.58 1.45 1.32 1.24

660 4.92 2.61 1.93 1.52 1.41 1.32 1.25

680 6.56 3.40 2.46 1.88 1.70 1.54 1.42

700 13.96 8.24 5.49 4.09 3.53 2.96 2.60



326


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)t3706 34.75 19.6 63.9 0.94 11.48 861 2.22 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

8 1 only 1 9.1853 8.8494 9.1124 8.8452 2.97% 0.177% 0.517% 9.9 0.34

8 1--2 2 9.2492 8.9176 9.241 8.9307 3.63% 0.325% 0.788% 19.4 0.41

8 1--3 3 9.3365 9.0043 9.3891 9.0301 4.27% 0.501% 1.064% 30.5 0.47

8 1--4 4 9.2811 8.9443 9.389 8.9828 4.97% 0.664% 1.509% 40.6 0.44

8 1--5 5 9.2993 8.9629 9.3567 9.0165 4.39% 0.828% 2.083% 49.1 0.40

8 1--6 6 9.2632 8.9339 9.406 9.0083 5.28% 1.124% 3.184% 60.7 0.35

8 1--6,6 7 9.3886 9.0562 9.5544 9.1498 5.50% 1.262% 3.760% 65.6 0.34


Wave-

length


400 17.65 12.10 8.97 7.14 6.11 4.89 4.47

420 22.11 15.93 12.12 9.71 8.19 6.33 5.76

440 21.39 14.99 11.16 8.73 7.27 5.57 5.04

460 19.18 12.93 9.37 7.24 5.97 4.55 4.12

480 17.36 11.23 7.89 5.95 4.87 3.71 3.36

500 15.73 9.89 6.78 5.07 4.12 3.15 2.87

520 13.77 8.27 5.45 4.04 3.29 2.55 2.33

540 11.44 6.63 4.30 3.19 2.61 2.04 1.88

560 10.10 5.63 3.63 2.71 2.22 1.79 1.65

580 8.75 4.72 3.04 2.31 1.93 1.58 1.49

600 7.40 3.90 2.56 1.98 1.68 1.43 1.36

620 6.35 3.33 2.22 1.75 1.51 1.34 1.27

640 5.35 2.79 1.91 1.56 1.38 1.25 1.19

660 4.86 2.59 1.82 1.51 1.36 1.25 1.19

680 6.40 3.37 2.33 1.88 1.63 1.45 1.38

700 13.32 8.02 5.42 4.09 3.41 2.78 2.56



327


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1142 34.75 19.6 63.9 0.946 11.49 742 3.4 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

7.1 1 only 1 7.2284 7.0323 7.2354 7.0342 2.89% 0.207% 0.507% 9.6 0.41

7.1 1--2 2 7.3446 7.1456 7.4288 7.1571 3.96% 0.359% 0.839% 21.8 0.43

7.1 1--3 3 7.3514 7.1554 7.4505 7.1775 4.12% 0.455% 1.076% 30.8 0.42

7.1 1--4 4 7.2888 7.0958 7.4793 7.1321 5.40% 0.619% 1.523% 40.8 0.41

7.1 1--5 5 7.1916 6.9923 7.3246 7.0431 4.75% 0.756% 1.928% 47.0 0.39

7.1 1--6 6 7.251 7.055 7.4416 7.1208 5.48% 0.956% 2.795% 57.0 0.34

7.1 1--6,6 7 7.2646 7.0636 7.4684 7.1509 5.73% 1.125% 3.410% 62.7 0.33


Wave-

length


400 18.11 11.10 8.77 7.16 6.19 5.25 4.57

420 22.76 14.61 11.78 9.67 8.15 6.74 5.76

440 21.83 13.61 10.78 8.61 7.22 5.89 5.03

460 19.51 11.69 9.09 7.12 5.94 4.80 4.10

480 17.61 10.09 7.63 5.83 4.85 3.89 3.33

500 15.89 8.86 6.55 4.95 4.11 3.30 2.84

520 13.93 7.35 5.30 3.95 3.30 2.65 2.30

540 11.59 5.90 4.20 3.12 2.65 2.13 1.90

560 10.24 5.03 3.57 2.67 2.28 1.87 1.70

580 8.92 4.23 3.01 2.29 2.01 1.67 1.55

600 7.55 3.52 2.54 1.97 1.78 1.52 1.44

620 6.50 3.04 2.23 1.77 1.64 1.44 1.41

640 5.50 2.61 1.99 1.64 1.58 1.43 1.44

660 4.98 2.47 1.94 1.64 1.63 1.50 1.54

680 6.53 3.19 2.46 2.04 1.94 1.78 1.78

700 13.46 7.31 5.45 4.24 3.75 3.23 2.97



328


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1142 34.75 19.6 63.9 0.946 11.49 742 3.4 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

12 1 only 1 6.3876 6.2068 6.4218 6.218 3.46% 0.207% 0.560% 10.9 0.37

12 1--2 2 6.3814 6.2032 6.4725 6.2262 4.34% 0.381% 0.818% 20.9 0.47

12 1--3 3 6.3095 6.1344 6.4446 6.168 5.06% 0.602% 1.128% 32.3 0.53

12 1--4 4 6.2744 6.0969 6.4446 6.141 5.70% 0.744% 1.533% 41.0 0.49

12 1--5 5 6.352 6.1726 6.5428 6.2305 6.00% 0.922% 1.989% 47.8 0.46

12 1--6 6 6.4709 6.286 6.6476 6.3654 5.75% 1.177% 2.875% 57.8 0.41

12 1--6,6 7 6.347 6.1699 6.5511 6.2549 6.18% 1.395% 3.524% 63.6 0.40


Wave-

length


400 16.18 11.29 8.42 6.95 6.01 4.98 4.40

420 20.37 14.85 11.29 9.25 7.82 6.33 5.52

440 19.61 13.89 10.30 8.27 6.91 5.54 4.81

460 17.56 11.96 8.64 6.87 5.70 4.52 3.94

480 15.85 10.38 7.22 5.67 4.66 3.70 3.22

500 14.36 9.17 6.21 4.84 3.99 3.15 2.77

520 12.56 7.63 5.01 3.89 3.21 2.56 2.26

540 10.46 6.14 3.97 3.09 2.58 2.08 1.86

560 9.26 5.25 3.40 2.66 2.24 1.85 1.69

580 8.08 4.43 2.88 2.29 1.98 1.68 1.55

600 6.85 3.69 2.45 1.99 1.77 1.54 1.45

620 5.93 3.19 2.16 1.80 1.65 1.46 1.40

640 5.07 2.74 1.96 1.69 1.61 1.47 1.44

660 4.66 2.59 1.91 1.69 1.68 1.57 1.55

680 5.99 3.33 2.41 2.08 2.00 1.82 1.79

700 12.16 7.59 5.19 4.21 3.72 3.14 2.91



329


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1126 34.75 19.6 63.9 1.051 11.38 792 3.32 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 8.7651 8.4139 8.6682 8.4 3.02% 0.188% 0.539% 10.4 0.35

6.3 1--2 2 8.2092 7.8849 8.1745 7.8886 3.67% 0.342% 0.837% 21.7 0.41

6.3 1--3 3 8.2085 7.8872 8.2382 7.8986 4.45% 0.544% 1.270% 35.8 0.43

6.3 1--4 4 8.3558 8.0246 8.4065 8.0616 4.76% 0.727% 1.847% 45.9 0.39

6.3 1--5 5 8.5064 8.1656 8.5507 8.2185 4.72% 0.915% 2.615% 55.2 0.35

6.3 1--6 6 8.2067 7.8703 8.2531 7.9356 4.86% 1.010% 2.894% 58.0 0.35


Wave-

length


400 17.20 11.28 7.93 6.42 5.51 5.09

420 21.84 14.99 10.74 8.62 7.16 6.59

440 21.06 14.00 9.78 7.70 6.31 5.79

460 18.84 12.01 8.16 6.37 5.17 4.74

480 16.95 10.34 6.76 5.22 4.22 3.86

500 15.31 9.08 5.77 4.43 3.56 3.27

520 13.32 7.50 4.62 3.54 2.86 2.65

540 11.01 5.99 3.64 2.80 2.28 2.13

560 9.64 5.05 3.07 2.37 1.95 1.85

580 8.30 4.21 2.59 2.04 1.72 1.66

600 6.93 3.49 2.19 1.77 1.53 1.49

620 5.91 2.98 1.91 1.59 1.40 1.39

640 4.99 2.55 1.73 1.48 1.34 1.35

660 4.53 2.37 1.66 1.44 1.31 1.34

680 6.03 3.10 2.11 1.76 1.56 1.56

700 12.91 7.35 4.75 3.75 3.15 2.99



330


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1126 34.75 19.6 63.9 1.051 11.38 792 3.32 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

8 1 only 1 9.4125 9.2 9.4641 9.1953 2.87% 0.192% 0.525% 10.1 0.37

8 1--2 2 9.2127 9.0388 9.3955 9.0539 3.95% 0.350% 0.806% 20.3 0.43

8 1--3 3 9.4864 9.2298 9.6258 9.2625 4.29% 0.521% 1.087% 31.2 0.48

8 1--4 4 9.3524 9.1666 9.618 9.2176 4.92% 0.657% 1.461% 39.7 0.45

8 1--5 5 9.6241 9.1361 9.6072 9.2005 5.16% 0.933% 2.377% 52.6 0.39

8 1--6 6 9.4108 9.0548 9.5177 9.1357 5.11% 1.060% 2.924% 58.3 0.36


Wave-

length


400 17.77 11.87 8.95 7.35 5.75 5.19

420 22.37 15.71 12.11 9.99 7.52 6.74

440 21.44 14.64 11.02 8.92 6.61 5.88

460 19.11 12.56 9.22 7.38 5.40 4.79

480 17.22 10.85 7.73 6.05 4.40 3.89

500 15.55 9.55 6.61 5.14 3.71 3.28

520 13.58 7.94 5.33 4.11 2.98 2.65

540 11.27 6.37 4.19 3.25 2.38 2.12

560 9.90 5.39 3.53 2.75 2.04 1.84

580 8.55 4.51 2.97 2.35 1.80 1.64

600 7.21 3.73 2.49 2.01 1.60 1.48

620 6.19 3.20 2.16 1.78 1.47 1.37

640 5.27 2.73 1.93 1.64 1.43 1.35

660 4.83 2.56 1.84 1.60 1.43 1.36

680 6.32 3.31 2.37 2.00 1.69 1.59

700 13.10 7.76 5.38 4.27 3.33 3.04



331


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1126B 34.75 19.6 63.9 1.157 11.05 817 1.56 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 8.1808 7.8405 8.0988 7.8212 3.29% 0.177% 0.520% 9.9 0.34

6.3 1--2 2 8.2137 7.871 8.1732 7.8627 3.84% 0.328% 0.807% 20.3 0.41

6.3 1--3 3 8.2085 7.8738 8.2324 7.8896 4.55% 0.514% 1.103% 31.6 0.47

6.3 1--4 4 8.1237 7.792 8.225 7.814 5.56% 0.625% 1.347% 37.5 0.46

6.3 1--5 5 7.7693 7.4351 7.8435 7.475 5.49% 0.757% 1.916% 46.8 0.40

6.3 1--6 6 8.323 7.9781 8.4272 8.0408 5.63% 0.999% 2.889% 57.9 0.35


Wave-

length


400 17.47 11.66 8.46 7.43 6.14 4.94

420 22.07 15.33 11.29 9.93 7.96 6.21

440 21.33 14.39 10.42 9.04 7.14 5.52

460 19.10 12.43 8.85 7.61 5.99 4.62

480 17.27 10.79 7.46 6.35 4.97 3.83

500 15.64 9.51 6.43 5.44 4.23 3.26

520 13.66 7.92 5.20 4.38 3.41 2.66

540 11.35 6.35 4.12 3.46 2.72 2.16

560 9.98 5.39 3.48 2.95 2.33 1.87

580 8.63 4.50 2.94 2.50 2.02 1.67

600 7.26 3.72 2.48 2.13 1.77 1.51

620 6.23 3.20 2.18 1.88 1.62 1.41

640 5.26 2.72 1.93 1.70 1.51 1.36

660 4.77 2.54 1.85 1.63 1.48 1.33

680 6.26 3.24 2.30 2.02 1.75 1.52

700 13.11 7.66 5.16 4.38 3.59 2.88



332


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1126B 34.75 19.6 63.9 1.157 11.05 817 1.56 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

8 1 only 1 12.302 11.8549 12.2783 11.8331 3.57% 0.202% 0.550% 10.7 0.37

8 1--2 2 9.2127 8.8729 9.2975 8.8858 4.79% 0.312% 0.779% 19.0 0.40

8 1--3 3 9.2118 8.8698 9.3328 8.899 5.22% 0.499% 1.102% 31.6 0.45

8 1--4 4 9.2176 8.8863 9.4257 8.933 6.07% 0.688% 1.517% 40.7 0.45

8 1--5 5 9.1641 8.8245 9.3425 8.8805 5.87% 0.865% 2.077% 49.0 0.42

8 1--6 6 9.1681 8.8336 9.3633 8.9096 6.00% 1.055% 2.732% 56.4 0.39


Wave-

length


400 16.99 12.28 8.46 6.91 5.89 5.12

420 21.56 16.12 11.27 9.10 7.57 6.45

440 20.74 15.10 10.43 8.22 6.77 5.73

460 18.47 13.03 8.85 6.92 5.67 4.79

480 16.61 11.32 7.48 5.76 4.70 3.97

500 15.00 9.99 6.44 4.93 4.01 3.38

520 13.07 8.37 5.22 3.97 3.24 2.75

540 10.81 6.75 4.14 3.16 2.59 2.22

560 9.47 5.73 3.50 2.71 2.22 1.93

580 8.15 4.81 2.94 2.32 1.95 1.71

600 6.83 3.99 2.49 2.00 1.71 1.54

620 5.84 3.41 2.19 1.79 1.57 1.44

640 4.93 2.90 1.94 1.65 1.48 1.36

660 4.50 2.69 1.85 1.60 1.45 1.35

680 5.87 3.44 2.31 1.94 1.70 1.56

700 12.46 8.03 5.17 4.04 3.40 2.99



333


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1126 34.75 19.6 63.9 1.117 11.55 771 2.79 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 8.1062 7.7651 8.0002 7.7641 3.03% 0.186% 0.540% 10.4 0.34

6.3 1--2 2 8.2555 7.9106 8.2317 7.9256 4.06% 0.382% 0.833% 21.5 0.46

6.3 1--3 3 8.3467 8.01 8.3753 8.0304 4.56% 0.546% 1.218% 34.6 0.45

6.3 1--4 4 8.3702 8.0196 8.3981 8.0532 4.72% 0.662% 1.562% 41.5 0.42

6.3 1--5 5 8.2585 7.9182 8.3323 7.9726 5.23% 0.833% 2.222% 50.8 0.37

6.3 1--6 6 8.2929 7.9479 8.363 8.0079 5.22% 1.083% 3.241% 61.2 0.33

6.3 1--6,6 7 8.3391 7.9963 8.4083 8.0759 5.15% 1.235% 3.864% 66.4 0.32


Wave-

length


400 16.85 11.19 7.94 6.81 5.78 4.73 4.25

420 21.42 14.78 10.65 9.19 7.54 6.08 5.41

440 20.68 13.76 9.71 8.24 6.69 5.33 4.72

460 18.55 11.80 8.17 6.86 5.52 4.36 3.87

480 16.70 10.15 6.79 5.63 4.49 3.55 3.16

500 15.12 8.94 5.83 4.82 3.84 3.04 2.71

520 13.17 7.40 4.69 3.85 3.07 2.45 2.20

540 10.92 5.95 3.73 3.07 2.48 2.00 1.83

560 9.58 5.06 3.16 2.62 2.13 1.75 1.62

580 8.29 4.26 2.69 2.26 1.87 1.58 1.48

600 6.97 3.56 2.30 1.97 1.66 1.45 1.38

620 5.98 3.08 2.02 1.76 1.52 1.36 1.31

640 5.04 2.64 1.83 1.63 1.45 1.34 1.30

660 4.56 2.50 1.76 1.60 1.44 1.36 1.32

680 6.06 3.24 2.25 1.98 1.74 1.61 1.53

700 12.84 7.37 4.86 4.06 3.42 2.88 2.65



334


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1126 34.75 19.6 63.9 1.117 11.55 771 2.79 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

8 1 only 1 6.2123 6.0011 6.1837 5.9981 3.04% 0.204% 0.562% 11.0 0.36

8 1--4 4 6.0963 5.8867 6.2185 5.9163 5.64% 0.879% 1.553% 41.3 0.57

8 1--5 5 6.0526 5.8445 6.147 5.8863 5.18% 0.926% 2.153% 49.9 0.43

8 1--6 6 6.2229 6.005099 6.3646 6.061 5.99% 1.279% 3.107% 60.0 0.41

8 1--6,6 7 6.0154 5.8229 6.1585 5.8883 5.76% 1.403% 3.387% 62.5 0.41


Wave-

length


400 16.92 7.06 5.97 5.02 4.66

420 21.53 9.58 7.87 6.50 5.96

440 20.66 8.54 6.95 5.68 5.21

460 18.40 7.06 5.72 4.63 4.25

480 16.48 5.78 4.66 3.74 3.45

500 14.86 4.92 3.97 3.19 2.95

520 12.86 3.93 3.17 2.56 2.38

540 10.59 3.11 2.54 2.06 1.95

560 9.25 2.64 2.16 1.79 1.71

580 7.94 2.27 1.89 1.60 1.55

600 6.62 1.95 1.67 1.45 1.43

620 5.64 1.73 1.52 1.34 1.35

640 4.73 1.59 1.44 1.30 1.34

660 4.30 1.57 1.43 1.31 1.36

680 5.75 1.95 1.76 1.55 1.61

700 12.53 4.12 3.51 2.95 2.84



335


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1126A 34.75 19.6 63.9 1.174 10.98 826 1.57 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 8.2781 7.934 8.196 7.9298 3.30% 0.195% 0.584% 11.6 0.33

6.3 1--2 2 8.3137 7.9781 8.2875 7.9807 3.88% 0.337% 0.832% 21.5 0.41

6.3 1--3 3 8.3089 7.9721 8.329 7.9888 4.48% 0.489% 1.106% 31.7 0.44

6.3 1--5 5 8.2309 7.9008 8.3304 7.9474 5.44% 0.812% 2.084% 49.1 0.39

6.3 1--6 6 8.2494 7.9121 8.3354 7.9723 5.35% 1.033% 2.924% 58.3 0.35


Wave-

length


400 16.20 11.15 8.47 5.86 4.89

420 20.62 14.64 11.27 7.55 6.12

440 19.82 13.74 10.40 6.75 5.46

460 17.61 11.86 8.85 5.65 4.57

480 15.78 10.28 7.48 4.68 3.80

500 14.20 9.05 6.44 3.98 3.24

520 12.31 7.51 5.21 3.22 2.64

540 10.11 6.03 4.12 2.58 2.13

560 8.83 5.11 3.49 2.22 1.86

580 7.54 4.27 2.93 1.93 1.66

600 6.27 3.55 2.47 1.71 1.50

620 5.36 3.05 2.16 1.57 1.41

640 4.52 2.61 1.92 1.48 1.36

660 4.16 2.46 1.82 1.47 1.34

680 5.45 3.15 2.31 1.74 1.53

700 11.83 7.30 5.18 3.44 2.90



336


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)t3738 34.75 19.6 63.9 1.409 11.36 874 2.35 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 8.2544 7.9397 8.1588 7.9409 2.76% 0.210% 0.611% 12.4 0.34

