Coefficients of Equilibrium Sorption %IOWY Power Function - Digital ...

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: total 

percent 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 the 

observational 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.

© Copyright 2011 by Richard Moore Holbert, Jr. 

All Rights Reserved

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

Chain Rope Indigo Dye Ranges 

Warren Jasper 

Jon Rust 

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: 

Richard Gould 

Peter Hauser 

Chair of Advisory Committee

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. 

ii

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". 

iii

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 34 

1.4.3. 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 


Concentration Affect on Penetration Factor after One and Six Dip Indigo Dyeing 

Conditions 119 

3.2.5 Determine Optimum Settings for Laboratory Preparation Procedure 126 

iv

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 219 

4.3.4 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 

v

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. 9 

Table 1-3: Additional indigo stock mix recipes. 10 

Table 1-4: Estimated diffusion coefficients for disperse Red 11 (D, cm 2 /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. 111 


%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 

vi

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 measured 

penetration 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 


production yarn %IOWY. 261 


production yarn Integ. 262 

vii


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. 371 

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

viii

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. 3 

Figure 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 end 

yarn 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/r 2 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. 60 

Figure 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 

ix

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. 78 

Figure 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. 108 

Figure 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 

x

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. 123 

Figure 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 Etters 20 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 data 

under 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 

xi


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 various 

numbers 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. 164 

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. 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 

xii

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 range 

set-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 


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 


5. Empirical and Theoretical Dye Model simulation and validation 

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. 242 

Figure 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 

xiii

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 

6. Summary of Results, Discussions, and Recommendations 

xiv

LIST OF EQUATIONS 


Equation 1-1: First law of thermodynamics. 6 

Equation 1-2: Example calculation of percent indigo shade. 7 

Equation 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. 37 

Equation 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. 46 

Equation 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 


xv

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. 92 

Equation 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. 181 

Equation 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 

xvi

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

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 

xviii

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 20 th 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 1988 19 , “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. 

1

1.1 Commercial Indigo Dyeing 

Indigo dye (C.I. Vat Blue 1) is insoluble in water. In order to effectively be used it must be 

reduced to the leuco-soluble form using a suitable reducing agent with an alkali such as sodium 

hydroxide. There are three main types of dye ranges used in traditional indigo dyeing which are 

summarized below and shown in figure 1-1. 

1. The long chain or rope type dye range which is characterized by multiple dye boxes that 

allows great production rate and flexibility. 

2. The sheet or slasher dye range which can have multiple boxes but with reduced 

production capability. 

3. The looptex dye range which has a common dye box. This machine has limited number of 

dip capability. Figure 1-1 graphically illustrates the three types of machines. 

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

2

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 prescouring 

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 

3

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 unfixed 

surface 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 

4

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. 

5

Figure 1-5: Re-circulation 

system on loong 

chain indigoo 

dye range to mmaintain 

dye boox 

uniformity. 1 

Since dye liquor l is circuulated 

through 

the dye boxxes 

to maintaain 

uniform cooncentrationss, 

the 

indigoo 

dye boxes can c be modeleed 

as one giant 

dye box. TThe 

conservattion 

of mass principle for a 

controol 

volume undergoing 

a prrocess 

can bee 

expressed as 

equation 1--1.

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 rate 

3673 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 removed 

during 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 

7

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 with 

the 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.

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 As is % OWI 100% Total Theory Excess Excess 

#/Gal g/l 

g/l Moles Moles Moles 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 24 180 

Liq. Hydro 170g/l 340 3250 4.06 65 490 

Water 46 382 - - - 

Total Volume 800 

9

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

Plant 20% Indigo 50% Caustic Hydro (g/l) 50% Caustic Hydro (%I) 

Paste (g/l) Soda (g/l) 

Soda (%I) 

1 450 143 68 31.77 15.11 

2 414 140 54 33.77 13.09 

3 382 140 71 36.79 18.55 

4 400 118 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. 

10

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. The 

first ionization step produces the more soluble mono-ionic form of indigo, HI - as shown in equation 

1-4.

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

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

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. 

14

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 

15

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 

16

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

indigo and sodium hydrosulfite concentrations. Westbroek 51 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. 

Sahin 53 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 

17

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 250 

ml 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 Merritt 29 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. 