6.3 1--2 2 8.2514 7.945 8.2044 7.9675 3.26% 0.428% 0.959% 26.9 0.45

6.3 1--3 3 8.3209 8.012 8.3459 8.0561 4.17% 0.645% 1.444% 39.4 0.45

6.3 1--4 4 8.2785 7.9614 8.3492 8.0302 4.87% 1.028% 2.584% 54.8 0.40

6.3 1--5 5 8.2834 7.9686 8.3555 8.0528 4.86% 1.268% 3.389% 62.5 0.37

6.3 1--6 6 8.2551 7.9297 8.344 8.0413 5.22% 1.661% 4.650% 72.0 0.36

6.3 1--6,6 7 8.3067 7.9951 8.4212 8.119 5.33% 1.869% 5.491% 77.1 0.34


Wave-

length


400 15.83 9.91 7.38 5.51 4.71 3.86 3.50

420 20.69 13.58 10.21 7.26 6.11 4.87 4.39

440 19.71 12.52 9.18 6.37 5.33 4.21 3.78

460 17.30 10.53 7.57 5.19 4.32 3.43 3.09

480 15.33 8.92 6.18 4.21 3.51 2.79 2.53

500 13.71 7.71 5.24 3.56 2.99 2.42 2.21

520 11.74 6.18 4.16 2.84 2.41 1.97 1.81

540 9.53 4.84 3.26 2.26 1.94 1.65 1.55

560 8.30 4.08 2.77 1.96 1.72 1.50 1.43

580 7.07 3.41 2.36 1.73 1.55 1.40 1.34

600 5.87 2.83 2.01 1.54 1.41 1.31 1.25

620 4.97 2.43 1.78 1.42 1.33 1.26 1.22

640 4.14 2.10 1.61 1.35 1.29 1.27 1.20

660 3.76 1.97 1.57 1.35 1.30 1.31 1.22

680 4.97 2.54 1.92 1.56 1.46 1.43 1.30

700 11.45 6.23 4.29 3.10 2.72 2.36 2.10



337


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1099 32.92 20.7 67.5 1.827 11.71 867 3.11 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 7.8393 7.7815 7.976 7.7521 2.50% 0.250% 0.665% 14.2 0.38

6.3 1--2 2 7.86 7.8393 8.1362 7.8361 3.79% 0.482% 1.024% 29.2 0.47

6.3 1--3 3 7.9407 7.9407 8.3054 7.9527 4.59% 0.789% 1.758% 44.6 0.45

6.3 1--4 4 7.9155 7.9155 8.3465 7.943 5.45% 0.916% 2.343% 52.2 0.39

6.3 1--5 5 7.9914 7.9914 8.4123 8.0618 5.27% 1.249% 3.742% 65.4 0.33

6.3 1--6 6 7.9182 7.9182 8.3955 7.9999 6.03% 1.488% 4.678% 72.2 0.32


Wave-

length


400 14.89 9.33 6.61 5.63 4.37 3.75

420 19.50 12.71 8.92 7.37 5.56 4.67

440 18.45 11.65 7.94 6.50 4.86 4.06

460 16.04 9.73 6.53 5.31 3.95 3.33

480 14.10 8.20 5.34 4.33 3.23 2.75

500 12.53 7.04 4.53 3.67 2.75 2.37

520 10.70 5.68 3.63 2.95 2.25 1.96

540 8.62 4.48 2.87 2.38 1.86 1.66

560 7.43 3.76 2.44 2.07 1.64 1.51

580 6.22 3.14 2.10 1.82 1.49 1.40

600 5.12 2.62 1.81 1.62 1.38 1.32

620 4.35 2.28 1.63 1.50 1.33 1.28

640 3.66 2.03 1.53 1.47 1.32 1.29

660 3.39 1.93 1.49 1.47 1.34 1.32

680 4.49 2.47 1.82 1.71 1.50 1.45

700 10.57 5.81 3.85 3.33 2.66 2.36



338


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1099 32.92 20.7 67.5 1.738 11.71 873 3.07 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

7.1 1 only 1 7.13 6.9251 7.1227 6.9058 2.85% 0.274% 0.687% 15.0 0.40

7.1 1--2 2 7.1819 6.9748 7.2357 6.978 3.74% 0.445% 0.996% 28.2 0.45

7.1 1--3 3 6.9886 6.7835 7.1097 6.8007 4.81% 0.699% 1.506% 40.5 0.46

7.1 1--4 4 6.9426 6.7426 7.12 6.7755 5.60% 0.868% 2.107% 49.4 0.41

7.1 1--5 5 7.201 6.9919 7.3966 7.0434 5.79% 1.199% 3.289% 61.6 0.36

7.1 1--6 6 7.1282 6.9184 7.3011 6.9913 5.53% 1.388% 4.546% 71.3 0.31

7.1 1--6,3 7 7.068 6.8735 7.3049 6.9644 6.28% 1.701% 5.162% 75.2 0.33


Wave-

length


400 14.21 9.55 7.18 6.03 4.78 3.92 3.62

420 18.66 12.96 9.75 7.96 6.13 4.95 4.52

440 17.58 11.89 8.72 7.04 5.34 4.30 3.91

460 15.22 9.95 7.17 5.76 4.34 3.50 3.20

480 13.35 8.40 5.87 4.70 3.53 2.87 2.63

500 11.84 7.24 4.99 3.98 2.99 2.46 1.94

520 10.11 5.86 4.00 3.19 2.43 2.02 1.88

540 8.18 4.62 3.16 2.55 1.98 1.68 1.60

560 7.08 3.90 2.69 2.18 1.73 1.52 1.47

580 5.96 3.25 2.29 1.90 1.57 1.39 1.35

600 4.95 2.72 1.98 1.68 1.43 1.31 1.29

620 4.23 2.37 1.77 1.55 1.37 1.27 1.26

640 3.58 2.10 1.67 1.49 1.35 1.28 1.26

660 3.33 2.00 1.64 1.49 1.38 1.30 1.29

680 4.33 2.55 2.01 1.75 1.56 1.41 1.39

700 9.91 5.97 4.24 3.51 2.84 2.37 2.26



339


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1099 32.92 20.7 67.5 1.827 11.71 867 3.11 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

8 1 only 1 9.2313 8.896 9.177 8.8828 3.16% 0.314% 0.704% 15.7 0.45

8 1--2 2 9.192 8.8576 9.2629 8.8629 4.58% 0.610% 1.051% 30.1 0.58

8 1--3 3 9.2144 8.8863 9.3232 8.9124 4.92% 0.946% 1.615% 42.4 0.59

8 1--6 6 9.3212 8.8924 9.4782 9.0115 6.59% 1.815% 4.990% 74.2 0.36


Wave-

length


400 14.02 9.11 6.90 3.71

420 18.46 12.39 9.38 4.61

440 17.39 11.34 8.35 4.01

460 15.05 9.46 6.86 3.28

480 13.17 7.96 5.61 2.69

500 11.66 6.83 4.76 2.32

520 9.92 5.51 3.82 1.92

540 7.98 4.35 3.03 1.63

560 6.84 3.67 2.58 1.48

580 5.70 3.05 2.20 1.36

600 4.70 2.57 1.90 1.28

620 4.00 2.24 1.71 1.24

640 3.38 2.00 1.60 1.24

660 3.15 1.93 1.57 1.27

680 4.18 2.48 1.91 1.41

700 9.84 5.70 4.06 2.33



340


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1099 32.92 20.7 67.5 1.615 11.61 863 3.12 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

12 1 only 1 6.2704 6.0839 6.3259 6.0759 3.98% 0.293% 0.649% 13.7 0.45

12 1--2 2 6.3197 6.137 6.4326 6.1427 4.82% 0.543% 0.982% 27.7 0.55

12 1--3 3 6.2591 6.0727 6.4005 6.0945 5.40% 0.883% 1.669% 43.2 0.53

12 1--4 4 6.3126 6.1273 6.5078 6.172 6.21% 1.084% 2.499% 53.9 0.43

12 1--5 5 6.1723 5.9917 6.3383 6.0469 5.78% 1.322% 3.318% 61.9 0.40

12 1--6 6 6.2837 6.0954 6.4653 6.1761 6.07% 1.534% 4.365% 70.1 0.35

12 1--6,3 7 6.2179 6.032 6.4599 6.1393 7.09% 1.915% 5.421% 76.7 0.35


Wave-

length


400 15.29 9.62 6.82 5.55 4.70 4.05 3.46

420 19.99 12.97 9.17 7.20 6.02 5.11 4.28

440 18.80 11.88 8.13 6.33 5.25 4.46 3.69

460 16.28 9.96 6.67 5.15 4.28 3.62 3.01

480 14.30 8.42 5.45 4.19 3.48 2.96 2.47

500 12.70 7.26 4.63 3.54 2.96 2.53 2.15

520 10.89 5.89 3.71 2.87 2.42 2.07 1.80

540 8.84 4.67 2.95 2.30 1.97 1.73 1.55

560 7.67 3.95 2.51 1.99 1.74 1.55 1.43

580 6.49 3.31 2.15 1.76 1.56 1.40 1.34

600 5.40 2.78 1.88 1.58 1.44 1.31 1.28

620 4.62 2.44 1.70 1.48 1.37 1.27 1.28

640 3.91 2.17 1.60 1.44 1.36 1.28 1.31

660 3.64 2.10 1.61 1.47 1.38 1.27 1.36

680 4.72 2.67 1.94 1.69 1.54 1.42 1.49

700 10.63 6.04 3.99 3.26 2.80 2.44 2.28



341


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)x3319 27.43 25 81 1.848 12.19 801 2.55 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 7.2411 6.9752 7.1837 6.9426 2.99% 0.361% 0.788% 19.4 0.46

6.3 1--2 2 7.2213 6.9499 7.2304 6.9491 4.04% 0.657% 1.229% 34.9 0.53

6.3 1--6 6 7.0463 6.7812 7.2084 6.879 6.30% 2.210% 6.007% 79.9 0.37


Wave-

length


400 12.41 7.98 3.14

420 16.61 10.98 3.77

440 15.48 9.97 3.23

460 13.23 8.28 2.67

480 11.42 6.84 2.20

500 10.02 5.83 1.94

520 8.33 4.67 1.66

540 6.65 3.69 1.48

560 5.61 3.13 1.39

580 4.65 2.65 1.33

600 3.83 2.25 1.32

620 3.25 1.99 1.32

640 2.79 1.82 1.40

660 2.60 1.76 1.48

680 3.38 2.17 1.61

700 8.24 4.79 2.27



342


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)x3319 27.43 25 81 1.848 12.19 801 2.55 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

12 1 only 1 3.7058 3.5809 3.7472 3.5754 4.64% 0.484% 0.823% 21.1 0.59

12 1--2 2 3.6324 3.5067 3.6773 3.5192 4.86% 0.947% 1.511% 40.6 0.63

12 1--3 3 3.759 3.6322 3.8482 3.6585 5.95% 1.426% 2.462% 53.5 0.58

12 1--6 6 3.7118 3.5766 3.857 3.6567 7.84% 2.595% 6.728% 83.3 0.39


Wave-

length


400 11.65 7.15 5.53 3.15

420 15.58 9.74 7.20 3.82

440 14.43 8.68 6.31 3.27

460 12.29 7.16 5.14 2.68

480 10.57 5.87 4.18 2.20

500 9.27 5.00 3.56 1.93

520 7.68 4.00 2.87 1.62

540 6.15 3.16 2.31 1.43

560 5.19 2.69 2.01 1.32

580 4.33 2.30 1.78 1.26

600 3.59 1.97 1.60 1.22

620 3.07 1.76 1.49 1.22

640 2.66 1.66 1.46 1.27

660 2.51 1.61 1.47 1.34

680 3.25 1.96 1.70 1.47

700 7.58 4.15 3.22 2.14



343


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)q1910 34.75 19.4 63.9 1.831 11.54 875 4.56 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 8.2323 7.9272 8.3113 7.9373 4.85% 0.304% 0.767% 18.5 0.40

6.3 1--2 2 8.2581 7.9618 8.4448 8 6.07% 0.519% 1.273% 35.9 0.41

6.3 1--3 3 8.485 8.1695 8.6831 8.2328 6.29% 0.770% 2.292% 51.6 0.34

6.3 1--4 4 8.3714 8.0747 8.7107 8.1577 7.88% 1.223% 4.101% 68.2 0.30

6.3 1--5 5 8.3184 8.0223 8.6216 8.1279 7.47% 1.433% 5.208% 75.5 0.28

6.3 1--6 6 8.2286 7.9186 8.5442 8.0586 7.90% 1.806% 6.792% 83.6 0.27

6.3 1--6,6 7 8.3819 8.0795 8.7471 8.2544 8.26% 2.010% 8.190% 89.2 0.25


Wave-

length


400 12.54 7.89 5.79 4.22 3.72 3.13 2.85

420 16.85 10.93 7.79 5.49 4.79 3.90 3.51

440 15.81 9.93 6.87 4.78 4.14 3.37 3.03

460 13.58 8.23 5.61 3.87 3.35 2.75 2.48

480 11.76 6.78 4.53 3.12 2.70 2.23 2.02

500 10.37 5.79 3.85 2.67 2.34 1.98 1.80

520 8.63 4.60 3.06 2.15 1.89 1.63 1.51

540 6.92 3.61 2.44 1.76 1.59 1.43 1.34

560 5.87 3.05 2.09 1.57 1.43 1.31 1.25

580 4.91 2.58 1.82 1.43 1.32 1.25 1.19

600 4.04 2.18 1.62 1.33 1.24 1.20 1.16

620 3.42 1.91 1.47 1.27 1.19 1.17 1.14

640 2.89 1.71 1.39 1.26 1.18 1.17 1.15

660 2.71 1.68 1.40 1.30 1.21 1.22 1.21

680 3.59 2.17 1.69 1.51 1.39 1.36 1.36

700 8.67 4.84 3.37 2.62 2.32 2.04 1.94



344


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)q1910 34.75 19.4 63.9 1.831 11.54 875 4.56 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

7.1 1 only 1 7.2029 7.0332 7.3818 7.0399 4.96% 0.310% 0.760% 18.2 0.41

7.1 1--2 2 7.333 7.1592 7.552 7.1788 5.49% 0.640% 1.296% 36.4 0.49

7.1 1--3 3 7.2629 7.0885 7.5579 7.1394 6.62% 0.994% 2.462% 53.5 0.40

7.1 1--4 4 7.3773 7.2105 7.7982 7.2833 8.15% 1.484% 4.344% 69.9 0.34

7.1 1--5 5 7.2513 7.0835 7.671 7.1767 8.29% 1.705% 5.098% 74.8 0.33

7.1 1--6 6 7.1983 7.0364 7.6291 7.1597 8.42% 1.984% 6.156% 80.6 0.32

7.1 1--6,6 7 7.2217 7.0393 7.6763 7.1922 9.05% 2.450% 8.627% 90.7 0.28


Wave-

length


400 12.44 7.84 5.71 4.19 3.74 3.32 2.80

420 16.73 10.85 7.68 5.45 4.81 4.21 3.46

440 15.77 9.86 6.77 4.73 4.16 3.62 2.97

460 13.60 8.17 5.50 3.81 3.36 2.93 2.44

480 11.79 6.71 4.44 3.06 2.71 2.36 1.97

500 10.45 5.74 3.76 2.62 2.34 2.07 1.76

520 8.75 4.56 2.98 2.10 1.89 1.70 1.49

540 7.04 3.57 2.37 1.72 1.60 1.47 1.32

560 5.99 3.02 2.01 1.53 1.44 1.35 1.22

580 5.03 2.55 1.76 1.39 1.33 1.27 1.18

600 4.15 2.16 1.55 1.29 1.26 1.23 1.15

620 3.52 1.88 1.41 1.23 1.21 1.19 1.12

640 2.96 1.69 1.33 1.23 1.22 1.20 1.16

660 2.75 1.65 1.35 1.29 1.26 1.27 1.21

680 3.63 2.12 1.64 1.50 1.44 1.43 1.37

700 8.60 4.70 3.29 2.57 2.35 2.14 1.92



345


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)q1910 34.75 19.4 63.9 1.831 11.54 875 4.56 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

8 1 only 1 9.3656 9.0787 9.5368 9.0704 5.05% 0.334% 0.736% 17.1 0.45

8 1--2 2 9.2041 8.899 9.4735 8.9336 6.46% 0.649% 1.253% 35.5 0.52

8 1--3 3 9.2402 8.9373 9.6106 9.0075 7.53% 1.042% 2.284% 51.5 0.46

8 1--4 4 9.3055 9.0069 9.7547 9.1089 8.30% 1.467% 4.250% 69.2 0.35

8 1--5 5 9.3216 9.035 9.7564 9.1587 7.98% 1.667% 4.942% 73.9 0.34

8 1--6 6 9.5513 9.2395 10.0173 9.4061 8.42% 1.982% 6.549% 82.5 0.30

8 1--6,6 7 9.4464 9.1405 10.0175 9.3583 9.59% 2.447% 8.610% 90.6 0.28


Wave-

length


400 12.96 7.94 5.73 4.20 3.76 3.25 2.77

420 17.29 10.94 7.67 5.41 4.80 4.07 3.36

440 16.26 9.91 6.77 4.69 4.16 3.49 2.88

460 14.05 8.23 5.51 3.80 3.38 2.84 2.38

480 12.19 6.75 4.43 3.06 2.72 2.28 1.94

500 10.79 5.78 3.77 2.61 2.35 2.00 1.73

520 9.11 4.61 3.01 2.11 1.92 1.66 1.48

540 7.34 3.63 2.41 1.74 1.62 1.44 1.32

560 6.29 3.08 2.08 1.54 1.46 1.33 1.24

580 5.32 2.62 1.84 1.41 1.36 1.25 1.19

600 4.41 2.22 1.64 1.31 1.28 1.20 1.16

620 3.77 1.97 1.51 1.26 1.24 1.18 1.15

640 3.19 1.77 1.45 1.24 1.23 1.19 1.18

660 2.98 1.72 1.46 1.27 1.28 1.26 1.22

680 3.84 2.20 1.75 1.48 1.47 1.43 1.38

700 8.82 4.78 3.37 2.54 2.36 2.13 1.92



346


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)q1910 34.75 19.4 63.9 1.831 11.54 875 4.56 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

12 1 only 1 6.3961 6.2118 6.5552 6.2301 5.53% 0.365% 0.760% 18.1 0.48

12 1--2 2 6.4423 6.2676 6.6617 6.3022 6.29% 0.743% 1.405% 38.6 0.53

12 1--3 3 6.4742 6.2971 6.7834 6.3538 7.72% 1.062% 2.284% 51.5 0.47

12 1--4 4 6.4341 6.2628 6.8095 6.3536 8.73% 1.618% 3.944% 67.0 0.41

12 1--5 5 6.6569 6.4754 7.0561 6.5851 8.97% 1.891% 5.059% 74.6 0.37

12 1--6 6 6.3026 6.1314 6.6941 6.2694 9.18% 2.194% 6.088% 80.3 0.36

12 1--6,6 7 6.2438 6.0627 6.6495 6.2253 9.68% 2.695% 8.236% 89.3 0.33


Wave-

length


400 12.78 7.56 5.88 4.32 3.82 3.41 2.89

420 17.00 10.36 7.85 5.57 4.86 4.27 3.55

440 15.90 9.34 6.91 4.83 4.20 3.68 3.04

460 13.67 7.72 5.63 3.92 3.40 2.99 2.48

480 11.82 6.31 4.53 3.15 2.73 2.41 2.01

500 10.42 5.38 3.84 2.69 2.35 2.11 1.78

520 8.73 4.29 3.06 2.18 1.91 1.73 1.51

540 7.03 3.37 2.44 1.79 1.60 1.48 1.33

560 5.98 2.84 2.09 1.59 1.44 1.34 1.25

580 5.02 2.41 1.83 1.46 1.34 1.28 1.19

600 4.15 2.04 1.62 1.35 1.25 1.21 1.16

620 3.54 1.79 1.48 1.30 1.21 1.18 1.14

640 2.99 1.63 1.41 1.30 1.22 1.21 1.17

660 2.79 1.61 1.42 1.35 1.27 1.26 1.24

680 3.67 2.05 1.71 1.56 1.46 1.45 1.39

700 8.66 4.50 3.39 2.65 2.37 2.19 1.95



347


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)x3313 32.92 20.7 67.5 1.762 12.31 795 3.12 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 7.0088 6.7264 7.0731 6.8342 5.15% 0.384% 0.777% 18.9 0.49

6.3 1--2 2 7.2426 6.9697 7.2378 6.957 3.85% 0.625% 1.221% 34.7 0.51

6.3 1--3 3 7.1191 6.8402 7.1819 6.8554 5.00% 0.985% 2.327% 52.0 0.42

6.3 1--4 4 7.3453 7.058 7.4495 7.0843 5.55% 1.284% 3.179% 60.6 0.40

6.3 1--5 5 7.1441 6.874 7.2638 6.9278 5.67% 1.590% 4.411% 70.4 0.36

6.3 1--6 6 7.2771 7.0013 7.3976 7.0653 5.66% 1.847% 5.147% 75.1 0.36


Wave-

length


400 12.20 7.93 5.70 4.73 3.99 3.57

420 16.25 10.89 7.50 6.03 5.02 4.42

440 15.18 9.88 6.58 5.25 4.32 3.77

460 13.01 8.18 5.34 4.25 3.48 3.05

480 11.30 6.77 4.34 3.46 2.84 2.48

500 9.99 5.80 3.69 2.95 2.44 2.16

520 8.36 4.65 2.95 2.40 1.98 1.79

540 6.72 3.68 2.38 1.97 1.67 1.55

560 5.73 3.14 2.06 1.75 1.52 1.44

580 4.81 2.66 1.81 1.59 1.41 1.36

600 3.99 2.27 1.62 1.48 1.34 1.32

620 3.44 2.04 1.53 1.44 1.33 1.34

640 2.91 1.84 1.47 1.43 1.34 1.36

660 2.76 1.85 1.53 1.54 1.48 1.53

680 3.55 2.30 1.83 1.78 1.69 1.73

700 8.21 4.90 3.45 3.04 2.66 2.53



348


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)x3313 32.92 20.7 67.5 1.762 12.31 795 3.12 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

7.1 1 only 1 5.8487 5.7 5.8979 5.6788 3.47% 0.359% 0.742% 17.3 0.48

7.1 1--2 2 6.5628 6.3415 6.6026 6.3355 4.12% 0.615% 1.146% 32.8 0.54

7.1 1--3 3 6.499 6.2929 6.5905 6.3009 4.73% 1.011% 2.175% 50.2 0.46

7.1 1--4 4 6.5925 6.3731 6.7401 6.4029 5.76% 1.360% 3.362% 62.3 0.40


Wave-

length


400 12.95 8.44 5.89 4.70

420 17.18 11.61 7.83 6.06

440 16.15 10.54 6.89 5.25

460 13.91 8.72 5.60 4.23

480 12.14 7.25 4.55 3.44

500 10.77 6.20 3.87 2.91

520 9.07 4.97 3.10 2.37

540 7.32 3.92 2.48 1.94

560 6.24 3.33 2.14 1.71

580 5.23 2.80 1.87 1.55

600 4.32 2.38 1.66 1.43

620 3.70 2.12 1.56 1.39

640 3.11 1.91 1.49 1.36

660 2.96 1.89 1.55 1.46

680 3.84 2.38 1.85 1.71

700 8.95 5.18 3.55 2.94



350


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)x3313 32.92 20.7 67.5 1.762 12.31 795 3.12 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

12 1 only 1 3.7928 3.6563 3.8136 3.6513 4.30% 0.500% 0.810% 20.4 0.62

12 1--2 2 3.6681 3.5419 3.6959 3.5516 4.35% 0.848% 1.339% 37.3 0.63

12 1--3 3 3.6897 3.5664 3.7866 3.5817 6.17% 1.298% 2.361% 52.4 0.55

12 1--4 4 3.7325 3.5998 3.8364 3.6348 6.57% 1.727% 3.586% 64.1 0.48

12 1--5 5 3.7053 3.581 3.8509 3.6372 7.54% 2.167% 4.842% 73.2 0.45

12 1--6 6 3.7607 3.6263 3.912 3.6989 7.88% 2.614% 5.975% 79.7 0.44


Wave-

length


400 11.65 7.71 5.70 4.55 3.83 3.27

420 15.46 10.50 7.47 5.80 4.74 3.98

440 14.38 9.43 6.55 5.02 4.07 3.41

460 12.30 7.79 5.33 4.05 3.28 2.79

480 10.65 6.40 4.34 3.30 2.67 2.28

500 9.38 5.47 3.68 2.80 2.29 1.99

520 7.82 4.37 2.95 2.27 1.88 1.67

540 6.29 3.46 2.37 1.87 1.59 1.47

560 5.35 2.94 2.05 1.66 1.47 1.37

580 4.49 2.49 1.80 1.51 1.36 1.30

600 3.72 2.12 1.61 1.40 1.31 1.28

620 3.22 1.90 1.52 1.37 1.33 1.31

640 2.74 1.71 1.46 1.37 1.35 1.35

660 2.63 1.72 1.53 1.47 1.50 1.54

680 3.39 2.17 1.82 1.71 1.72 1.73

700 7.80 4.62 3.45 2.87 2.60 2.41



353


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)4223 32.92 20.7 67.5 2.07 12.49 907 3.75 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

8 1 only 1 5.7344 5.661 5.8671 5.6131 3.64% 0.321% 0.693% 15.3 0.46

8 1--2 2 5.6597 5.5909 5.8276 5.5547 4.23% 0.634% 0.995% 28.2 0.64


Wave-

length


400 14.29 9.50

420 18.79 12.85

440 17.78 11.85

460 15.42 9.95

480 13.46 8.39

500 11.93 7.24

520 10.12 5.84

540 8.15 4.63

560 7.01 3.91

580 5.86 3.26

600 4.82 2.73

620 4.07 2.36

640 3.44 2.09

660 3.21 2.00

680 4.29 2.59

700 10.14 6.00



354


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)4223 32.92 20.7 67.5 2.07 12.49 907 3.75 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

12 1 only 1 3.5474 3.4913 3.6178 3.4652 3.62% 0.398% 0.746% 17.5 0.53

12 2 only 1 3.6069 3.5505 3.6872 3.522 3.85% 0.480% 0.813% 20.6 0.59

12 1--2 2 3.7068 3.6437 3.7792 3.6242 3.72% 0.757% 1.065% 30.5 0.71

12 1--2,1 3 3.5935 3.543 3.6935 3.5284 4.25% 0.902% 1.317% 36.9 0.68

12 1--2,2 3 3.6744 3.6178 3.805 3.6117 5.17% 1.026% 1.538% 41.1 0.67


Wave-

length


400 12.96 11.86 8.98 7.76 7.05

420 17.20 15.87 12.21 10.58 9.62

440 16.21 14.78 11.22 9.60 8.62

460 13.93 12.54 9.37 7.94 7.09

480 12.14 10.81 7.86 6.55 5.81

500 10.75 9.52 6.78 5.59 4.95

520 9.05 7.88 5.44 4.47 3.96

540 7.29 6.31 4.29 3.52 3.13

560 6.21 5.35 3.62 2.98 2.66

580 5.21 4.45 3.04 2.53 2.28

600 4.28 3.66 2.54 2.15 1.95

620 3.61 3.10 2.20 1.87 1.74

640 3.05 2.66 1.96 1.71 1.62

660 2.89 2.55 1.90 1.68 1.61

680 3.84 3.36 2.45 2.11 1.98

700 9.12 8.05 5.66 4.64 4.17



355


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)x3313 32.92 20.7 67.5 1.93 12.33 800 3.26 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

12 1 only 1 3.6373 3.5076 3.6763 3.5062 4.81% 0.530% 0.819% 20.9 0.65

12 1--2 2 3.7084 3.5745 3.7704 3.5885 5.48% 0.957% 1.407% 38.7 0.68

12 1--3 3 3.6452 3.5159 3.7292 3.5398 6.07% 1.489% 2.513% 54.1 0.59

12 1--4 4 3.7243 3.5849 3.8534 3.6266 7.49% 1.857% 3.874% 66.4 0.48

12 1--5 5 3.6299 3.5014 3.7814 3.5641 8.00% 2.271% 4.897% 73.6 0.46

12 1--6 6 3.605 3.466 3.7744 3.5592 8.90% 2.730% 6.648% 83.0 0.41


Wave-

length


400 11.68 7.46 5.57 4.40 3.74 3.16

420 15.55 10.15 7.21 5.57 4.60 3.83

440 14.36 9.04 6.29 4.79 3.94 3.25

460 12.22 7.44 5.09 3.87 3.20 2.65

480 10.53 6.11 4.13 3.15 2.61 2.17

500 9.27 5.20 3.49 2.67 2.26 1.90

520 7.67 4.16 2.81 2.18 1.85 1.60

540 6.16 3.30 2.27 1.79 1.59 1.41

560 5.24 2.81 1.97 1.60 1.46 1.32

580 4.37 2.39 1.74 1.46 1.37 1.26

600 3.63 2.06 1.58 1.37 1.32 1.24

620 3.20 1.87 1.51 1.35 1.33 1.28

640 2.67 1.71 1.46 1.35 1.37 1.32

660 2.56 1.76 1.55 1.48 1.52 1.49

680 3.32 2.17 1.84 1.70 1.71 1.66

700 7.61 4.48 3.36 2.81 2.56 2.31



356


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath

pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)4223 32.92 20.67 67.5 2.011 12.7 924 4.12 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 7.03 6.771999 7.0441 6.7844 4.02% 0.262% 0.701% 15.6 0.37

6.3 1--2 2 7.021 6.725472 7.043 6.7478 4.72% 0.519% 0.944% 26.3 0.55


Wave-

length


400 14.13 10.18

420 18.70 13.85

440 17.66 12.77

460 15.22 10.68

480 13.28 9.02

500 11.76 7.82

520 9.94 6.29

540 7.98 4.95

560 6.87 4.18

580 5.74 3.49

600 4.71 2.88

620 3.97 2.48

640 3.31 2.15

660 3.07 2.04

680 4.10 2.64

700 9.88 6.42



357


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath

pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)4223 32.92 20.67 67.5 2.011 12.7 924 4.12 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

7.1 1 only 1 6.301 6.07168 6.3521 6.1162 4.62% 0.298% 0.689% 15.1 0.43

7.1 1--2 2 6.0678 5.845112 6.191 5.9095 5.92% 0.545% 0.942% 26.3 0.58


Wave-

length


400 14.39 9.99

420 18.94 13.57

440 17.91 12.60

460 15.48 10.60

480 13.57 8.98

500 12.02 7.80

520 10.22 6.31

540 8.22 4.98

560 7.10 4.21

580 5.95 3.52

600 4.88 2.92

620 4.11 2.50

640 3.42 2.15

660 3.18 2.06

680 4.27 2.65

700 10.15 6.40



358


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath

pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)4223 32.92 20.67 67.5 2.011 12.7 924 4.12 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

8 1 only 1 5.582 5.377141 5.6381 5.4209 4.85% 0.278% 0.636% 13.2 0.44

8 1--2 2 5.621 5.414709 5.7319 5.484 5.86% 0.520% 0.913% 25.1 0.57


Wave-

length


400 15.70 10.35

420 20.49 14.00

440 19.55 13.00

460 17.06 10.97

480 15.05 9.33

500 13.42 8.12

520 11.44 6.58

540 9.22 5.20

560 7.99 4.41

580 6.70 3.68

600 5.49 3.04

620 4.61 2.61

640 3.83 2.24

660 3.50 2.11

680 4.81 2.75

700 11.48 6.67



359


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath

pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)4223 32.92 20.67 67.5 2.011 12.7 924 4.12 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

12 1 only 1 3.525 3.395633 3.5906 3.4191 5.74% 0.360% 0.690% 15.2 0.52

12 1--2 2 3.5068 3.3781 3.5844 3.4127 6.11% 0.734% 1.047% 30.0 0.70


Wave-

length


400 14.50 9.13

420 19.11 12.33

440 18.06 11.38

460 15.59 9.55

480 13.63 8.05

500 12.07 6.93

520 10.23 5.59

540 8.23 4.41

560 7.09 3.73

580 5.93 3.11

600 4.85 2.58

620 4.09 2.22

640 3.42 1.93

660 3.18 1.82

680 4.30 2.38

700 10.24 5.70



360


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)t3663 34.75 19.6 63.9 2.053 11.84 865 4.29 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 8.1651 7.8331 8.1628 7.8071 4.21% 0.299% 0.776% 18.9 0.39

6.3 1--2 2 8.3718 8.0264 8.4349 8.0296 5.09% 0.602% 1.338% 37.3 0.45

6.3 1--3 3 8.2892 7.9509 8.4839 7.9736 6.70% 0.959% 2.362% 52.4 0.41

6.3 1--4 4 8.2337 7.9014 8.4259 7.951 6.64% 1.268% 3.931% 66.9 0.32

6.3 1--5 5 8.0853 7.756 8.3329 7.8362 7.44% 1.602% 5.611% 77.8 0.29

6.3 1--6 6 8.301 7.9584 8.5545 8.0585 7.49% 1.750% 6.144% 80.6 0.28

6.3 1--7 7 8.3284 7.9843 8.6764 8.1288 8.67% 2.127% 7.807% 87.8 0.27


Wave-

length


400 12.87 7.86 5.86 4.40 3.62 3.33 2.88

420 17.39 10.92 7.87 5.68 4.57 4.14 3.50

440 16.14 9.83 6.87 4.92 3.93 3.56 2.99

460 13.70 8.06 5.54 3.97 3.17 2.89 2.47

480 11.76 6.57 4.46 3.21 2.58 2.37 2.04

500 10.28 5.57 3.75 2.73 2.22 2.06 1.81

520 8.52 4.42 2.99 2.21 1.82 1.71 1.55

540 6.79 3.46 2.39 1.82 1.55 1.50 1.38

560 5.74 2.93 2.04 1.62 1.40 1.37 1.29

580 4.78 2.47 1.80 1.46 1.30 1.29 1.22

600 3.92 2.10 1.59 1.34 1.22 1.23 1.19

620 3.32 1.84 1.46 1.27 1.17 1.18 1.16

640 2.81 1.67 1.38 1.23 1.15 1.17 1.15

660 2.64 1.62 1.38 1.24 1.17 1.20 1.19

680 3.45 2.04 1.66 1.44 1.34 1.34 1.34

700 8.51 4.57 3.30 2.55 2.18 2.07 1.92



361


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1472 34.75 19.6 63.9 2.259 11.85 858 4.17 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 8.032 7.8333 8.2375 7.8335 5.16% 0.369% 0.814% 20.6 0.45

6.3 1--2 2 8.2171 8.0055 8.534 8.0456 6.60% 0.680% 1.487% 40.2 0.46

6.3 1--3 3 7.9604 7.7594 8.3303 7.8241 7.36% 1.140% 3.216% 61.0 0.35

6.3 1--4 4 8.2216 8.0146 8.6908 8.1186 8.44% 1.579% 5.254% 75.8 0.30

6.3 1--5 5 8.1625 7.9496 8.6538 8.078 8.86% 1.893% 6.629% 82.9 0.29

6.3 1--6 6 8.1076 7.896 8.5833 8.0701 8.70% 2.320% 9.206% 92.5 0.25

6.3 1--6,6 7 8.1482 7.9452 8.6776 8.1481 9.22% 2.776% 12.658% 101.2 0.22


Wave-

length


400 12.13 7.48 5.11 3.85 3.32 2.79 2.40

420 16.28 10.29 6.72 4.93 4.16 3.42 2.90

440 15.12 9.19 5.85 4.24 3.57 2.93 2.47

460 12.87 7.56 4.72 3.42 2.91 2.41 2.06

480 11.06 6.17 3.80 2.77 2.35 1.97 1.70

500 9.69 5.22 3.20 2.36 2.04 1.74 1.53

520 8.00 4.15 2.56 1.92 1.70 1.48 1.33

540 6.35 3.25 2.04 1.59 1.45 1.31 1.21

560 5.33 2.73 1.76 1.43 1.32 1.22 1.14

580 4.39 2.30 1.55 1.30 1.23 1.15 1.10

600 3.58 1.94 1.39 1.21 1.17 1.10 1.06

620 3.04 1.71 1.29 1.16 1.13 1.08 1.05

640 2.58 1.58 1.26 1.15 1.14 1.09 1.08

660 2.44 1.55 1.26 1.17 1.18 1.13 1.13

680 3.22 1.93 1.50 1.34 1.32 1.28 1.28

700 8.04 4.37 2.94 2.33 2.13 1.90 1.79



362


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1472 34.75 19.6 63.9 2.158 11.88 846 4.4 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