18

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 and 

shade 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. 

X dx 

Surface of paint film 

I J 

Substrate 

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

19

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

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 

21

=() −() 

() () 

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 the 

substrate, the reflectance absorptivity coefficient is a measure of the “color yield” that is obtained 

for a given system 25 . As the value of “a” increases, the greater the depth of shade for a given unit of 

fixed dye. 

 

=

ed 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.

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 R 2 and a statistically optimum zero value for the intercept are found. 

Etters plotted the R 2 versus Rs values for blue, red, and yellow reactive dye on velour cotton in figure 

1-13. It is revealed the R 2 value for the blue dye is insensitive to surface reflectance with all the 

values being greater than 0.99. On the other hand, R 2 for the red dye exhibits much greater 

sensitivity to surface reflectance, with the maximum R 2 occurring at an Rs of about 0.01. R 2 for the 

yellow dye has only limited sensitivity to surface reflectance, with the R 2 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 optimum 

value 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 

24

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 R 2 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 R 2 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. 

25

Corrected 

Corrected 

Corrected 

Original 

Original 

Original 

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

26

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 better 

ring 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. 

27

% Indigo Pick-up 

14 

12 

10 

8 

6 

4 

2 

0 

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 

1.5 5 10 20 30 45.5 61.2 80 88.2 

50% NaOH Concentration (opg) 

Mild Alkali Causticizing Mercerizing 

28

% Reflectance 

3.5 

3 

2.5 

2 

1.5 

1 

0.5 

% Reflectance Values of Typical 6 Dip Indigo Dye Shade 

0 

400 450 500 550 600 650 700 

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. 

K/S Corrected 

60 

50 

40 

30 

20 

10 

0 

Wavelength (nm) 

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

400 450 500 550 600 650 700 


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. 

29

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 

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

r 

p 

30

The volume of a yarn can be defined as Vm =πr 2 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. 

 

=

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 dye 

system. 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 Weisz 3 and McGregor 4 . 

1.4.1. Fundamental Sequence of Events during Dyeing 

Etters 28 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. 

32

Figure 1-21: Basic sequ uence of eventss 

in dyeing fibers 

The rate of 

sorption of dye by textilee 

materials is controlled byy 

several funddamental 

phyysico 

chemical 

paramete ers. 

s. 28 

1. 

Denier of fiber, f which iss 

proportionaal 

to radius off 

the cylinder fiber. 

2. 

Liquor ratio, 

the ratio oof 

volume of ddye 

bath to thhe 

volume of fiber mass. 

3. 

Distributio on coefficient or ratio of thhe 

equilibriumm 

concentration 

of dye in bboth 

the 

application n medium and 

the fiber. 

4. 

Diffusion coefficient c of the dye in booth 

the appliccation 

mediumm 

and the fibber. 

5. 

Fundamen ntal nature off 

the dyeing syystem: 

infinitte 

or finite baath 

condition. . 

6. 

Thickness of the diffusional 

boundarry 

layer at thee 

fiber surfacee. 

Rate of dyeing 

for a given 

system is inversely proportional 

to tthe 

denier of the fiber. Ass 

the 

denieer 

of a given fi iber increasess, 

the surfacee 

area decreases 

for a giveen 

mass of fiber 

available ffor 

33

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. 

34

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 1-20. 

 

=

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

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

38

The sorption curves on figure 1-22 are defined by the dimensionless parameter Dt/a 2 . 

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 Hill 31 has developed a solution for infinite dye bath conditions in the 

absence of surface barrier effects, equation 1-25. 

 

 

=1−∑

=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.

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.

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. 

42

Table 1-4: Estimated diffusion coefficients for disperse Red 11 (D, cm 2 /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 4.38 

2.00 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. 

43

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

1.4.4. Empirical Simplifications of Diffusion 

The formal solution to Fick’s 2 nd 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/r 2 , 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−

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−



 

 

=1−



 

 

=1−

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/r 2 =1) gives the parameter a, a=e I . 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 0.0625 

0.98 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.

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 be 

noted 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 Experiment 15 

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 a 

flattened 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 1 

Group 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 

49

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. 