12 1 only 1 6.447 6.2519 6.6002 6.2628 5.57% 0.414% 0.801% 20.0 0.52

12 1--2 2 6.3497 6.1528 6.5768 6.1785 6.89% 0.754% 1.457% 39.6 0.52

12 1--3 3 6.3301 6.1345 6.6115 6.1922 7.78% 1.154% 2.757% 56.6 0.42

12 1--4 4 6.4312 6.2393 6.8487 6.3386 9.77% 1.672% 4.750% 72.6 0.35

12 1--5 5 6.4161 6.2238 6.8584 6.3486 10.20% 2.008% 6.186% 80.8 0.32

12 1--6 6 6.5723 6.379 6.9502 6.527 8.95% 2.355% 7.485% 86.5 0.31

12 1--6,6 7 6.3727 6.1859 6.7831 6.3583 9.65% 2.824% 9.110% 92.2 0.31


Wave-

length


400 12.33 7.56 5.54 4.06 3.46 3.09 2.71

420 16.46 10.34 7.28 5.15 4.31 3.79 3.26

440 15.19 9.20 6.34 4.42 3.70 3.24 2.79

460 12.90 7.55 5.13 3.57 3.00 2.66 2.32

480 11.08 6.17 4.14 2.89 2.43 2.17 1.91

500 9.72 5.23 3.49 2.46 2.11 1.90 1.71

520 8.08 4.17 2.79 1.99 1.74 1.60 1.46

540 6.48 3.28 2.22 1.66 1.48 1.40 1.32

560 5.47 2.77 1.91 1.48 1.35 1.29 1.23

580 4.54 2.34 1.67 1.36 1.26 1.20 1.18

600 3.74 1.99 1.47 1.26 1.19 1.15 1.14

620 3.19 1.75 1.36 1.20 1.16 1.13 1.12

640 2.74 1.62 1.31 1.22 1.18 1.14 1.14

660 2.59 1.58 1.31 1.25 1.23 1.17 1.19

680 3.39 1.98 1.56 1.44 1.37 1.33 1.32

700 8.02 4.36 3.14 2.46 2.21 2.02 1.89



363


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath

pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)x3626 31.09 21.7 71.5 2.283 11.8 783 4.48 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 7.6676 7.3705 7.5957 7.3264 3.06% 0.269% 0.695% 15.4 0.39

6.3 1--2 2 7.5517 7.2591 7.5283 7.2227 3.71% 0.512% 1.085% 31.1 0.47

6.3 1--3 3 7.775 7.4737 7.8205 7.4725 4.64% 0.905% 2.283% 51.5 0.40

6.3 1--4 4 7.6524 7.3559 7.8012 7.3751 6.05% 1.257% 3.558% 63.9 0.35

6.3 1--5 5 7.6481 7.3518 7.8006 7.4118 6.10% 1.588% 4.585% 71.6 0.35

6.3 1--6 6 7.7748 7.4736 7.9554 7.5411 6.45% 1.915% 6.496% 82.3 0.29

6.3 1--7 7 7.7656 7.4647 7.977 7.5723 6.86% 2.168% 7.223% 85.5 0.30


Wave-

length


400 14.31 8.98 5.88 4.60 3.98 3.26 3.04

420 19.21 12.51 7.94 6.01 5.07 4.04 3.69

440 17.94 11.31 6.94 5.19 4.34 3.44 3.13

460 15.36 9.31 5.58 4.15 3.46 2.77 2.54

480 13.37 7.73 4.50 3.35 2.81 2.27 2.08

500 11.77 6.59 3.80 2.84 2.40 1.97 1.82

520 9.94 5.27 3.04 2.30 1.96 1.66 1.56

540 7.94 4.13 2.42 1.88 1.65 1.44 1.38

560 6.86 3.50 2.08 1.68 1.50 1.34 1.31

580 5.81 2.96 1.83 1.52 1.39 1.26 1.25

600 4.80 2.48 1.62 1.40 1.32 1.21 1.21

620 4.09 2.18 1.50 1.33 1.29 1.21 1.22

640 3.40 1.92 1.39 1.29 1.29 1.22 1.24

660 3.15 1.84 1.41 1.33 1.35 1.29 1.34

680 4.04 2.34 1.68 1.53 1.54 1.43 1.49

700 9.66 5.35 3.34 2.71 2.49 2.15 2.11



364


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)x3626 31.09 21.7 71.5 2.134 11.76 789 4.58 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

8 1 only 1 6.1223 5.9148 6.1102 5.8681 3.30% 0.323% 0.731% 16.8 0.44

8 1--2 2 6.0951 5.8885 6.1361 5.8684 4.20% 0.547% 1.152% 33.0 0.47

8 1--3 3 6.0795 5.8735 6.1711 5.8636 5.07% 0.772% 1.951% 47.3 0.40

8 1--4 4 6.0613 5.8559 6.2155 5.8792 6.14% 1.261% 3.184% 60.7 0.40

8 1--5 5 6.1556 5.947 6.2897 5.9884 5.76% 1.548% 4.060% 67.9 0.38

8 1--6 6 6.1024 5.8956 6.2778 5.955 6.48% 1.738% 4.785% 72.9 0.36


Wave-

length


400 13.69 8.60 6.29 4.86 4.25 3.84

420 18.39 11.95 8.63 6.36 5.50 4.86

440 17.06 10.78 7.59 5.51 4.72 4.15

460 14.51 8.85 6.14 4.41 3.77 3.32

480 12.57 7.31 4.96 3.57 3.05 2.70

500 11.04 6.22 4.19 3.03 2.60 2.32

520 9.27 4.97 3.34 2.46 2.12 1.91

540 7.41 3.89 2.65 2.00 1.76 1.62

560 6.35 3.31 2.28 1.77 1.59 1.49

580 5.36 2.80 1.99 1.59 1.45 1.38

600 4.43 2.37 1.73 1.46 1.36 1.31

620 3.78 2.09 1.59 1.38 1.31 1.28

640 3.15 1.84 1.49 1.33 1.28 1.28

660 2.93 1.79 1.48 1.36 1.32 1.34

680 3.77 2.24 1.78 1.55 1.51 1.50

700 9.00 5.03 3.59 2.82 2.54 2.39



365


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1139 28.35 24.1 78.4 2.261 11.69 810 5.09 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 8.2729 7.9479 8.207 7.9275 3.26% 0.290% 0.709% 15.9 0.41

6.3 1--2 2 8.3119 7.9733 8.3618 7.9816 4.87% 0.609% 1.181% 33.7 0.52

6.3 1--3 3 8.3462 8.0196 8.4306 8.05 5.12% 1.042% 2.285% 51.5 0.46

6.3 1--3,2 4 8.3676 8.0251 8.4956 8.0903 5.86% 1.258% 2.984% 58.8 0.42

6.3 1-3,2-3 5 8.2123 7.8902 8.3684 7.9789 6.06% 1.624% 4.320% 69.7 0.38

6.3

1-3,2-

3,2 6 8.2672 7.9373 8.4549 8.057 6.52% 1.986% 5.539% 77.4 0.36

6.3

1-3,2-

3,2-3 7 8.2995 7.9644 8.5276 8.1316 7.07% 2.410% 7.229% 85.5 0.33

% Reflectance ReadingsWave-

length


400 13.76 8.27 5.80 4.90 4.01 3.42 2.90

420 18.33 11.39 7.65 6.32 5.06 4.18 3.43

440 17.25 10.31 6.73 5.50 4.36 3.59 2.94

460 14.89 8.52 5.47 4.45 3.53 2.92 2.42

480 12.99 7.03 4.45 3.62 2.88 2.40 2.00

500 11.50 6.00 3.77 3.09 2.47 2.09 1.78

520 9.70 4.79 3.01 2.50 2.01 1.74 1.53

540 7.79 3.79 2.42 2.04 1.69 1.52 1.38

560 6.70 3.22 2.09 1.82 1.55 1.43 1.32580 5.62 2.73 1.83 1.63 1.43 1.35 1.27

600 4.64 2.34 1.63 1.52 1.36 1.30 1.27

620 3.93 2.05 1.50 1.44 1.30 1.27 1.26

640 3.32 1.88 1.45 1.44 1.33 1.32 1.32

660 3.10 1.85 1.46 1.50 1.40 1.40 1.44

680 4.09 2.31 1.73 1.71 1.57 1.55 1.57

700 9.65 5.07 3.40 3.02 2.55 2.30 2.13



366


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)x3669 31.09 21.7 71.5 2.277 11.92 880 5.14 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 7.8172 7.4743 7.7695 7.4467 3.95% 0.362% 0.755% 17.9 0.48

6.3 1--2 2 8.216 7.867 8.3122 7.8683 5.66% 0.680% 1.346% 37.5 0.51

6.3 1--3 3 8.3614 7.97 8.5573 8.0045 7.37% 1.075% 2.515% 54.1 0.43

6.3 1--4 4 7.8534 7.56 8.2356 7.6236 8.94% 1.442% 4.041% 67.7 0.36

6.3 1--5 5 8.384 8.0202 8.6356 8.1199 7.67% 1.798% 5.721% 78.4 0.31

6.3 1--6 6 8.3886 8.0244 8.6667 8.154 8.00% 2.114% 7.003% 84.5 0.30


Wave-

length


400 13.21 7.71 5.57 4.23 3.49 3.05

420 17.80 10.67 7.35 5.37 4.35 3.71

440 16.54 9.52 6.39 4.62 3.73 3.16

460 14.03 7.75 5.13 3.72 3.00 2.56

480 12.10 6.31 4.14 3.03 2.46 2.09

500 10.61 5.37 3.50 2.59 2.15 1.87

520 8.86 4.30 2.82 2.13 1.78 1.58

540 7.06 3.38 2.26 1.76 1.52 1.40

560 6.01 2.89 1.97 1.59 1.40 1.32

580 5.03 2.47 1.76 1.46 1.31 1.26

600 4.14 2.12 1.58 1.37 1.24 1.23

620 3.51 1.88 1.47 1.31 1.21 1.22

640 2.95 1.73 1.44 1.31 1.22 1.26

660 2.75 1.71 1.43 1.35 1.25 1.32

680 3.56 2.09 1.67 1.52 1.39 1.46

700 8.70 4.48 3.19 2.58 2.20 2.11



367


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1139 28.35 24.1 78.4 2.307 11.77 822 5.62 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

7.1 1 only 1 7.2476 7.0441 7.3261 7.0477 4.00% 0.351% 0.767% 18.5 0.46

7.1 1--2 2 7.2488 7.0476 7.4163 7.0762 5.23% 0.708% 1.338% 37.3 0.53

7.1 1--3 3 7.218 7.0199 7.4125 7.0754 5.59% 1.042% 2.061% 48.8 0.51

7.1 1-3,1 4 7.0859 6.8954 7.2841 6.9645 5.64% 1.249% 3.124% 60.1 0.40

7.1 1-3,1-2 5 7.263 7.0584 7.5089 7.1656 6.38% 1.588% 4.651% 72.0 0.34

7.1 1-3,1-3 6 6.9719 6.7815 7.243 6.9018 6.81% 1.839% 5.282% 75.9 0.35

7.1

1-3,1-

3,3 7 7.2627 7.0641 7.5541 7.204 6.94% 2.036% 6.052% 80.1 0.34


Wave-

length


400 12.76 7.67 6.12 4.87 3.87 3.48 3.19

420 17.03 10.49 8.22 6.26 4.88 4.32 3.93

440 15.87 9.46 7.23 5.46 4.21 3.73 3.38

460 13.55 7.79 5.87 4.41 3.41 3.04 2.76

480 11.70 6.39 4.76 3.59 2.78 2.48 2.26

500 10.27 5.44 4.02 3.04 2.38 2.16 1.99

520 8.57 4.34 3.21 2.47 1.96 1.79 1.67

540 6.89 3.44 2.57 2.01 1.65 1.56 1.48

560 5.85 2.92 2.19 1.76 1.49 1.43 1.38

580 4.91 2.48 1.92 1.60 1.39 1.36 1.31

600 4.05 2.13 1.69 1.47 1.31 1.30 1.28

620 3.47 1.89 1.57 1.42 1.29 1.30 1.27

640 2.96 1.75 1.52 1.42 1.31 1.34 1.32

660 2.80 1.75 1.55 1.47 1.38 1.40 1.40

680 3.63 2.18 1.85 1.66 1.50 1.54 1.53

700 8.56 4.67 3.62 2.95 2.43 2.30 2.20



368


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath

pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1134 26.52 25.7 83.8 3.228 11.4 873 6.15 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 8.3125 8.1211 8.5311 8.1202 5.05% 0.536% 1.134% 32.5 0.47

6.3 1--2 2 8.4711 8.2729 8.7909 8.3016 6.26% 0.985% 2.517% 54.1 0.39

6.3 1--3 3 8.1344 7.949 8.4708 8.0168 6.56% 1.390% 3.911% 66.7 0.36

6.3 1--4 4 8.0632 7.8635 8.4996 7.9789 8.09% 1.873% 6.196% 80.8 0.30

6.3 1--5 5 8.4616 8.2617 8.9728 8.4229 8.61% 2.404% 9.286% 92.8 0.26

6.3 1--6 6 8.2664 8.0742 8.7887 8.2648 8.85% 2.716% 11.748% 99.2 0.23


Wave-

length


400 8.80 5.75 4.49 3.36 2.72 2.42

420 11.99 7.57 5.77 4.17 3.27 2.87

440 10.84 6.59 4.97 3.56 2.79 2.46

460 8.98 5.33 4.00 2.89 2.30 2.04

480 7.45 4.30 3.23 2.35 1.89 1.69

500 6.37 3.63 2.74 2.04 1.67 1.51

520 5.10 2.90 2.21 1.69 1.45 1.33

540 4.01 2.31 1.81 1.47 1.29 1.22

560 3.38 1.99 1.60 1.36 1.23 1.18

580 2.81 1.73 1.45 1.27 1.16 1.12

600 2.37 1.55 1.34 1.23 1.14 1.11

620 2.07 1.42 1.28 1.19 1.13 1.10

640 1.87 1.36 1.26 1.21 1.16 1.13

660 1.86 1.38 1.30 1.29 1.22 1.21

680 2.42 1.68 1.52 1.46 1.38 1.37

700 5.46 3.32 2.70 2.22 1.90 1.81



369


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)1134 29.26 23.5 75.9 3.497 11.62 897 5.13 11.37 40.50 40.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 8.1467 7.9327 8.4423 7.9751 6.42% 0.572% 1.173% 33.5 0.49

6.3 1--2 2 8.0416 7.8292 8.4436 7.9149 7.85% 1.018% 2.575% 54.7 0.40

6.3 1--3 3 8.1968 7.9807 8.7331 8.1307 9.43% 1.740% 5.540% 77.4 0.31

6.3 1--4 4 8.8101 8.5772 9.5213 8.7939 11.01% 2.221% 7.437% 86.3 0.30

6.3 1--5 5 8.1834 7.9693 8.8128 8.2008 10.58% 2.837% 10.632% 96.5 0.27

6.3 1--6 6 8.2567 8.0436 8.9386 8.344 11.13% 3.520% 15.773% 106.8 0.22


Wave-

length


400 8.39 5.54 3.61 3.07 2.53 2.15

420 11.38 7.28 4.57 3.79 3.04 2.51

440 10.33 6.39 3.95 3.26 2.61 2.16

460 8.62 5.20 3.21 2.67 2.18 1.81

480 7.18 4.22 2.62 2.18 1.80 1.55

500 6.14 3.57 2.25 1.89 1.60 1.39

520 4.92 2.86 1.84 1.60 1.39 1.25

540 3.89 2.29 1.56 1.39 1.25 1.15

560 3.28 1.96 1.40 1.29 1.19 1.11

580 2.75 1.72 1.29 1.20 1.13 1.07

600 2.32 1.53 1.22 1.15 1.11 1.05

620 2.02 1.41 1.17 1.13 1.09 1.05

640 1.86 1.38 1.19 1.15 1.13 1.09

660 1.84 1.41 1.27 1.22 1.22 1.21

680 2.38 1.72 1.47 1.41 1.40 1.39

700 5.27 3.31 2.37 2.09 1.90 1.76



370

Section A- 4-2a: Convergence test - standard errors from empirical model %COWY parameter.

Table A-4-2a: Convergence test - standard errors from empirical model %COWY parameter.

Replica Yarn Count Speed Dye Bath pH speed^2 pHxspeed

0 0.003113 0.003133 0.01738 0.02172 0.000914 0.01364

1 0.00315 0.003396 0.018228 0.021433 0.000958 0.0143122 0.00313 0.003355 0.017996 0.021339 0.000951 0.01421

3 0.00314 0.00342 0.018731 0.021787 0.000964 0.014765

4 0.003112 0.003084 0.017408 0.021387 0.000915 0.013797

5 0.003115 0.003153 0.017462 0.021557 0.00094 0.013836

6 0.003113 0.00314 0.017343 0.021474 0.000932 0.013792

7 0.0031 0.003098 0.017026 0.020976 0.000919 0.013469

8 0.00307 0.003052 0.016932 0.020782 0.000914 0.013297

9 0.003068 0.003037 0.0168 0.020657 0.000908 0.013199

10 0.003062 0.00301 0.016887 0.020668 0.000891 0.012464

11 0.00306 0.002926 0.016651 0.020338 0.000825 0.010533

12 0.003 0.002943 0.016492 0.020163 0.000823 0.010474

13 0.00298 0.002965 0.01632 0.020056 0.000824 0.01046

14 0.00297 0.002928 0.016272 0.02 0.00082 0.010441

15 0.00298 0.002958 0.016713 0.020503 0.000838 0.01073

16 0.002985 0.002952 0.016678 0.020059 0.000835 0.01056117 0.002975 0.002985 0.01681 0.020034 0.000841 0.010593

18 0.002978 0.002926 0.016542 0.019788 0.000837 0.010441

19 0.002978 0.002915 0.016484 0.01984 0.000837 0.010467

20 0.002979 0.00291 0.016437 0.019681 0.000833 0.010433

Section A-4-2b: Convergence test - standard errors from empirical model %IOWY parameter.

Table A-4-2b: Convergence test - standard errors from empirical model %IOWY parameter.

Replica Yarn Count speed dye pH

0 0.002927 0.002615 0.016024 0.019996

1 0.002895 0.002653 0.016316 0.0189782 0.002864 0.002628 0.016038 0.018823

3 0.002844 0.002658 0.016224 0.018855

4 0.00281 0.002469 0.015318 0.01855

5 0.002798 0.002544 0.015398 0.018731

6 0.002756 0.002528 0.015238 0.018597

7 0.002694 0.002502 0.01498 0.018202

8 0.00268 0.002483 0.014918 0.018067

9 0.002645 0.00246 0.014809 0.017961

10 0.002598 0.002419 0.014756 0.017865

11 0.002545 0.00232 0.014578 0.017354

12 0.002531 0.002287 0.014245 0.016994

13 0.002528 0.002269 0.013943 0.016748

14 0.002522 0.00225 0.013844 0.016644

15 0.002509 0.002271 0.014003 0.016852

16 0.002507 0.002267 0.013973 0.01653117 0.002505 0.002263 0.013961 0.016384

18 0.002501 0.002239 0.013747 0.016199

19 0.0025 0.002232 0.013637 0.016157

20 0.002502 0.002252 0.013757 0.016186



371

Section A-4-2c: Convergence test - standard errors from empirical model Integ parameter.

Table A-4-2c: Convergence test - standard errors from empirical model Integ parameter.

Replica Yarn Count speed dye pH

0 0.00324 0.002894 0.017737 0.022134

1 0.00315 0.002874 0.01767 0.0205542 0.003058 0.002856 0.017427 0.020453

3 0.003011 0.002794 0.017054 0.019819

4 0.002984 0.002596 0.016104 0.019501

5 0.003008 0.002677 0.016204 0.019712

6 0.002993 0.002664 0.016064 0.019604

7 0.002981 0.002654 0.015895 0.019314

8 0.002943 0.002643 0.015879 0.01923

9 0.002924 0.002623 0.015789 0.01915

10 0.002901 0.002579 0.015733 0.019048

11 0.002858 0.002505 0.015736 0.018733

12 0.002843 0.002488 0.015494 0.018484

13 0.002821 0.00249 0.015302 0.018381

14 0.0028 0.00247 0.015197 0.01827

15 0.00274 0.002443 0.015062 0.018127

16 0.00272 0.002435 0.015011 0.01775917 0.00271 0.002421 0.014939 0.017532

18 0.00269 0.002413 0.014815 0.017459

19 0.00267 0.002409 0.014718 0.017438

20 0.00268 0.002412 0.014737 0.017339

Section A-4-2d: Convergence test - standard errors from empirical model Penetration Level

parameter.

Table A-4-2d: Convergence test - standard errors from empirical model penetration level parameter.

Replica Yarn Count speed dye pH speedxpH speed^20 0.00158 0.001596 0.005862 0.011468 0.007098 0.000474

1 0.001542 0.001644 0.005836 0.010732 0.007072 0.000471

2 0.001548 0.001627 0.005711 0.01069 0.007045 0.000468

3 0.001535 0.001561 0.005602 0.010299 0.006884 0.000447

4 0.001521 0.001432 0.00523 0.010235 0.006492 0.000431

5 0.001448 0.001417 0.005111 0.009974 0.006299 0.000428

6 0.001432 0.001411 0.005069 0.00928 0.006276 0.000424

7 0.001426 0.001395 0.004984 0.009734 0.006139 0.00042

8 0.001401 0.001375 0.00496 0.009651 0.006065 0.000417

9 0.001381 0.00137 0.004932 0.009603 0.006027 0.000415

10 0.001368 0.001347 0.004919 0.009538 0.005648 0.000404

11 0.001352 0.001315 0.004819 0.009392 0.004787 0.000378

12 0.001348 0.001319 0.00475 0.009294 0.004746 0.000377

13 0.001334 0.001319 0.004678 0.009185 0.004767 0.000374

14 0.001321 0.001297 0.004646 0.009123 0.00468 0.00037115 0.00131 0.001247 0.004562 0.00894 0.004608 0.000362

16 0.001288 0.001246 0.004558 0.008766 0.00454 0.000362

17 0.001281 0.001245 0.004541 0.008665 0.004502 0.00036

18 0.001279 0.001225 0.004409 0.008546 0.004456 0.000359

19 0.001278 0.001226 0.004387 0.008601 0.004485 0.00036

20 0.001279 0.001227 0.004383 0.008546 0.00448 0.000359



372

Section A-4-3a: Computer program to calculate dye coefficients given the input dye range set-up

conditions and target %COWY, %IOWY, and Integ shade values.

#include <stdio.h>

#include <fcntl.h>

#include <stdlib.h>

#include <math.h>

int main ()

{

FILE * pFile;

FILE * oFile;

double AA[61][61], BB[61][61], RBLgm[61], RBL1gm[61], Cj[61], Cj1[61], d[61],

TBL[61], TBL1[61], RBL[61], RBL1[61], OBL[61], OBL1[61];

double AAinvt[61][62], X[61], Xrbl[61], Xiowy[61], temp[61], IOWY[61],

COWY[61], IOWYoxd[61], temp1, Multi, fraction_dye_affinity

, fraction_oxy_affinity;

double OBLgm[61], OBL1gm[61], dumb[61], IOWYstep[61], gms_ctn_node[61],

liter_per_node[61], Df_constantAO[10], Dy_constantAO[10],

WP_constantAO[10], wash_constantAO[10];

double IOWYpre[61], COWYpre[61], dip_error[10], pickup_error[10],

Df_dip[5][10], Dy_dip[5][10], WP_dip[5][10], wash_dip[5][10];double dye_bath_dist[5][10][61], air_dist[5][10][61], IOWY_dist[5][10][61],

COWY_dist[5][10][61], Integ_save[5][10], IOWY_save[5][10],

COWY_save[5][10];

float input[1][20], num_time_steps, oxd_time_steps;

double Mt, Dy, DOy, Df, dt, DT, dr, radius, Monophenate_Ion, CompA, CompB, A,

AO[10], AO_old, AO_conv[10], AO_change, wash, old_wash, wetpickup,

gmIplit, gmNaOHplit, pH, Air, normal_ave[10], WP_normal_ave;

double lamda, alpha, beta, Ur, UOr, K, porosity, Kph, L, percent_to_grams,

grams_to_percent, Integ, num_cycles;

double IOWYtarget, IOWYsurface_target, COWYtarget, IOWYsurface,

IOWYoutside_old, IOWYtotal, COWYtotal, IOWYsurface_ratio,

IOWYtotal_ratio, COWYtotal_ratio;

double dwelltime, oxd_time, totalgramsperindigo, new_stdev[10], old_stdev[10],

Df_temp, Dy_temp, WP_temp, Df_total[10], Dy_total[10], WP_total[10];

double mean_dip, mean_pickup, slope, demon, Df_run_ave[10], Dy_run_ave[10],

WP_run_ave[10], Df_AO[10], Dy_AO[10], WP_AO[10], wash_AO[10];

long rows, cols;

int x, num_nodes, ts, yarn_count, num_yarns;

int z, ctx, cty, ctz, current_dip, num_dips;

int i, j, pivot, k;

double PI25DT = 3.141592653589793238462643;

// Iniatialization

num_dips=7; // this is now number of dips in data

num_cycles=1;

cols=1;

num_yarns = 4; // number of yarn counts processed

DT=0.01; // Define a actual time step to be used in dyeing and oxidation

num_nodes=21;

rows=num_nodes-1;

porosity=0.65;Ur = 0.0;

K = 1.0;

percent_to_grams = (0.0154 * porosity)/(1.0 - porosity);

grams_to_percent = 1.0/percent_to_grams;

totalgramsperindigo = 2.3884;

AO_old = 0.0;

wash = 0.1;



373

mean_dip = 0.0;

mean_pickup = 0.0;

slope = 1.0;

Df = 4.6e-10;

Dy = 1.18e-6;

wetpickup = 0.05;

yarn_count = 1;

for (cty = 1; cty <= num_yarns; cty++){

for (ctx = 1; ctx<=num_dips; ctx++)

{

new_stdev[ctx] = 0.5;

old_stdev[ctx] = 0.5;

Df_total[ctx] = 0.0;

Dy_total[ctx] = 0.0;

WP_total[ctx] = 0.0;

AO[ctx] = 0.02;

Df_AO[ctx] = 4.6e-10;

Dy_AO[ctx] = 1.18e-6;

WP_AO[ctx] = 0.05;

}

}

for (cty=0; cty<=num_yarns; cty++)

{

for (ctx = 0; ctx <= num_dips; ctx++) wash_dip[cty][ctx] = 0.01;

}

while (AO_change < 0.99 || AO_change > 1.01)

{ //while loop to cycle thru until stdev reaches limit

yarn_count = 1;

// Open each yarn count

while (yarn_count <= num_yarns)

{

printf ("Processing yarn # %i\n", yarn_count);

wash = wash_dip[yarn_count][1];

slope = 1.0;

while (slope < -0.005 || slope > 0.005

{

IOWYsurface_ratio = IOWYtotal_ratio = COWYtotal_ratio = 0.99;

for (ctx=0; ctx <= (num_dips+1); ctx++){

Df_constantAO[ctx]=0.0;

Dy_constantAO[ctx]=0.0;

WP_constantAO[ctx]=0.0;

dip_error[ctx]=0.0;

pickup_error[ctx]=0.0;

}

for (ctx=0; ctx<=rows; ctx++)

{

IOWYpre[ctx] = 0.0;

COWYpre[ctx] = 0.0;

IOWY[ctx] = 0.0;

IOWYoxd[ctx] = 0.0;

COWY[ctx] = 0.0;

}

for (x=0; x<=19; x++) input[0][x]=0.0;

for (current_dip = 1; current_dip <= num_dips; current_dip++)

{

printf ("Processing dip # %i\n", current_dip);

if (yarn_count == 1) oFile = fopen ("yarninput1.txt", "rb" );




374



if (oFile==NULL) {fputs ("File error",stderr); exit (1);}

while (input[0][0] != current_dip)

{

for (z=0; z<1; z++)

{

for (x = 0; x <=19; x++) fscanf (oFile, "%f", &input[0][x]);

}}

fclose (oFile);

printf ("%i\t%e\t%e\n", yarn_count, input[0][2], input[0][3]);

Df = Df_AO[current_dip];

Dy = Dy_AO[current_dip];

wetpickup = WP_AO[current_dip];

dwelltime = input[0][5];

oxd_time = input[0][6];

num_time_steps = dwelltime/DT;

dt = DT;

radius = (-0.1655+(1.951/sqrt(input[0][2])))/20.0; //cm

dr = radius/(rows); //cm

DOy = 0.219; //oxygen diffusion coefficient cm2/sec

Ur = 0.0;

UOr = -1.0 * input[0][19] * input[0][14]*100/60; //air velocity cm/sec

A = input[0][15];

IOWYsurface_ratio=0.0;

IOWYtotal_ratio=0.0;

COWYtotal_ratio=0.0;

gmIplit = input[0][7]; //g/l

gmNaOHplit = input[0][8]; // g/l

pH = input[0][9]; //dye bath pH

Integ = input[0][11]; //shade

IOWYtarget = input[0][10];

IOWYsurface_target = 0.0; // %IOWY at the surface from Integ conversion

COWYtarget = input[0][12];

// Conversion of Integ to target %IOWY at the surface of the yarn

IOWYsurface_target = 0.0;

IOWYsurface_target = -0.02646465 + (9.53859e-4*Integ) + (1.35931e-5*pow

((Integ-55.2088),2)) + (3.909e-8*pow((Integ-55.2088),3));

IOWYsurface_target = IOWYsurface_target + (2.42444e-9*pow((Integ-55.2088),4))+ (6.4303e-11*pow((Integ-55.2088),5));

for (ctx = 0; ctx<=rows; ctx++)

{

gms_ctn_node[ctx] = 1.54*porosity*2.0*PI25DT*ctx*dr*dr;

liter_per_node[ctx] = (1-porosity)*2.0*PI25DT*ctx*dr*dr;

}

gms_ctn_node[0] = 1.54*porosity*PI25DT*0.25*dr*dr;

liter_per_node[0] = (1-porosity)*PI25DT*0.25*dr*dr;

gms_ctn_node[rows] = 1.54*porosity*PI25DT*(radius*dr-(0.25*dr*dr));

liter_per_node[rows] = (1-porosity)*PI25DT*(radius*dr-(0.25*dr*dr));

while (COWYtotal_ratio < 0.995 || COWYtotal_ratio > 1.005 ||

IOWYsurface_ratio<0.995 || IOWYsurface_ratio>1.005||IOWYtotal_ratio<0.995

||IOWYtotal_ratio>1.005)

{

x=i=j=k=ctx=cty=0;

pivot=0;

IOWYtotal=0.0;

COWYtotal=0.0;

IOWYsurface=0.0;

// Set-up initial conditions


{



375

X[ctx]=0.0;

Cj[ctx]=0.0;

Cj1[ctx]=0.0;

d[ctx]=0.0;

temp[ctx]=0.0;

RBL[ctx]=0.0;

RBL1[ctx]=0.0;

RBLgm[ctx]=0.0;

RBL1gm[ctx]=0.0;IOWY[ctx]=0.0; //these will change for multiple dips

IOWYoxd[ctx]=0.0;

COWY[ctx]=0.0;

IOWYstep[ctx]=0.0;

dumb[ctx]=0.0;

OBL[ctx]=0.0;

OBL1[ctx]=0.0;

OBLgm[ctx]=0.0;

OBL1gm[ctx]=0.0;

TBL[ctx] = RBL[ctx] + OBL[ctx];

TBL1[ctx] = RBL1[ctx] + OBL1[ctx];

for(cty = 0; cty<=rows; cty++)

{

AA[ctx][cty]=0.0;

BB[ctx][cty]=0.0;

}

}

Cj[rows]=gmIplit;

Cj1[rows]=gmIplit;

lamda = (Dy*dt)/(2.0*dr*dr);

alpha = (Ur*dt)/(4.0*dr);

beta = (Dy*dt)/(4.0*dr);

for (ctx = 0; ctx <rows; ctx++)

{

AA[ctx][ctx]=1.0 + (2.0*lamda);

BB[ctx][ctx]=1.0 + (-2.0*lamda);

}

for (ctx = 1; ctx <(rows-1); ctx++)

{

AA[ctx][ctx+1]=(-beta/(ctx*dr))-lamda+(alpha);

AA[ctx+1][ctx]=(beta/((ctx+1)*dr))-lamda-(alpha);BB[ctx][ctx+1]=(beta/(ctx*dr))+lamda-(alpha);

BB[ctx+1][ctx]=(-beta/((ctx+1)*dr))+lamda+(alpha);

}

AA[0][1]=-2.0*lamda;

AA[1][0]=(beta/dr)-lamda-(alpha);

BB[0][1]=2.0*lamda;

BB[1][0]=(-beta/dr)+lamda+(alpha);

Monophenate_Ion = 1.0/(1.0 + (pow(10,(9.5-pH))) + (pow(10,(pH-12.7))));

CompA = (0.016492 * Monophenate_Ion) + 0.003465;

CompB = (-0.244296 * Monophenate_Ion) + 0.816158;

for (ts = 1; ts <= num_time_steps; ts++)

{

for (ctx = 0; ctx <= rows; ctx++)

{

Cj[ctx]=Cj1[ctx];

RBL[ctx]=RBL1[ctx];

OBL[ctx]=OBL1[ctx];

TBL[ctx]=TBL1[ctx];

RBLgm[ctx]=RBL1gm[ctx];

OBLgm[ctx]=OBL1gm[ctx];

temp[ctx]=0.0;

}



376

Mt = (((4.0/pow(PI25DT,0.5))*(pow((Df*dwelltime/(0.0009*0.0009)),0.5)))

-(Df*dwelltime/(0.0009*0.0009))-((1.0/(3.0*pow(PI25DT,0.5)))*(pow((Df*

dwelltime/(0.0009*0.0009)),(3.0/2.0)))))/num_time_steps;

for (ctx = 0; ctx < rows; ctx++)

{

if (Cj[ctx] <= 0.0) IOWYstep[ctx] = 0.0;

else IOWYstep[ctx] = Mt*CompA*pow(Cj[ctx],CompB);d[ctx] = -1.0 * gms_ctn_node[ctx] * IOWYstep[ctx] / liter_per_node[ctx];

}

d[rows-1] = d[rows-1] + (Cj[rows]*2.0*((beta/(radius))+lamda-alpha));

if (Cj[rows] <= 0.0) IOWYstep[rows] = 0.0;

else IOWYstep[rows] = Mt*CompA*pow(Cj[rows],CompB);

// Find new dye concentration by Guass-Jordan elimination


{

for (cty = 0; cty <rows; cty++) temp[ctx]=temp [ctx]+BB[ctx][cty]*Cj[cty];

}


{

temp[ctx] = temp[ctx]+d[ctx];

}


{

for (cty = 0; cty < rows; cty++) AAinvt[ctx][cty] = AA[ctx][cty];

}


{

AAinvt[ctx][rows]=temp[ctx];

}

for (i = 0; i < rows; i++)

{

if (AAinvt[i][i] == 0)

{

pivot = 0;

j = i + 1;

while ((pivot == 0) && (j <= rows))

{

if (AAinvt[j][i] != 0.0){

pivot = j;

}

j = j + 1;

}

if (pivot == 0 ) printf("Stop, matrix is singular");

}

if(pivot == (j-1))

{

for (j = 0; j < (rows+1); j++)

{

temp1 = AAinvt[i][j];

AAinvt[i][j]=AAinvt[pivot][j];

AAinvt[pivot][j] = temp1;

}

}

for (j = (i+1); j < rows; j++)

{

Multi = -AAinvt[j][i] / AAinvt[i][i];

for (k = i; k < (rows+1); k++)

{

AAinvt[j][k] = AAinvt[j][k] + (Multi * AAinvt[i][k]);



377

}

}

}

Cj1[rows-1] = AAinvt[rows-1][rows] / AAinvt[rows-1][rows-1];

for (j = (rows-2); j >= 0; j--)

{

Cj1[j] = AAinvt[j][rows];

for ( k = (j+1); k < rows; k++)

{Cj1[j] = Cj1[j] - (AAinvt[j][k] * Cj1[k]);

}

Cj1[j] = Cj1[j] / AAinvt[j][j];

}

// End Gauss-Jordan

{

IOWY[0] = IOWY[0] + IOWYstep[0];

}


{

{

IOWY[ctx] = IOWY[ctx] + IOWYstep[ctx];

}

}

IOWY[rows] = IOWY[rows] + IOWYstep[rows];


dye_bath_dist[yarn_count][current_dip][ctx] = Cj1[ctx];

} // Close time step loop for process in dye box

// Nip process


{

RBL1[ctx] = Cj1[ctx];

RBL1gm[ctx] = Cj1[ctx] * liter_per_node[ctx] * wetpickup;

OBL1gm[ctx] = (COWYpre[ctx] - IOWYpre[ctx]) * gms_ctn_node[ctx] * wash;

if (OBL1gm[ctx] < 0.0) OBL1gm[ctx] = 0.0;

}

IOWYtotal=0.0;

IOWYsurface=0.0;

COWYtotal=0.0;

oxd_time_steps = oxd_time/DT;

dt=DT;Air = 0.2541; // gm per liter of oxygen


{

Cj[ctx]=0.0; // g/l of oxygen

Cj1[ctx]=0.0;

d[ctx]=0.0;

X[ctx]=0.0;

Xrbl[ctx]=0.0;

Xiowy[ctx]=0.0;


{

AA[ctx][cty]=0.0;

BB[ctx][cty]=0.0;

}

}

Cj1[rows]=Air;

lamda = (DOy*dt)/(2.0*dr*dr);

alpha = (UOr*dt)/(4.0*dr);

beta = (DOy*dt)/(4.0*dr);


{




378


}


{


AA[ctx+1][ctx]=(beta/((ctx+1)*dr))-lamda-(alpha);