50

Table 1-7: Etters 1989 data set. 15 

Dyebath Dye in Fiber 

Group pH (g/L) (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 

51

Annis and Etter 1991 Experiment 19 

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 AATCC 

were 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 0.04 

12.1 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 0.018 

7.7 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 

52

Etters 1991 Experiment 20 

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 proprietary 

buffered 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 

53

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 2.111 

0.0375 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 Experiment 27 

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. 

54

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. 

55

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 Experiment 29 

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. 

calculated. 

After each dyeing the color yield as expressed by Kubelka-Munk K/S at 660 nm was 

56

Xin 2000 Experiment 46 

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 30 

minutes 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.

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. 

K/S 

30 

25 

20 

15 

10 

Effect of Oxidization Time on Depth of Shade 

30 60 90 120 150 180 

Figure 1-26: Effect of oxidation time on color. 29 

Oxidization Time (sec) 

58

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 course 

the 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 

59

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 of 

immersion time. 

Figure 1-28: Effect of immersion time on shade. 46 

Chong 29 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. 

60

K/S 

30 

25 

20 

15 

10 

Effect of Immersion Time on Depth of Shade 

15 30 45 60 75 90 

Immersion Time (sec) 

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 8 th 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. 

61

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. 

Chong 29 and Xin 46 independently confirm the results. 

62

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 Xin 46 . 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 bath 

concentration was increased. 

63

Figure 1-32: Relationship between dye bath concentration and shade. 46 

Chong 29 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. 

64

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. 

65

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. 

66

Figure 1-35: K/S shade e vs % indigo on weight of yarn at various pH’s 3 

Etters & Hou 

have noteed 

ring dyeingg 

of cotton yaarn 

can be cauused 

by a high 

strike rate oof 

the 

dye foor 

the cotton fiber in the yyarn 

surface, i.e. the dye exhausts 

rapiddly 

onto the fibers 

in the oouter 

zoness 

of the yarn at a the expensse 

of fibers in the yarn inteerior. 

Vickersstaff 

has obseerved 

that "… the 

diffussion 

rate cann not indicate thhe 

actual proogress 

of dyeing 

in the initiial 

stages, as tthis 

is determmined 

by thee 

affinity of th he dye. If twoo 

dyes are present 

in a binnary 

mixture, the dye whicch 

is first adsoorbed 

by thee 

fiber is that having the higher 

affinityy, 

irrespectivee 

of their relattive 

diffusion rates." 

Affinity or substantivityy 

of a dye for a fiber can bee 

expressed in 

terms of ann 

equilibrium 

distribbution 

coeffic cient or K, thee 

ratio of concentrations 

oof 

dye in fiberr 

to dye in dyee 

bath at 

equilibrium. 

Relat tively high values 

of distribbution 

coefficient 

indicate relatively higgh 

substantiviity 

or 

affinitty 

of the dye for the fiber. Figure 1-36 illustrates thee 

ratio of dyee 

in denim yarrn 

to dye in an 

infinitte 

indigo dye bath as givenn 

from 5 dip laboratory 

dyeings 

conduccted 

at pH 11 and 13. Thesse 

values 

may be rega arded as techhnical 

quantitties 

since theyy 

were not obbtained 

under 

equilibrium 

conditions. 

Both pH p ranges exhhibit 

a linear rrelationship, 

but the slopee 

of the lowerr 

pH line is muuch 

steeper. 

This data suggest thatt 

either the “aaffinity” 

of the 

dye for the fiber is muchh 

higher at the 

30 . 

67

lowerr 

pH or the dif ffusion of thee 

dye into thee 

fiber is muchh 

more rapid at the lower pH. Either wway 

the diistribution 

co oefficients aree 

much higher 

at lower pH values than at higher pH values. 

Figure 1-36: Non-equilibrium 

Concenttration 

of dye inn 

fiber (g/100g) vvs 

concentration 

of dye in bathh 

(g/100g). 20 

Equilibrium m sorption isootherms 

for inndigo 

on cottton 

fiber weree 

obtained att 

two dye bath 

pH 

rangees 

(11.1-11.3) and (13.1-133.3) 

from 8 hoour 

dyeings. TThese 

isotherrms 

show a laarge 

differencce 

in 

technnical 

paramete ers such as dyye 

uptake, yaarn 

penetratioon, 

and color yield. To clarify 

this pointt, 

the 

equilibrium 

sorptio on data are plotted 

in figure 

1-37. The indigo uptakke 

is significanntly 

higher forr 

the 

dyeings 

at the lower 

pH. Furtheermore, 

the isotherms 

aree 

not linear ass 

were the noon-equilibriumm 

isotheerms 

given in figure 1-36. For the expeerimental 

conditions 

used, no obvious aapproach 

to a 

limitinng 

fiber satur ration value iss 

evident for ddyeings 

at eitther 

pH rangee. 