BB[ctx][ctx+1]=(beta/(ctx*dr))+lamda-(alpha);


}AA[0][1]=-2.0*lamda;


BB[0][1]=2.0*lamda;


// Start time step for oxidation

for (ts = 1; ts <= oxd_time_steps; ts++)

{


{

Cj[ctx]=Cj1[ctx];

RBL[ctx]=RBL1[ctx];



temp[ctx]=0.0;

}


{

if (Cj[ctx] <= 0.0)

{

Xrbl[ctx] = 0.0;

Xiowy[ctx] = 0.0;

X[ctx] = Xrbl[ctx] + Xiowy[ctx];

}

else

{

if (RBLgm[ctx] > 0.0) X[ctx]=1/(AO[current_dip]*Cj[ctx]*

liter_per_node[ctx]*dt/(RBLgm[ctx]+(IOWY[ctx]*gms_ctn_node[ctx])));

else if (IOWY[ctx] > 0.0) X[ctx]=1/(AO[current_dip]*Cj[ctx]*

liter_per_node[ctx]*dt/((IOWY[ctx]*gms_ctn_node[ctx])));

else X[ctx]=0.0;

}if (X[ctx] > 1.0) X[ctx]=1.0;

d[ctx] = -1.0 * X[ctx] * Cj[ctx] * dt;

if (d[ctx] > 0.0) d[ctx] = 0.0;

}

d[rows-1] = d[rows-1] + (Cj[rows]*2*((beta/radius)+lamda-alpha));

// Find new oxygen concentration by Guass-Jordan elimination


{

for (cty = 0; cty <rows; cty++) temp[ctx]=temp[ctx]+BB[ctx][cty]*Cj[cty];

}


{


}


{


}


{


}



379

for (i = 0; i < rows; i++)

{


{

pivot = 0;

j = i + 1;


{

if (AAinvt[j][i] != 0.0){

pivot = j;

}

j = j + 1;

}


}

if(pivot == (j-1))

{

for (j = 0; j < (rows+1); j++)

{




}

}

for (j = (i+1); j < rows; j++)

{


for (k = i; k < (rows+1); k++)

{


}

}

}


for (j = (rows-2); j >= 0; j--)

{


for ( k = (j+1); k < rows; k++){

Cj1[j] = Cj1[j] - (AAinvt[j][k] * Cj1[k]);

}


}

// End Gauss-Jordan

Mt = (((4.0/pow(PI25DT,0.5))*(pow((Df*oxd_time/(0.0009*0.0009)),0.5)))

-(Df*oxd_time/(0.0009*0.0009))-((1.0/(3.0*pow(PI25DT,0.5)))*(pow(

(Df*oxd_time/(0.0009*0.0009)),(3.0/2.0)))))/oxd_time_steps;

for (ctx = 0; ctx <=rows; ctx++)

{

if (RBLgm[ctx] > 0.0)

{

dumb[ctx] = (AO[current_dip]*Cj1[ctx]*liter_per_node[ctx]*

dt)/RBLgm[ctx];

if (dumb[ctx] > 1.0)

{

RBL1gm[ctx] = 0.0;

RBL1[ctx] = 0.0;

OBL1gm[ctx] = OBLgm[ctx] + RBLgm[ctx];

}

else



380

{

RBL1gm[ctx] = RBLgm[ctx] - (dumb[ctx]*RBLgm[ctx]);

RBL1[ctx] = RBL[ctx] - (dumb[ctx]*RBLgm[ctx]/(liter_per_node[ctx]

*wetpickup));

OBL1gm[ctx] = OBLgm[ctx] + (dumb[ctx]*RBLgm[ctx]);

if (RBL1gm[ctx] <= 0.0) RBL1gm[ctx] = 0.0;

if (RBL1[ctx] <= 0.0) RBL1[ctx] = 0.0;

IOWY[ctx] = IOWY[ctx] + ((CompA*pow(RBL1[ctx],CompB))*Mt);

RBL1gm[ctx] = RBL1gm[ctx] - ((CompA*pow(RBL1[ctx],CompB)) * Mt* gms_ctn_node[ctx]);

RBL1[ctx] = RBL1[ctx] - (((CompA*pow(RBL1[ctx],CompB)) * Mt

* gms_ctn_node[ctx])/(liter_per_node[ctx] * wetpickup));


if (RBL1[ctx] <= 0.0) RBL1[ctx] = 0.0;

}

}

else if (IOWY[ctx] > 0.0)

{

dumb[ctx]=((AO[current_dip]*Cj1[ctx]*liter_per_node[ctx]*dt)

/(IOWY[ctx]*gms_ctn_node[ctx]));


{

IOWYoxd[ctx] = IOWYoxd[ctx] + IOWY[ctx];

IOWY[ctx] = 0.0;

}

else

{

IOWYoxd[ctx] = IOWYoxd[ctx] + (dumb[ctx]*IOWY[ctx]);

IOWY[ctx] = IOWY[ctx] - (dumb[ctx]*IOWY[ctx]);

if (IOWY[ctx] <= 0.0) IOWY[ctx]=0.0;

}

}

}

for (ctx = 0; ctx <= rows; ctx++) air_dist[yarn_count][current_dip][ctx]

=Cj1[ctx];

} // end oxidation time step loop


{

IOWYoxd[ctx] = IOWYoxd[ctx] + IOWYpre[ctx];

COWY[ctx]=IOWYoxd[ctx]*totalgramsperindigo+IOWY[ctx]*totalgramsperindigo;COWY[ctx] =COWY[ctx]+(OBL1gm[ctx]*totalgramsperindigo/gms_ctn_node[ctx]);

COWY[ctx] =COWY[ctx]+(RBL1gm[ctx]*totalgramsperindigo/gms_ctn_node[ctx]);

IOWYtotal = IOWYtotal+(IOWYoxd[ctx]*gms_ctn_node[ctx])+(IOWY[ctx]

*gms_ctn_node[ctx]);

COWYtotal = COWYtotal + (COWY[ctx]*gms_ctn_node[ctx]);

}

IOWYtotal = IOWYtotal / (1.54*porosity*PI25DT * radius * radius);

COWYtotal = COWYtotal / (1.54*porosity*PI25DT * radius * radius);

IOWYsurface = IOWYoxd[rows] + IOWY[rows];

IOWYsurface_ratio = IOWYsurface_target/IOWYsurface;

IOWYtotal_ratio = IOWYtarget/IOWYtotal;

COWYtotal_ratio = COWYtarget/COWYtotal;

IOWY_save[yarn_count][current_dip] = IOWYtotal;

COWY_save[yarn_count][current_dip] = COWYtotal;

Integ_save[yarn_count][current_dip] = 0.0;

Integ_save[yarn_count][current_dip] = 45.60937 + (592.19421*IOWYsurface) -

(9928.5539*pow((IOWYsurface-0.045773),2))

+ (1.83538e+5*pow((IOWYsurface-0.045773),3));

Integ_save[yarn_count][current_dip] = Integ_save[yarn_count][current_dip]

- (1.522451e+6*pow((IOWYsurface-0.045773),4))

+ (4.27080e+6*pow((IOWYsurface-0.045773),5));



382

if (wash <= 0.0)

{

wash = 0.0;

wash_constantAO[current_dip] = wash;

}

printf("slope, wash %e\t%e\n", slope, wash);

} // Close wash convergence loop

// Open and save other yarn counts

for (ctx = 1; ctx <=num_dips; ctx++){

Df_dip[yarn_count][ctx] = Df_constantAO[ctx];

Dy_dip[yarn_count][ctx] = Dy_constantAO[ctx];

WP_dip[yarn_count][ctx] = WP_constantAO[ctx];

wash_dip[yarn_count][ctx] = wash_constantAO[ctx];

}

yarn_count = yarn_count + 1;

}

// this is the oxidation optimumize section

for (ctx = 1; ctx <=num_dips; ctx++)

{


normal_ave[ctx] = 0.0;

}

for (cty = 1; cty <=num_yarns; cty++)

{


{

Df_AO[ctx] = 0.0;

Dy_AO[ctx] = 0.0;

WP_AO[ctx] = 0.0;

}

}


{


{

Df_total[ctx] = Df_total[ctx] + Df_dip[cty][ctx];

Dy_total[ctx] = Dy_total[ctx] + Dy_dip[cty][ctx];

WP_total[ctx] = WP_total[ctx] + WP_dip[cty][ctx];

Df_AO[ctx] = Df_AO[ctx] + Df_dip[cty][ctx];Dy_AO[ctx] = Dy_AO[ctx] + Dy_dip[cty][ctx];

WP_AO[ctx] = WP_AO[ctx] + WP_dip[cty][ctx];

}

}


{

Df_run_ave[ctx] = Df_total[ctx] / (num_cycles * num_yarns);

Dy_run_ave[ctx] = Dy_total[ctx] / (num_cycles * num_yarns);

WP_run_ave[ctx] = WP_total[ctx] / (num_cycles * num_yarns);

Df_AO[ctx] = Df_AO[ctx] / num_yarns;

Dy_AO[ctx] = Dy_AO[ctx] / num_yarns;

WP_AO[ctx] = WP_AO[ctx] / num_yarns;

}


{


{

Df_dip[cty][ctx] = Df_dip[cty][ctx]/Df_run_ave[ctx];

Dy_dip[cty][ctx] = Dy_dip[cty][ctx]/Dy_run_ave[ctx];

WP_dip[cty][ctx] = WP_dip[cty][ctx]/WP_run_ave[ctx];

}

}



383

for (ctx = 1; ctx <= num_dips; ctx++)

{


{

normal_ave[ctx] = normal_ave[ctx] + Df_dip[cty][ctx] + Dy_dip[cty][ctx]

+ WP_dip[cty][ctx];

}

}

for (ctx = 1; ctx<=num_dips; ctx++) normal_ave[ctx] = normal_ave[ctx]/ (3.0 * num_yarns);


{

for (cty = 1; cty <=num_yarns;cty++)

{

new_stdev[ctx] = new_stdev[ctx] + pow((Df_dip[cty][ctx]

- normal_ave[ctx]), 2.0);

new_stdev[ctx] = new_stdev[ctx] + pow((Dy_dip[cty][ctx]


new_stdev[ctx] = new_stdev[ctx] + pow((WP_dip[cty][ctx]


}

}


{

new_stdev[ctx] = new_stdev[ctx] / ((3.0 * num_yarns) - 1.0);

new_stdev[ctx] = pow(new_stdev[ctx], 0.5);

AO_conv[ctx] = old_stdev[ctx] / new_stdev[ctx];

old_stdev[ctx] = new_stdev[ctx];

AO[ctx] = AO[ctx] * AO_conv[ctx];

}

AO_change = 0.0;


{

if (AO_conv[ctx] > AO_change) AO_change = AO_conv[ctx];

}

num_cycles = num_cycles + 1.0;

printf("This completes an oxidation loop!!!!!!!!\n");

for (ctx=1; ctx <= num_dips; ctx++) printf("%e\t%e\t%e\t%e\n", num_cycles,

AO[ctx], AO_conv[ctx], new_stdev[ctx]);

} // Close stdev convergence loop to optimize oxidationfor (ctx = 1; ctx <= num_dips; ctx++)

{

for (cty = 1; cty <= num_yarns; cty++) wash_AO[ctx] = wash_AO[ctx]

+ wash_dip[cty][ctx];

}

pFile = fopen ("output_model.out","a");

fprintf(pFile, "number of cycles to converge: %e\n", num_cycles);

fprintf(pFile, "Dips\t Df\t Dy\t pickup\t Oxidation\n");

for (x = 1; x <= num_dips; x++)

{

fprintf(pFile, "%i\t%e\t%e\t%e\t%e\n", x, Df_AO[x], Dy_AO[x],

WP_AO[x], AO[x]);

}

fprintf(pFile, "yarns\t wash\n");

for (x = 1; x <= num_yarns; x++) fprintf(pFile, "%i\t%e\n", x,

wash_dip[x][1]);

for (cty = 1; cty <= num_yarns; cty++)

{

fprintf(pFile, "yarn: %i IOWY\t COWY\t Integ\n", cty);


{

fprintf(pFile, "dip:\t %i\t%e\t%e\t%e\n", ctx, IOWY_save[cty][ctx],



384

COWY_save[cty][ctx], Integ_save[cty][ctx]);

}

}

cty = 1;

for (ctz = 1; ctz <=num_dips ; ctz++) fprintf(pFile, "%i\t", ctz);

fprintf(pFile, "\n");


{

for (ctz = 1; ctz <=num_dips ; ctz++) fprintf(pFile, "%e\t",dye_bath_dist[cty][ctz][ctx]);


}

cty = num_yarns;




{

for (ctz = 1; ctz <=num_dips ; ctz++) fprintf(pFile, "%e\t",

dye_bath_dist[cty][ctz][ctx]);


}

cty = 1;




{


air_dist[cty][ctz][ctx]);


}

cty = num_yarns;




{


air_dist[cty][ctz][ctx]);


}

cty = 1;for (ctz = 1; ctz <=num_dips ; ctz++) fprintf(pFile, "%i\t", ctz);



{


IOWY_dist[cty][ctz][ctx]);


}

cty = num_yarns;




{


IOWY_dist[cty][ctz][ctx]);


}

cty = 1;




{



385


COWY_dist[cty][ctz][ctx]);


}

cty = num_yarns;




{for (ctz = 1; ctz <=num_dips ; ctz++) fprintf(pFile, "%e\t",

COWY_dist[cty][ctz][ctx]);


}

fclose (pFile);

return 0;

}



386

Section A-4-3b: Computer program to calculate %COWY, %IOWY, and Integ shade values given the

input dye range set-up conditions.

#include <stdio.h>

#include <fcntl.h>

#include <stdlib.h>

#include <math.h>

int main ()

{

FILE * pFile;

FILE * oFile;

FILE * o2File;

FILE * o3File;

FILE * o4File;

double AA[61][61], BB[61][61], RBLgm[61], RBL1gm[61], Cj[61], Cj1[61], d[61], TBL[61], TBL1[61], RBL[61], RBL1[61], OBL[61], OBL1[61];

double AAinvt[61][62], X[61], Xrbl[61], Xiowy[61], temp[61], IOWY[61], COWY[61], IOWYoxd[61], temp1, Multi, fraction_dye_affinity,

fraction_oxy_affinity;

double OBLgm[61], OBL1gm[61], dumb[61], IOWYstep[61], gms_ctn_node[61], liter_per_node[61], Df_constantAO[10],

Dy_constantAO[10], WP_constantAO[10], wash_constantAO[10];

double IOWYpre[61], COWYpre[61], dip_error[10], pickup_error[10], Df_dip[5][10], Dy_dip[5][10], WP_dip[5][10], wash_dip[5][10];

double dye_bath_dist[5][10][61], air_dist[5][10][61], IOWY_dist[5][10][61], COWY_dist[5][10][61], Integ_save[5][10], IOWY_save[5][10],

COWY_save[5][10];

float input[1][22], num_time_steps, oxd_time_steps;

double Mt, Dy, DOy, Df, dt, DT, dr, radius, Monophenate_Ion, CompA, CompB, A, AO[10], AO_old, AO_conv[10], AO_change, wash,

old_wash, wetpickup, gmIplit, gmNaOHplit, pH, Air, normal_ave[10], WP_normal_ave;

double lamda, alpha, beta, Ur, UOr, K, porosity, Kph, L, percent_to_grams, grams_to_percent, Integ, num_cycles;

double IOWYtarget, IOWYsurface_target, COWYtarget, IOWYsurface, IOWYoutside_old, IOWYtotal, COWYtotal, IOWYsurface_ratio,

IOWYtotal_ratio, COWYtotal_ratio;

double dwelltime, oxd_time, totalgramsperindigo, new_stdev[10], old_stdev[10], Df_temp, Dy_temp, WP_temp, Df_total[10],

Dy_total[10], WP_total[10];

double mean_dip, mean_pickup, slope, demon, Df_run_ave[10], Dy_run_ave[10], WP_run_ave[10], Df_AO[10], Dy_AO[10], WP_AO[10],

wash_AO[10];

double speed, mV, nip_pressure, Total_IOWY_pre, Total_COWY_pre;

long rows, cols;

int x, num_nodes, ts, yarn_count, num_yarns;

int z, ctx, cty, ctz, current_dip, num_dips;int i, j, pivot, k;

double PI25DT = 3.141592653589793238462643;

// Iniatialization

num_dips=5; // this is now number of dips in data

num_cycles=1;

cols=1;

num_yarns = 1; // number of yarn counts processed

DT=0.01; // Define a actual time step to be used in dyeing and oxidization

num_nodes=21;

rows=num_nodes-1;

porosity=0.65;

Ur = 0.0;

K = 1.0;

percent_to_grams = (0.0154 * porosity)/(1.0 - porosity);

grams_to_percent = 1.0/percent_to_grams;totalgramsperindigo = 2.3884;

AO_old = 0.0;

wash = 0.1;

mean_dip = 0.0;

mean_pickup = 0.0;

slope = 1.0;



387

yarn_count = 1;


{


{


old_stdev[ctx] = 0.5;

Df_total[ctx] = 0.0;

Dy_total[ctx] = 0.0;WP_total[ctx] = 0.0;

AO[ctx] = 0.02;

}

}

for (cty=0; cty<=num_yarns; cty++)

{

for (ctx = 0; ctx <= num_dips; ctx++) wash_dip[cty][ctx] = 0.01;

}

yarn_count = 1;

printf ("Processing yarn # %i\n", yarn_count);

slope = 1.0;

Total_IOWY_pre = 0.0;

Total_COWY_pre = 0.0;

for (ctx=0; ctx <= (num_dips+1); ctx++)

{

Df_constantAO[ctx]=0.0;

Dy_constantAO[ctx]=0.0;

WP_constantAO[ctx]=0.0;

dip_error[ctx]=0.0;

pickup_error[ctx]=0.0;

}

for (ctx=0; ctx<=rows; ctx++)

{

IOWYpre[ctx] = 0.0;

COWYpre[ctx] = 0.0;

IOWY[ctx] = 0.0;

IOWYoxd[ctx] = 0.0;

COWY[ctx] = 0.0;

}

for (x=0; x<=19; x++) input[0][x]=0.0;

for (current_dip = 1; current_dip <= num_dips; current_dip++){

printf ("Processing dip # %i\n", current_dip);





if (oFile==NULL) {fputs ("File error",stderr); exit (1);}

while (input[0][0] != current_dip)

{

for (z=0; z<1; z++)

{

for (x = 0; x <=21; x++) fscanf (oFile, "%f", &input[0][x]);

}

}

fclose (oFile);

printf ("%i\t%e\t%e\n", yarn_count, input[0][2], input[0][3]);

dwelltime = input[0][5];

oxd_time = input[0][6];

num_time_steps = dwelltime/DT;

dt = DT;

radius = (-0.1655+(1.951/sqrt(input[0][2])))/20.0; //cm

dr = radius/(rows); //cm



388

DOy = 0.219; //oxygen diffusion coefficient cm2/sec

Ur = 0.0;