The previoously 

observed 

pH 

effectt 

on dye uptake 

appears too 

be caused bby 

a real difference 

in appaarent 

affinity. 

68

Figure 1-37: Equilibrium 

isotherm for dye concentration 

in dye bath and fiber (g/100 

When figure 

1-37 is recconfigured 

onn 

a logarithmic 

scale, an exxcellent 

linearr 

correlation 

betweeen 

equilibriu um concentraation 

of dye inn 

the fiber annd 

dye in the ddye 

bath is obbtained 

as shown 

in figuure 

1-38. This s indicates thhat 

equilibriumm 

sorption in both pH’s arre 

effectively described by the 

Freunndlich 

isotherm 

20 . A Freundlich 

isothermm 

is characteerized 

by the ppower 

functioon 

or linear 

relatioonship 

on log g by log scale. . 

0g). 20 

69

Figure 1-38: Logarithm mic plot of equiliibrium 

isothermms 

for dye conce 

The mean technical disttribution 

coefficient 

is calcculated 

by divviding 

the inddigo 

concentrration 

in yarrn 

by indigo concentration 

in dye bath. In figure 1-39 

the relationnship 

betweeen 

dye bath pH 

and teechnical 

distr ribution coeffficient, 

K, andd 

the coefficieent 

of variatioon 

of %CV aree 

given. The 

technnical 

distributi ion coefficiennt 

decreases wwith 

increasinng 

pH and thee 

%CV increasses. 

This meaans 

substantivity 

assoc ciated with ring 

dyeing andd 

color yield bbecome 

moree 

variable witth 

increasing pH. 

Although 

this infor rmation is bassed 

on laboraatory 

dyeings according too 

Etters 30 , the results from 

commmercial 

dyeing gs tend to connfirm 

the connstancy 

of subbstantivity 

of indigo for deenim 

yarn wheen 

dye bath 

pH is mai intained within 

the range of 10.8 to 11.2. 

entration. 20 

70

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 – p 2 )]; 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 

respectively 33 . 

71

Etters' equ uation makes use of the true 

reflectancce 

absorptivity 

coefficient. However in 

practiical 

indigo dyeing 

processees 

true reflectance 

absorpptivity 

coefficiients 

must bee 

replaced by 

apparrent 

coefficients. 

The relationship 

betwween 

apparennt 

reflectancee 

absorptivityy 

coefficient aand 

dye bath 

pH is illus strated in figuure 

1-40. As tthe 

dye bath pH decreasess 

from 13 to 111 

there is moore 

ring ddyeing 

and an increasing appparent 

refleectance 

absorrptivity 

coefficcient. 

It has bbeen 

found thhat 

betweeen 

pH 10.8 and a 11.2, the greatest coloor 

yield is achieved. 

Figure 1-40: Apparent reflectance abssorptivity 

coefficcient 

vs pH. 30 

Figure 1-41 

illustrates the 

apparent reflectance aabsorptivity 

cooefficients 

off 

figure 1-40 

plotteed 

as a functio on of the techhnical 

distribution 

coefficients 

with addditional 

data points addedd 

from other dye bat th pH’s. As thhe 

distributioon 

coefficient increases, thhe 

color yield also increasees. 

It 

may bbe 

concluded from figure 11-41 

that the yarn ring dyeeing 

phenomeenon 

is highlyy 

correlated wwith 

increaasing 

substan ntivity and strike 

of indigo for cotton fibber 

that is asssociated 

with lower pH dyee 

bathss. 

The fact tha at the appareent 

reflectancce 

absorptivitty 

coefficientss 

found in theese 

experiments 

72

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 

Etters 15 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.