UOr = -1.0 * input[0][19] * input[0][14]*100/60; //air velocity propagation cm/sec

A = input[0][15]; // dye affinity 1/sec

IOWYsurface_ratio=0.0;

IOWYtotal_ratio=0.0;

COWYtotal_ratio=0.0;

gmIplit = input[0][7]; //gm/lit

gmNaOHplit = input[0][8]; // gm/litpH = input[0][9]; //dye bath pH

Integ = input[0][11]; //shade

IOWYtarget = input[0][10];

IOWYsurface_target = 0.0; // %IOWY at the surface from Integ conversion

COWYtarget = input[0][12];

mV = input[0][20];

nip_pressure = input[0][21];

speed = input[0][4];

if (current_dip == 1)

{

Df = exp(-27.3480169 + (0.7766363*gmIplit) + (0.4031649*pH));

Dy = exp(-17.3699775 - (0.503326*gmIplit) + (0.588888*pH) - (0.0736707*dwelltime));

AO[current_dip] = exp(-10.4653532 + (0.1263413*speed) + (0.0685300*oxd_time) - (0.0010179*mV));

}

else if (current_dip == 2)

{

Df = exp(-27.3480169 - 0.3903350 + (0.7766363*gmIplit) + (0.4031649*pH));

Dy = exp(-17.3699775 - 0.0516144 - (0.503326*gmIplit) + (0.588888*pH) - (0.0736707*dwelltime));

AO[current_dip] = exp(-10.4653532 -0.4685870 + (0.1263413*speed) + (0.0685300*oxd_time) - (0.0010179*mV));

}


{

Df = exp(-27.3480169 + 0.2868312 + (0.7766363*gmIplit) + (0.4031649*pH));



}


{

Df = exp(-27.3480169 + 0.5783337 + (0.7766363*gmIplit) + (0.4031649*pH));


AO[current_dip] = exp(-10.4653532 -0.9826215 + (0.1263413*speed) + (0.0685300*oxd_time) - (0.0010179*mV));}


{

Df = exp(-27.3480169 + 0.9180302 + (0.7766363*gmIplit) + (0.4031649*pH));



}


{

Df = exp(-27.3480169 + 1.0879995 + (0.7766363*gmIplit) + (0.4031649*pH));



}


{

Df = exp(-27.3480169 + 0.9494075 + (0.7766363*gmIplit) + (0.4031649*pH));



}

wash = -0.1043059 + (0.0043698*speed) - (0.0174137*dwelltime) + (0.00064822*mV) - (0.06827879*gmIplit);

wetpickup = 0.07959512 - (0.000159807*nip_pressure) - (0.01133595*gmIplit) - (3960.68825*Dy);

IOWYsurface_target = 0.0;



389

IOWYsurface_target = -0.02646465 + (9.53859e-4*Integ) + (1.35931e-5*pow((Integ-55.2088),2)) + (3.909e-8*pow((Integ-55.2088),3));

IOWYsurface_target = IOWYsurface_target + (2.42444e-9*pow((Integ-55.2088),4)) + (6.4303e-11*pow((Integ-55.2088),5));


{

gms_ctn_node[ctx] = 1.54*porosity*2.0*PI25DT*ctx*dr*dr;

liter_per_node[ctx] = (1-porosity)*2.0*PI25DT*ctx*dr*dr;

}

gms_ctn_node[0] = 1.54*porosity*PI25DT*0.25*dr*dr;

liter_per_node[0] = (1-porosity)*PI25DT*0.25*dr*dr;gms_ctn_node[rows] = 1.54*porosity*PI25DT*(radius*dr-(0.25*dr*dr));

liter_per_node[rows] = (1-porosity)*PI25DT*(radius*dr-(0.25*dr*dr));

x=i=j=k=ctx=cty=0;

pivot=0;

IOWYtotal=0.0;

COWYtotal=0.0;

IOWYsurface=0.0;

// Set-up initial conditions


{

X[ctx]=0.0;

Cj[ctx]=0.0;

Cj1[ctx]=0.0;

d[ctx]=0.0;

temp[ctx]=0.0;

RBL[ctx]=0.0;

RBL1[ctx]=0.0;

RBLgm[ctx]=0.0;

RBL1gm[ctx]=0.0;

IOWY[ctx]=0.0; //these will change for multiple dips

IOWYoxd[ctx]=0.0; //here

COWY[ctx]=0.0; // here

IOWYstep[ctx]=0.0;

dumb[ctx]=0.0;

OBL[ctx]=0.0;

OBL1[ctx]=0.0;

OBLgm[ctx]=0.0;

OBL1gm[ctx]=0.0;

TBL[ctx] = RBL[ctx] + OBL[ctx];

TBL1[ctx] = RBL1[ctx] + OBL1[ctx];

for(cty = 0; cty<=rows; cty++){

AA[ctx][cty]=0.0;

BB[ctx][cty]=0.0;

}

}

Cj[rows]=gmIplit;

Cj1[rows]=gmIplit;

lamda = (Dy*dt)/(2.0*dr*dr);

alpha = (Ur*dt)/(4.0*dr);

beta = (Dy*dt)/(4.0*dr);


{



}


{





}



390

AA[0][1]=-2.0*lamda;


BB[0][1]=2.0*lamda;


Monophenate_Ion = 1.0/(1.0 + (pow(10,(9.5-pH))) + (pow(10,(pH-12.7))));

CompA = (0.016492 * Monophenate_Ion) + 0.003465;

CompB = (-0.244296 * Monophenate_Ion) + 0.816158;

for (ts = 1; ts <= num_time_steps; ts++)

{for (ctx = 0; ctx <= rows; ctx++)

{

Cj[ctx]=Cj1[ctx];

RBL[ctx]=RBL1[ctx];

OBL[ctx]=OBL1[ctx];

TBL[ctx]=TBL1[ctx];



temp[ctx]=0.0;

}

Mt = (((4.0/pow(PI25DT,0.5))*(pow((Df*dwelltime/(0.0009*0.0009)),0.5)))-(Df*dwelltime/(0.0009*0.0009))-

((1.0/(3.0*pow(PI25DT,0.5)))*(pow((Df*dwelltime/(0.0009*0.0009)),(3.0/2.0)))))/num_time_steps;


{

if (Cj[ctx] <= 0.0) IOWYstep[ctx] = 0.0;

else IOWYstep[ctx] = Mt*CompA*pow(Cj[ctx],CompB);

d[ctx] = -1.0 * gms_ctn_node[ctx] * IOWYstep[ctx] / liter_per_node[ctx];

}

d[rows-1] = d[rows-1] + (Cj[rows]*2.0*((beta/(radius))+lamda-alpha));

if (Cj[rows] <= 0.0) IOWYstep[rows] = 0.0;

else IOWYstep[rows] = Mt*CompA*pow(Cj[rows],CompB);

// Find new dye concentration by Guass-Jordan elimination


{

for (cty = 0; cty <rows; cty++) temp[ctx] = temp [ctx] + BB[ctx][cty]*Cj[cty];

}


{


}

for (ctx = 0; ctx < rows; ctx++){


}


{


}

for (i = 0; i < rows; i++)

{


{

pivot = 0;

j = i + 1;


{

if (AAinvt[j][i] != 0.0)

{

pivot = j;

}

j = j + 1;

}




391

}

if(pivot == (j-1))

{

for (j = 0; j < (rows+1); j++)

{




}}

for (j = (i+1); j < rows; j++)

{


for (k = i; k < (rows+1); k++)

{


}

}

}


for (j = (rows-2); j >= 0; j--)

{


for ( k = (j+1); k < rows; k++)

{


}


}

// End Gauss-Jordan

{

IOWY[0] = IOWY[0] + IOWYstep[0];

}


{

{

IOWY[ctx] = IOWY[ctx] + IOWYstep[ctx];

}

}IOWY[rows] = IOWY[rows] + IOWYstep[rows];

for (ctx = 0; ctx <= rows; ctx++) dye_bath_dist[yarn_count][current_dip][ctx] = Cj1[ctx];

} // Close time step loop for process in dye box

// Nip process


{

RBL1[ctx] = Cj1[ctx];

RBL1gm[ctx] = Cj1[ctx] * liter_per_node[ctx] * wetpickup;

OBL1gm[ctx] = (COWYpre[ctx] - IOWYpre[ctx]) * gms_ctn_node[ctx] * wash;

if (OBL1gm[ctx] < 0.0) OBL1gm[ctx] = 0.0;

}

IOWYtotal=0.0;

IOWYsurface=0.0;

COWYtotal=0.0;

oxd_time_steps = oxd_time/DT;

dt=DT;

Air = 0.2541; // gm per liter of oxygen


{

Cj[ctx]=0.0; // gm/lit of oxygen

Cj1[ctx]=0.0;

d[ctx]=0.0;



392

X[ctx]=0.0;

Xrbl[ctx]=0.0;

Xiowy[ctx]=0.0;


{

AA[ctx][cty]=0.0;

BB[ctx][cty]=0.0;

}

}Cj1[rows]=Air;

lamda = (DOy*dt)/(2.0*dr*dr);

alpha = (UOr*dt)/(4.0*dr);

beta = (DOy*dt)/(4.0*dr);


{



}


{





}

AA[0][1]=-2.0*lamda;


BB[0][1]=2.0*lamda;


// Start time step for oxidization

for (ts = 1; ts <= oxd_time_steps; ts++)

{


{

Cj[ctx]=Cj1[ctx];

RBL[ctx]=RBL1[ctx];



temp[ctx]=0.0;

}for (ctx = 0; ctx <= rows; ctx++)

{

if (Cj[ctx] <= 0.0)

{

Xrbl[ctx] = 0.0;

Xiowy[ctx] = 0.0;

X[ctx] = Xrbl[ctx] + Xiowy[ctx];

}

else

{

if (RBLgm[ctx] > 0.0) X[ctx]=1/(AO[current_dip]*Cj[ctx]*liter_per_node[ctx]*dt/(RBLgm[ctx]+(IOWY[ctx]*gms_ctn_node[ctx])));

else if (IOWY[ctx] > 0.0) X[ctx]=1/(AO[current_dip]*Cj[ctx]*liter_per_node[ctx]*dt/((IOWY[ctx]*gms_ctn_node[ctx])));

else X[ctx]=0.0;

}

if (X[ctx] > 1.0) X[ctx]=1.0;

d[ctx] = -1.0 * X[ctx] * Cj[ctx] * dt;

if (d[ctx] > 0.0) d[ctx] = 0.0;

}

d[rows-1] = d[rows-1] + (Cj[rows]*2*((beta/radius)+lamda-alpha));

// Find new oxygen concentration by Guass-Jordan elimination


{



393

for (cty = 0; cty <rows; cty++) temp[ctx] = temp [ctx] + BB[ctx][cty]*Cj[cty];

}


{


}


{

for (cty = 0; cty < rows; cty++) AAinvt[ctx][cty] = AA[ctx][cty];}


{


}

for (i = 0; i < rows; i++)

{


{

pivot = 0;

j = i + 1;


{

if (AAinvt[j][i] != 0.0)

{

pivot = j;

}

j = j + 1;

}


}

if(pivot == (j-1))

{

for (j = 0; j < (rows+1); j++)

{




}

}

for (j = (i+1); j < rows; j++){


for (k = i; k < (rows+1); k++)

{


}

}

}


for (j = (rows-2); j >= 0; j--)

{


for ( k = (j+1); k < rows; k++)

{


}


}

// End Gauss-Jordan

Mt = (((4.0/pow(PI25DT,0.5))*(pow((Df*oxd_time/(0.0009*0.0009)),0.5)))-(Df*oxd_time/(0.0009*0.0009))-

((1.0/(3.0*pow(PI25DT,0.5)))*(pow((Df*oxd_time/(0.0009*0.0009)),(3.0/2.0)))))/oxd_time_steps;




394

{

if (RBLgm[ctx] > 0.0)

{

dumb[ctx] = (AO[current_dip]*Cj1[ctx]*liter_per_node[ctx]*dt)/RBLgm[ctx];


{

RBL1gm[ctx] = 0.0;

RBL1[ctx] = 0.0;

OBL1gm[ctx] = OBLgm[ctx] + RBLgm[ctx];}

else

{

RBL1gm[ctx] = RBLgm[ctx] - (dumb[ctx]*RBLgm[ctx]);

RBL1[ctx] = RBL[ctx] - (dumb[ctx]*RBLgm[ctx]/(liter_per_node[ctx]*wetpickup));

OBL1gm[ctx] = OBLgm[ctx] + (dumb[ctx]*RBLgm[ctx]);


if (RBL1[ctx] <= 0.0) RBL1[ctx] = 0.0;

IOWY[ctx] = IOWY[ctx] + ((CompA*pow(RBL1[ctx],CompB))*Mt);

RBL1gm[ctx] = RBL1gm[ctx] - ((CompA*pow(RBL1[ctx],CompB)) * Mt * gms_ctn_node[ctx]);

RBL1[ctx] = RBL1[ctx] - (((CompA*pow(RBL1[ctx],CompB)) * Mt * gms_ctn_node[ctx])/(liter_per_node[ctx] * wetpickup));


if (RBL1[ctx] <= 0.0) RBL1[ctx] = 0.0;

}

}

else if (IOWY[ctx] > 0.0)

{

dumb[ctx]=((AO[current_dip]*Cj1[ctx]*liter_per_node[ctx]*dt)/(IOWY[ctx]*gms_ctn_node[ctx]));


{

IOWYoxd[ctx] = IOWYoxd[ctx] + IOWY[ctx];

IOWY[ctx] = 0.0;

}

else

{

IOWYoxd[ctx] = IOWYoxd[ctx] + (dumb[ctx]*IOWY[ctx]);

IOWY[ctx] = IOWY[ctx] - (dumb[ctx]*IOWY[ctx]);

if (IOWY[ctx] <= 0.0) IOWY[ctx]=0.0;

}

}

}for (ctx = 0; ctx <= rows; ctx++) air_dist[yarn_count][current_dip][ctx] = Cj1[ctx];

} // end oxidization time step loop

for (ctx = 0; ctx<=rows; ctx++) if (RBL1[ctx] >0.0) printf("Node: %i\t RBL Not all oxidized\n", ctx);

for (ctx = 0; ctx<=rows; ctx++) if (IOWY[ctx] >0.0) printf("Node: %i\t IOWY Not all oxidized\n", ctx);


{

IOWYoxd[ctx] = IOWYoxd[ctx] + IOWYpre[ctx];

COWY[ctx] = IOWYoxd[ctx]*totalgramsperindigo + IOWY[ctx]*totalgramsperindigo;

COWY[ctx] = COWY[ctx] + (OBL1gm[ctx]*totalgramsperindigo/gms_ctn_node[ctx]);

COWY[ctx] = COWY[ctx] + (RBL1gm[ctx]*totalgramsperindigo/gms_ctn_node[ctx]);

IOWYtotal = IOWYtotal + (IOWYoxd[ctx]*gms_ctn_node[ctx])+ (IOWY[ctx]*gms_ctn_node[ctx]);

COWYtotal = COWYtotal + (COWY[ctx]*gms_ctn_node[ctx]);

}

IOWYtotal = IOWYtotal / (1.54*porosity*PI25DT * radius * radius);

COWYtotal = COWYtotal / (1.54*porosity*PI25DT * radius * radius);

IOWYsurface = IOWYoxd[rows] + IOWY[rows];

IOWYsurface_ratio = IOWYsurface_target/IOWYsurface; // greater then 1 means to increase diffusion coeff Df

IOWYtotal_ratio = IOWYtarget/IOWYtotal; // greater then 1 means to increase diffusion coeff Dy

COWYtotal_ratio = COWYtarget/COWYtotal;

IOWY_save[yarn_count][current_dip] = IOWYtotal;

COWY_save[yarn_count][current_dip] = COWYtotal;

Integ_save[yarn_count][current_dip] = 0.0;



395

Integ_save[yarn_count][current_dip] = 45.60937 + (592.19421*IOWYsurface) - (9928.5539*pow((IOWYsurface-0.045773),2)) +

(1.83538e+5*pow((IOWYsurface-0.045773),3));

Integ_save[yarn_count][current_dip] = Integ_save[yarn_count][current_dip] - (1.522451e+6*pow((IOWYsurface-0.045773),4))+

(4.27080e+6*pow((IOWYsurface-0.045773),5));

Total_IOWY_pre = IOWYtotal;

Total_COWY_pre = COWYtotal;

// Save IOWY & COWY amount and distribution


{IOWYpre[ctx] = IOWYoxd[ctx];

COWYpre[ctx] = COWY[ctx];

}

for (ctx = 0; ctx <= rows; ctx++) IOWY_dist[yarn_count][current_dip][ctx] = IOWYoxd[ctx];

for (ctx = 0; ctx <= rows; ctx++) COWY_dist[yarn_count][current_dip][ctx] = COWY[ctx];

IOWYsurface_ratio = IOWYtotal_ratio = COWYtotal_ratio = 0.99;

Df_constantAO[current_dip] = Df;

Dy_constantAO[current_dip] = Dy;

WP_constantAO[current_dip] = wetpickup;

wash_constantAO[current_dip] = wash;

Df_AO[current_dip] = Df;

Dy_AO[current_dip] = Dy;

WP_AO[current_dip] = wetpickup;

} // This ends the yarn count calculations at specific oxidization rate value


{

Df_dip[yarn_count][ctx] = Df_constantAO[ctx]; // reset Df_dip after each AO step

Dy_dip[yarn_count][ctx] = Dy_constantAO[ctx];

WP_dip[yarn_count][ctx] = WP_constantAO[ctx];

wash_dip[yarn_count][ctx] = wash_constantAO[ctx];

}


{

for (cty = 1; cty <= num_yarns; cty++) wash_AO[ctx] = wash_AO[ctx] + wash_dip[cty][ctx];

}

pFile = fopen ("output_model.out","a");

fprintf(pFile, "number of cycles to converge: %e\n", num_cycles);

fprintf(pFile, "Dips\t Df\t Dy\t pickup\t Oxidization\n");

for (x = 1; x <= num_dips; x++)

{

fprintf(pFile, "%i\t%e\t%e\t%e\t%e\n", x, Df_AO[x], Dy_AO[x], WP_AO[x], AO[x]);}

fprintf(pFile, "yarns\t wash\n");

for (x = 1; x <= num_yarns; x++) fprintf(pFile, "%i\t%e\n", x, wash_dip[x][1]);


{

fprintf(pFile, "yarn: %i IOWY\t COWY\t Integ\n", cty);


{

fprintf(pFile, "%e\t%e\t%e\n", IOWY_save[cty][ctx], COWY_save[cty][ctx], Integ_save[cty][ctx]);

}

}

fclose (pFile);

return 0;

}



396

Section A-5-1: Observational Study Raw Data -Dye Range Parameters

Table A-5-1: Independent indigo dye range raw data set

Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)