Here pK1 and pK2 are a the pKa vaalues 

associated 

with the two step ioniization 

of reduced 

indigo 15 

Meann 

values of mo ono-ionic formm 

are plottedd 

in figure 1-442 

as a functioon 

of dye bath 

pH. It is nooted 

abovee 

pH 11.5 the fraction of inndigo 

that exiists 

as a monoo-anion 

beginns 

to drop offf 

rather severrely 

and continues 

to decrease d as pH 

increases. This is due too 

more of thee 

mono-ionic fform 

ionizingg 

furtheer 

to produce e the more sooluble 

di-ionicc 

form. At dyee 

bath pH of 12.7 about haalf 

of the indiigo 

existss 

as mono-ion nic and half haas 

di-ionic forrm. 

Figure 1-42: Relationship 

of Mono-ionnic 

species of inddigo 

and pH. 30 

The mean technical disttribution 

coefficients 

are pplotted 

as a function 


mean fractiion 

of 

reducce 

indigo that t exists as a mmono-ionic 

forrm 

at various dye bath pH’s, 

figure 1-433. 

There is ann 

excepptionally 

high linear correlaation 

betweeen 

the substanntivity 

of indigo 

for cottonn 

fiber and thee 

fractioon 

of indigo that t exists in mono-ionic foorm. 

Etters 155 

concluded that 

the monoo-ionic 

form oof 

indigoo 

has a much higher substaantivity 

for cootton 

fiber thhen 

does the ddi-ionic 

form. . 

5 . 

74

Figure 1-43: Relationship 

between meean 

technical distribution 

coeffficient 

and fraction 

of indigo existing 

as mono- ionic 

form. 300 

Recall redu uced indigo can 

exist in twwo 

forms: monophenolate 

ion or biphennolate 

ion. Shade 

depthh 

for a given amount a of fixed 

dye is shown 

to be highhly 

correlatedd 

with the fractional 

amouunt 


indigoo 

that exists as a a monopheenolate 

ion inn 

dye bath. Thhe 

correlationn 

is explainedd 

as an increaased 

apparrent 

affinity of o the mono aanion 

form. AAs 

the affinityy 

increases, thhe 

strike rate of the dye foor 

the 

yarn ssurfaces 

incre eases, leadingg 

to a more ring 

dyed yarnn. 

It is readily y seen that thhe 

fractional aamount 


mono-ionicc 

form is maxiimum 

near thhe 

regionn 

of maximum m reflectancee 

absorptivity. 

By converting 

the apparent 

reflectance 

absorptivity 

into a fractional fo orm and superimposing 

on top of the fractional 

amoount 

of mono-ionic 

form ass 

a 

functiion 

of pH, the e relationshipp 

becomes cleearer, 

figure 11-44. 

Only at low pH valuees 

does this 

75

elationship 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 

76

1.5.2. g Interrelatio onship of Dye Concentratioon 

and pH on Shade 

Given the strong effect dye bath conncentration 

and 

pH indepeendently 

havee 

on the resulting 

dye uptake, 

penetration, 

and shhade; 

a more in-depth disccussion 

is warranted. 

Figuure 

1-45 

demoonstrates 

the mean indigo concentratioon 

in the dye bbath 

needed to produce a given shade 

depthh 

(K/S) at various 

dye bath pH values. FFor 

example tthe 

indigo conncentration 

reequired 

to 

produuce 

a rather dark d shade (K/ /S = 100) is about 

3 g/l at pH 12.5. But only 1 g/l of indigo in dyee 

bath 

is required 

to prod duce the samee 

shade depth 

at pH 11.0. This is the reesult 

of dye ddistribution 

wwithin 

the crross 

section of o yarn. 

Figure 1-45: Indigo con 

laborattory 

dyeing 30 ncentration in ddye 

bath requireed 

to produce a given shade deppth 

at various pH’s 

from a 5 dipp 

. 

When the dye uptake ddata 

is plottedd 

vs. dye bathh 

pH, the folloowing 

relationnship 

developps, 

figuree 

1-46. It is sh hown the maxximum 

uptakke 

at a particuular 

pH depennds 

on the concentration 

oof 

dye inn 

the dye bath h. Maximum uptake occurs 

between ppH 

9.25 – 10.55. 

As the concentration 

off 

dye 

in thee 

dye bath inc creases the mmaximum 

uptaake 

occurs at lower and lower 

pH valuees 

within the 

speciffied 

range. It t could be thaat 

all of the dyye 

extracted ffrom 

the knitted 

yarn tubee 

was not in ffact 

77

“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. 

78

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. 

79

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 Etters 30 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. 

80

Figure 1-49: Estimated d concentration of unfixed indiggo 

on yarn at coorresponding 

dye 

bath concentrration 

and pH. 300 

1.5.2. h Empirical in ndigo dye moodel 

The Holy Grail G for indigo 

dyers worlddwide 

would be a dye moddel 

relating inndigo 

on weigght 


yarn aand 

shade to various contrrollable 

dye rrange 

parameeters. 

This onne 

equation hhas 

not yet beeen 

deriveed. 

But an em mpirical modeel 

based on a 5 dip laborattory 

experimeent 

has been proposed byy 

Etterss 

21 . In this mo odel the dye bath indigo concentration 

and pH is used 

to predict the distributtion 

coeffiicient, 

indigo on weight off 

yarn, and subsequently 

thhe 

final yarn sshade. 

The empirical 

model is based on thee 

Southeasterrn 

Section 15 and 

Annis reseearch 

19 . The ddata 

obtainned 

from bot th investigatioons 

is based oon 

5 dip, 15 seecond 

immerrsions 

of knittted 

denim yarn 

tubess 

as previously y outlined. By 

analyzing thhese 

two dataa 

sets, Etters 2 

matheematical 

mod del. 

21 developed 

The techni ical distribution 

coefficient, 

K, is defined 

in equationn 

1-39 to equaal 

the 

conceentration 

of dye d in the fibeer, 

Cf, divided by the conceentration 

of ddye 

in the dyee 

bath, Cb. Thhe 

conceentrations 

are e expressed inn 

terms of graams 

of dye peer 

100 grams of fiber or water. 

the followingg 

81

Figure 1-49: Estimated d concentration of unfixed indiggo 

on yarn at coorresponding 

dye 

bath concentrration 

and pH. 300 

1.5.2. h Empirical in ndigo dye moodel 

The Holy Grail G for indigo 

dyers worlddwide 

would be a dye moddel 

relating inndigo 

on weigght 


yarn aand 

shade to various contrrollable 

dye rrange 

parameeters. 

This onne 

equation hhas 

not yet beeen 

deriveed. 

But an em mpirical modeel 

based on a 5 dip laborattory 

experimeent 

has been proposed byy 

Etterss 

21 . In this mo odel the dye bath indigo concentration 

and pH is used 

to predict the distributtion 

coeffiicient, 

indigo on weight off 

yarn, and subsequently 

thhe 

final yarn sshade. 

The empirical 

model is based on thee 

Southeasterrn 

Section 15 and 

Annis reseearch 

19 . The ddata 

obtainned 

from bot th investigatioons 

is based oon 

5 dip, 15 seecond 

immerrsions 

of knittted 

denim yarn 

tubess 

as previously y outlined. By 

analyzing thhese 

two dataa 

sets, Etters 2 

matheematical 

mod del. 

21 developed 

The techni ical distribution 

coefficient, 

K, is defined 

in equationn 

1-39 to equaal 

the 

conceentration 

of dye d in the fibeer, 

Cf, divided by the conceentration 

of ddye 

in the dyee 

bath, Cb. Thhe 


are e expressed inn 

terms of graams 

of dye peer 

100 grams of fiber or water. 

the followingg 

81

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. 

83

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 tubes 

or 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. Chong 29 

and Xin 46 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, Chong 29 and Xin 46 have demonstrated the significant affect 

number of dyes has on the resulting shade. Since indigo dye uptake and/or degree of penetration 

84

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 experiments 

was 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. 

85

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. - Zhou 48 

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. 

86

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 

87

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. 

88

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 

89

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 cotton 

ropes 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. The 

contact 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. 

90

%

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 water 

7.2 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: 

%

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. 

%

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 Xin 46 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.

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. 

K/S shade value 

50.0 

45.0 

40.0 

35.0 

30.0 

25.0 

20.0 

15.0 

10.0 

5.0 

0.0 

K/S Shade Values by Wavelength for Typical 3.0 

gm/lit Indigo Dye Set-up 

400 450 500 550 600 650 700 


1 dip 3 dip 6 dip 7 dip 

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 

95

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. 