443 29.00 20.1 73.6 1.262 12.18 813 2.58 9.70 38.90 95.00


Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 8.2301 7.885 8.1841 7.8671 1.72% 0.166% 0.437% 8.1 0.38

6.3 1--2 2 7.7329 7.3991 7.7581 7.3974 2.75% 0.286% 0.740% 17.2 0.39

6.3 1--3 3 8.3473 8.0082 8.4238 8.0085 3.09% 0.455% 1.034% 29.5 0.44

6.3 1--4 4 7.7045 7.3799 7.7854 7.4011 3.38% 0.510% 1.269% 35.8 0.40

6.3 1--5 5 8.2838 7.9276 8.3811 7.9722 3.61% 0.744% 2.164% 50.1 0.34

6.3 1--6 6 8.3773 8.0322 8.44 8.0778 4.30% 0.885% 2.836% 57.4 0.31

% Reflectance ReadingsWave-

length


400 19.43 13.08 9.08 7.95 5.99 5.19

420 24.21 16.95 12.03 10.62 7.70 6.55

440 23.52 16.01 11.13 9.70 6.89 5.83

460 21.30 13.98 9.51 8.20 5.80 4.90

480 19.39 12.24 8.09 6.83 4.78 4.04

500 17.66 10.86 7.00 5.84 4.07 3.44

520 15.57 9.17 5.66 4.68 3.25 2.75

540 13.12 7.40 4.48 3.68 2.58 2.20

560 11.61 6.28 3.76 3.09 2.18 1.89

580 10.10 5.21 3.11 2.58 1.87 1.65

600 8.65 4.31 2.61 2.18 1.64 1.48

620 7.52 3.70 2.26 1.91 1.48 1.37

640 6.50 3.16 2.01 1.72 1.41 1.32

660 5.93 2.98 1.94 1.67 1.40 1.34

680 7.72 3.93 2.59 2.21 1.78 1.66

700 15.16 9.11 5.91 4.95 3.68 3.26



397


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)

443 29.00 20.1 73.6 1.262 12.18 813 2.58 9.70 38.90 95.00Yarn Skein Response Variables

Yarn

Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

7.1 1 only 1 6.9605 6.7511 7.0156 6.7396 1.84% 0.180% 0.533% 10.3 0.34

7.1 1--2 2 6.9388 6.7247 7.0592 6.7256 2.87% 0.312% 0.765% 18.3 0.41

7.1 1--3 3 7.1311 6.9206 7.3021 6.9363 3.40% 0.490% 1.013% 28.8 0.48

7.1 1--4 4 7.0685 6.8668 7.2129 6.8864 2.94% 0.612% 1.498% 40.4 0.41

7.1 1--5 5 7.2281 7.0148 7.4632 7.0448 4.26% 0.732% 1.911% 46.8 0.38

7.1 1--6 6 7.0234 6.8175 7.1867 6.852 4.60% 0.911% 2.825% 57.3 0.32


Wave-

length


400 17.74 12.72 9.40 7.36 6.47 5.42

420 22.38 16.60 12.49 9.81 8.43 6.90

440 21.50 15.58 11.53 8.84 7.54 6.10

460 19.20 13.50 9.81 7.42 6.32 5.05

480 17.26 11.77 8.34 6.13 5.21 4.15

500 15.58 10.39 7.22 5.23 4.44 3.50

520 13.55 8.76 5.84 4.17 3.54 2.79

540 11.22 7.05 4.62 3.27 2.79 2.22

560 9.80 5.96 3.86 2.74 2.35 1.89

580 8.35 4.93 3.19 2.30 1.99 1.64

600 6.99 4.07 2.66 1.94 1.72 1.46

620 6.00 3.49 2.30 1.72 1.54 1.34

640 5.10 2.97 2.03 1.57 1.45 1.30

660 4.69 2.79 1.96 1.55 1.44 1.31

680 6.33 3.72 2.61 2.01 1.85 1.63

700 13.33 8.61 6.04 4.47 3.92 3.27



398


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)


Yarn

Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

7.1 1 only 1 7.0115 6.8131 7.0888 6.7928 1.97% 0.157% 0.438% 8.1 0.36

7.1 1--2 2 7.0284 6.831 7.1646 6.8207 2.79% 0.285% 0.737% 17.1 0.39

7.1 1--3 3 7.0272 6.8247 7.1861 6.8223 3.19% 0.431% 0.960% 26.9 0.45

7.1 1--4 4 7.2151 7.0028 7.369 7.0351 3.12% 0.546% 1.315% 36.8 0.42

7.1 1--5 5 7.207 6.9949 7.4293 7.0223 4.09% 0.687% 1.866% 46.2 0.37

7.1 1--6 6 7.1864 6.9674 7.3599 7.0164 4.70% 0.865% 2.665% 55.7 0.32


Wave-

length


400 19.83 13.28 9.85 7.79 6.53 5.49

420 24.69 17.19 12.97 10.31 8.58 6.97

440 23.93 16.18 12.02 9.42 7.69 6.20

460 21.62 14.08 10.27 7.98 6.43 5.18

480 19.68 12.32 8.79 6.65 5.30 4.25

500 17.92 10.92 7.65 5.69 4.51 3.61

520 15.75 9.25 6.21 4.56 3.59 2.88

540 13.25 7.47 4.93 3.60 2.83 2.30

560 11.70 6.35 4.13 3.02 2.39 1.96

580 10.12 5.26 3.41 2.52 2.02 1.69

600 8.63 4.34 2.84 2.13 1.74 1.49

620 7.48 3.72 2.46 1.86 1.55 1.38

640 6.42 3.18 2.15 1.70 1.45 1.32

660 5.86 3.00 2.05 1.65 1.44 1.36

680 7.72 4.00 2.73 2.18 1.85 1.68

700 15.37 9.19 6.40 4.88 3.95 3.36



399


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)


Yarn

Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 7.8005 7.4685 7.7353 7.4733 3.57% 0.322% 0.725% 16.6 0.44

6.3 1--2 2 8.2502 7.9087 8.294 7.9319 4.87% 0.556% 1.263% 35.7 0.44

6.3 1--3 3 8.2 7.8407 8.3168 7.9097 6.07% 0.811% 2.327% 52.0 0.35

6.3 1--4 4 7.9116 7.5711 8.0109 7.6461 5.81% 1.049% 3.291% 61.6 0.32

6.3 1--5 5 7.7039 7.3753 7.8447 7.4811 6.36% 1.372% 4.751% 72.7 0.29

6.3 1--6 6 8.2011 7.8532 8.3437 7.9801 6.50% 1.670% 6.416% 81.9 0.26


Wave-

length


400 13.64 7.99 5.82 4.81 3.84 3.28

420 18.04 10.83 7.57 6.15 4.77 3.98

440 16.94 9.81 6.67 5.37 4.14 3.44

460 14.65 8.17 5.50 4.39 3.42 2.85

480 12.75 6.75 4.49 3.58 2.82 2.35

500 11.26 5.75 3.80 3.04 2.42 2.05

520 9.49 4.60 3.04 2.45 1.97 1.69

540 7.60 3.62 2.41 1.97 1.64 1.45

560 6.48 3.06 2.06 1.74 1.48 1.33

580 5.37 2.57 1.80 1.55 1.37 1.25

600 4.43 2.19 1.60 1.42 1.29 1.20

620 3.77 1.95 1.48 1.35 1.25 1.20

640 3.22 1.79 1.44 1.35 1.29 1.23

660 3.07 1.80 1.49 1.42 1.38 1.33

680 4.03 2.27 1.81 1.69 1.58 1.54

700 9.48 4.95 3.55 3.06 2.61 2.35



400


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)


Yarn

Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 7.7818 7.4511 7.7775 7.4437 3.13% 0.320% 0.725% 16.6 0.44

6.3 1--2 2 8.1611 7.8115 8.2261 7.8274 4.04% 0.550% 1.176% 33.6 0.47

6.3 1--3 3 7.8049 7.4705 7.9675 7.5075 5.37% 0.856% 2.150% 49.9 0.40

6.3 1--4 4 7.7129 7.3701 7.8701 7.4395 5.50% 1.164% 3.670% 64.8 0.32

6.3 1--5 5 7.8049 7.482 8.0171 7.559 5.87% 1.561% 5.577% 77.6 0.28

6.3 1--6 6 8.2905 7.945 8.4682 8.0669 5.31% 1.830% 6.629% 82.9 0.28


Wave-

length


400 13.25 8.47 6.07 4.59 3.58 3.16

420 17.46 11.43 7.96 5.83 4.43 3.78

440 16.47 10.41 7.05 5.10 3.84 3.27

460 14.25 8.70 5.80 4.18 3.16 2.72

480 12.45 7.25 4.74 3.42 2.60 2.26

500 11.02 6.20 4.01 2.90 2.24 1.98

520 9.37 4.98 3.22 2.35 1.84 1.66

540 7.57 3.91 2.56 1.89 1.53 1.44

560 6.49 3.29 2.17 1.65 1.40 1.34

580 5.42 2.73 1.87 1.47 1.28 1.25

600 4.49 2.30 1.64 1.35 1.22 1.21

620 3.86 2.02 1.51 1.30 1.21 1.21

640 3.26 1.79 1.41 1.25 1.22 1.23

660 3.12 1.80 1.49 1.34 1.35 1.38

680 4.03 2.35 1.84 1.60 1.58 1.60

700 9.14 5.27 3.69 2.91 2.49 2.34



401


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)


Yarn

Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

7.1 1 only 1 7.0215 6.8197 7.1193 6.8162 3.14% 0.354% 0.806% 20.3 0.44

7.1 1--2 2 7.0354 6.8369 7.2252 6.8568 4.41% 0.621% 1.488% 40.2 0.42

7.1 1--3 3 7.2442 7.0315 7.5124 7.0802 5.56% 0.885% 2.607% 55.1 0.34

7.1 1--4 4 7.0342 6.8316 7.272 6.8981 5.17% 1.210% 3.406% 62.6 0.36

7.1 1--5 5 7.0837 6.882 7.3738 6.963 5.86% 1.605% 4.657% 72.0 0.34

7.1 1--6 6 7.0648 6.8578 7.2998 6.9678 5.17% 1.974% 7.055% 84.8 0.28


Wave-

length


400 12.19 7.42 5.62 4.84 4.01 3.12

420 16.21 10.07 7.23 6.18 4.99 3.82

440 15.08 9.04 6.35 5.40 4.34 3.30

460 12.84 7.49 5.20 4.43 3.56 2.75

480 11.07 6.15 4.25 3.62 2.93 2.27

500 9.70 5.22 3.59 3.06 2.51 1.98

520 8.06 4.16 2.88 2.47 2.04 1.64

540 6.41 3.25 2.29 1.97 1.67 1.40

560 5.41 2.74 1.96 1.72 1.50 1.30

580 4.46 2.29 1.70 1.52 1.36 1.21

600 3.68 1.95 1.51 1.37 1.27 1.17

620 3.15 1.74 1.42 1.31 1.24 1.16

640 2.66 1.57 1.34 1.25 1.22 1.16

660 2.57 1.59 1.42 1.35 1.33 1.30

680 3.36 2.01 1.73 1.61 1.57 1.51

700 8.01 4.42 3.37 2.95 2.61 2.25



402


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)


Yarn

Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

8 1 only 1 9.3167 8.9763 9.3606 8.8991 3.03% 0.405% 0.821% 21.0 0.49

8 1--2 2 9.228 8.9051 9.4013 8.8917 4.31% 0.706% 1.382% 38.2 0.51

8 1--3 3 9.8658 9.4983 10.167 9.5727 5.76% 1.166% 2.780% 56.8 0.42

8 1--4 4 8.9274 8.5972 9.2155 8.7022 5.91% 1.481% 4.331% 69.8 0.34

8 1--5 5 9.2807 8.9442 9.6769 9.1161 6.89% 1.893% 6.248% 81.1 0.30

8 1--6 6 9.1866 8.8523 9.5417 9.0438 6.49% 2.194% 7.096% 84.9 0.31


Wave-

length


400 11.87 7.60 5.33 4.17 3.32 2.99

420 15.78 10.32 6.84 5.19 4.04 3.56

440 14.68 9.27 6.00 4.51 3.50 3.07

460 12.51 7.66 4.90 3.69 2.90 2.55

480 10.78 6.30 4.00 3.03 2.39 2.13

500 9.45 5.36 3.39 2.58 2.07 1.87

520 7.83 4.29 2.73 2.10 1.72 1.59

540 6.23 3.39 2.19 1.73 1.47 1.40

560 5.25 2.87 1.90 1.54 1.35 1.31

580 4.32 2.42 1.66 1.39 1.25 1.24

600 3.55 2.07 1.49 1.30 1.21 1.22

620 3.05 1.85 1.41 1.27 1.20 1.24

640 2.60 1.67 1.36 1.26 1.21 1.27

660 2.52 1.72 1.46 1.38 1.36 1.45

680 3.34 2.17 1.74 1.62 1.57 1.66

700 7.97 4.62 3.30 2.73 2.38 2.32



403


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)


Yarn

Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

6.3 1 only 1 7.9307 7.5955 7.9387 7.585 4.52% 0.333% 0.746% 17.5 0.45

6.3 1--2 2 8.2671 7.9191 8.3645 7.9288 5.62% 0.631% 1.248% 35.3 0.51

6.3 1--3 3 7.9353 7.5908 8.0965 7.6303 6.66% 0.996% 2.267% 51.3 0.44

6.3 1--4 4 7.6814 7.3619 7.8528 7.4163 6.67% 1.286% 3.834% 66.1 0.34

6.3 1--5 5 8.2861 7.9359 8.4814 8.0135 6.87% 1.602% 5.328% 76.2 0.30

6.3 1--6 6 7.9222 7.5824 8.0857 7.6956 6.64% 1.973% 7.164% 85.2 0.28


Wave-

length


400 12.93 8.01 5.89 4.38 3.62 3.02

420 17.05 10.81 7.71 5.58 4.52 3.64

440 16.03 9.84 6.81 4.88 3.93 3.16

460 13.84 8.22 5.61 4.02 3.24 2.63

480 12.07 6.81 4.58 3.28 2.65 2.16

500 10.67 5.84 3.87 2.79 2.29 1.89

520 9.05 4.71 3.12 2.27 1.89 1.61

540 7.30 3.71 2.48 1.85 1.58 1.40

560 6.21 3.13 2.12 1.63 1.43 1.31

580 5.15 2.60 1.82 1.46 1.31 1.22

600 4.25 2.20 1.60 1.34 1.23 1.18

620 3.62 1.94 1.47 1.28 1.20 1.18

640 3.09 1.77 1.43 1.29 1.23 1.25

660 2.93 1.76 1.48 1.36 1.34 1.38

680 3.88 2.31 1.85 1.65 1.59 1.62

700 8.91 5.01 3.64 2.88 2.54 2.30



404


Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)


Yarn

Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

7.1 1 only 1 7.0215 7.0117 7.3237 6.9992 4.45% 0.375% 0.782% 19.1 0.48

7.1 1--2 2 7.0354 7.0328 7.4309 7.0457 5.66% 0.655% 1.379% 38.1 0.48

7.1 1--3 3 7.2442 7.2045 7.6625 7.2414 6.36% 0.951% 2.484% 53.8 0.38

7.1 1--4 4 7.0342 7.0233 7.4485 7.0942 6.05% 1.493% 4.629% 71.9 0.32

7.1 1--5 5 7.0837 7.0282 7.5511 7.1115 7.44% 1.714% 5.414% 76.7 0.32

7.1 1--6 6 7.0648 6.9459 7.4152 7.0605 6.76% 2.162% 7.680% 87.3 0.28


Wave-

length


400 12.52 7.66 5.72 4.01 3.60 2.96

420 16.58 10.35 7.42 5.04 4.43 3.57

440 15.52 9.33 6.55 4.38 3.84 3.08

460 13.32 7.76 5.40 3.59 3.17 2.57

480 11.56 6.39 4.40 2.93 2.59 2.11

500 10.18 5.45 3.73 2.49 2.23 1.85

520 8.54 4.38 3.00 2.04 1.85 1.57

540 6.84 3.44 2.37 1.67 1.56 1.36

560 5.75 2.90 2.02 1.50 1.42 1.27

580 4.73 2.41 1.74 1.36 1.31 1.20

600 3.88 2.05 1.53 1.27 1.24 1.16

620 3.30 1.82 1.42 1.23 1.22 1.16

640 2.82 1.68 1.37 1.27 1.26 1.23

660 2.68 1.68 1.42 1.37 1.37 1.36

680 3.55 2.18 1.78 1.64 1.63 1.60

700 8.41 4.63 3.47 2.71 2.51 2.25




Shade

ID

Speed

(m/min)

Dwell

Time

(sec)

Oxidation

Time (sec)

Dye Bath

(gpl

100%

Indigo)

Dye

Bath pH

Dye

Bath

(mV)

Dye Bath

Alkalinity

(gpl)

Dwell

Length

(m)

Oxidation

Length (m)

Nip

Pressures

(psi)


Yarn

Count

Dye

route Dips

Greige

Weight

Boil Off

Weight

Dyed

Weight

Washed

Weight %COWY

Total

%IOWY

Surface

%IOWY Integ

Penetration

Level

12 1 only 1 6.1779 5.7167 5.9994 5.7123 4.95% 0.398% 0.772% 18.7 0.52

12 1--2 2 5.9573 5.7311 6.1273 5.7502 6.91% 0.755% 1.384% 38.2 0.55

12 1--3 3 6.0513 5.8758 6.2831 5.9182 6.93% 1.136% 2.339% 52.1 0.49

12 1--4 4 5.9588 5.7315 6.1815 5.8074 7.85% 1.607% 4.211% 69.0 0.38

12 1--6 6 5.8451 5.6216 6.1025 5.7299 8.55% 2.210% 6.725% 83.3 0.33

12 1--6 6 6.0562 5.8765 6.3204 5.9896 7.55% 2.330% 6.360% 81.6 0.37


Wave-

length


400 12.59 7.72 5.83 4.21 3.21 3.17

420 16.56 10.38 7.58 5.30 3.94 3.86

440 15.47 9.36 6.68 4.62 3.40 3.34

460 13.28 7.78 5.49 3.79 2.83 2.78

480 11.53 6.41 4.48 3.10 2.32 2.29

500 10.20 5.47 3.80 2.64 2.03 2.00

520 8.60 4.41 3.07 2.16 1.68 1.69

540 6.94 3.47 2.44 1.76 1.43 1.45

560 5.88 2.92 2.09 1.57 1.32 1.35

580 4.85 2.41 1.80 1.41 1.22 1.27

600 4.01 2.03 1.58 1.30 1.17 1.23

620 3.41 1.80 1.46 1.25 1.16 1.22

640 2.93 1.65 1.43 1.26 1.22 1.29

660 2.81 1.65 1.48 1.36 1.35 1.43

680 3.72 2.17 1.86 1.63 1.57 1.67

700 8.49 4.69 3.59 2.77 2.36 2.39

VCUniversity Estudo Indigo

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Transcript of VCUniversity Estudo Indigo