Integ or K/S Shade Value 

120.0 

100.0 

80.0 

60.0 

40.0 

20.0 

0.0 

Integ and K/S Shade at 580nm and 660nm vs %IOWY 

0.000% 0.500% 1.000% 1.500% 2.000% 2.500% 3.000% 3.500% 

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. 

%IOWY 

580nm 660nm Integ 

96

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 

97

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. 

98

Table 3-2: Time, temperature, and sodium hydroxide concentration levels plus response variable for one dip of indigo 

Pattern Time Temperature NaOH %Boil-Off %IOWY Integ Penetration Run 

(min) (°C) 

(g/l) Loss 

Factor 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 17 

000 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. 

99

Table 3-3: Time, temperature, and sodium hydroxide concentration levels plus response variable for six dips of indigo 

Pattern Time Temperature NaOH %Boil-Off %IOWY Integ Penetration Run 

(min) (°C) 

(g/l) Loss 

Factor 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 17 

00A 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 in 

section 3.1.3. 

100

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 as 

the 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 R 2 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. 

%Boil-off Loss 

4.00% 

3.50% 

3.00% 

2.50% 

2.00% 

1.50% 

1.00% 

0.50% 

0.00% 

Relationship of Time on %Boil-off Loss during 

Laboratory Preparation 

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

R² = 0.025 

20 25 30 35 40 

Time (minutes) 

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. 

101

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 R 2 value of 0.148. Again the low correlation was due 

the high variability of %Boil-off loss at various levels of sodium hydroxide concentration. 


4.00% 

3.50% 

3.00% 

2.50% 

2.00% 

1.50% 

1.00% 

0.50% 

0.00% 

Relationship of Sodium Hydroxide Concentration on 

%Boil-off Loss during Laboratory Preparation 

R² = 0.148 

0 2 4 6 8 10 12 14 16 

Caustic Concentration (g/l) 

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 R 2 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. 

102


4.00% 

3.50% 

3.00% 

2.50% 

2.00% 

1.50% 

1.00% 

0.50% 

0.00% 

Relationship of Temperature on %Boil-off Loss during 

Laboratory Preparation 

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 

70 75 80 85 90 95 100 

Temperature (C) 

103

Interaction Profiles 

0.04 

0.03 

Time 

0.02 

(min) 

0.01 

0.04 

100 

0.03 

% Boiloff 

Loss 


Loss 


Loss 

0.02 

0.01 

0.04 

0.03 

0.02 

0.01 

20 

25 

30 

35 

40 

76 

15 

0 

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 R 2 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. 

%Boil-off Loss Interaction Profile 

40 

20 

Temperature 

(C) 

80 

85 

90 

95 

100 

15 

0 

0 

NaOH 

(g/l) 

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 

5 

10 

40 

20 

100 

15 

76 

Time Temperature NaOH 

104

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 R 2 value for second order trend curve was higher than a linear trend line. The summary of 

fit produces a R 2 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. 

%

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. 


Loss 

0.030211 

±0.00233 

%Boil-off Loss Prediction Profile for Laboratory Preparation Process 

20 

25 

30 

Time (min) Temperature (C) NaOH (g/l) 

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 

35 

40 

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 R 2 value of 0.046. While the 

75 

correlation coefficient was obviously very low the general trend was an increasing %IOWY value 

80 

85 

90 

95 

100 

0 

5 

10 

15 

106

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 R 2 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. 

%IOWY (one dip) 

0.400% 

0.350% 

0.300% 

0.250% 

0.200% 

0.150% 

0.100% 

0.050% 

0.000% 

Effect of Time on %IOWY from One and Six Dips of Indigo 

R² = 0.034 

R² = 0.046 

20 25 30 35 40 


One Dip Six Dips 

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 R 2 value of 0.086. Increasing sodium hydroxide concentration resulted in 

2.500% 

2.000% 

1.500% 

1.000% 

0.500% 

0.000% 

increasing %IOWY until 9 g/l. Further increases in concentration resulted in decreased %IOWY as 

%IOWY (six dips) 

107

illustrated in figure 3-9. For six dips the best curve fit was described as essentially constant with a R 2 

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. 


0.400% 

0.350% 

0.300% 

0.250% 

0.200% 

0.150% 

0.100% 

0.050% 

0.000% 

Effect of Sodium Hydroxide Concentration on %IOWY from 

One and Six Dips of Indigo 

R² = 0.037 

R² = 0.086 

0 2 4 6 8 10 12 14 16 

Sodium Hydroxide Concentration (g/l) 


2.500% 

2.000% 

1.500% 

1.000% 

0.500% 

0.000% 

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 R 2 value of 0.708. 

After six dips of indigo the second order polynomial R 2 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 


108

variability around the curve fit appeared to reduce at higher temperatures for both one and six dip 

dyeings. 


0.400% 

0.350% 

0.300% 

0.250% 

0.200% 

0.150% 

0.100% 

0.050% 

0.000% 

Effect of Temperture on %IOWY from One and Six Dips of 

Indigo 

R² = 0.743 

R² = 0.708 

70 75 80 85 90 95 100 

Temperature (°C) 


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. 

2.500% 

2.000% 

1.500% 

1.000% 

0.500% 

0.000% 


109

%IOWY Interaction Profile for One Dip %IOWY Interaction Profile for Six Dips 

(min) (min) 

(C) (C) 

(g/l) (g/l) 

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 and 

second 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. 

110

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. 

%


0.002946 

±0.000895 

%IOWY Prediction Profile on One Dip of Indigo for Laboratory Preparation Process 

20 

25 

30 

35 

40 

75 

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 R 2 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. 

80 

85 


90 

95 

100 

0 

5 

10 

15 

112

Table 3-6: ANOVA analysis results for laboratory preparation parameters on %IOWY for six dips of indigo 

created. 

Using the parameter estimates from table 3-6, equation 3-11 for 6 dips of indigo was 

%


0.021429 

±0.001654 

%IOWY Prediction Profile on Six Dips of Indigo for Laboratory Preparation Process 

20 

25 

30 

35 

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 R 2 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. 

40 

75 

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 R 2 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 

80 

85 


90 

95 

100 

0 

5 

10 

15 

114

dip nor the six dip indigo dyeing condition exhibited a major contribution to Integ shade value due 

to time. 

Integ (one dip) 

34.0 

32.0 

30.0 

28.0 

26.0 

24.0 

22.0 

20.0 

Effect of Time on Integ from One and Six Dips of Indigo 

R² = 0.021 

R² = 0.245 

20 25 30 35 40 



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 R 2 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 

105.0 

100.0 

95.0 

90.0 

85.0 

80.0 

75.0 

Integ (six dips) 

115

concentrations. As the concentration is further increased the variability appears to reduce while the 

overall Integ shade value also decreased. 


34.0 

32.0 

30.0 

28.0 

26.0 

24.0 

22.0 

20.0 

Effect of Sodium Hydroxide Concentration on Integ from One 

and Six Dips of Indigo 

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 R 2 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 R 2 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 = 0.182 

R² = 0.187 

0 2 4 6 8 10 12 14 16 



105.0 

100.0 

95.0 

90.0 

85.0 

80.0 

75.0 


116


34.0 

32.0 

30.0 

28.0 

26.0 

24.0 

22.0 

20.0 

Effect of Temperture on Integ from One and Six Dips of 

Indigo 

R² = 0.015 

R² = 0.122 

70 75 80 85 90 95 100 



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 R 2 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. 

105.0 

100.0 

95.0 

90.0 

85.0 

80.0 

75.0 


117

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 fit 

and 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. 

118

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 R 2 correlation was very low at 0.088. If the single point at 1200+ penetration factor was 

removed, the function was flat with R 2 of 0.057. Time doesn't appear to affect penetration factor 

after one dip of indigo. 

119

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 R 2 correlation was very low at 0.03 and is basically 

constant over all times. 

Penetration Factor (one dip) 

1400.00 

1200.00 

1000.00 

800.00 

600.00 

400.00 

200.00 

0.00 

Effect of Time on Penetration Factor from One and Six Dips 

of Indigo 

R² = 0.03 

R² = 0.088 

20 25 30 35 40 



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 R 2 values of 0.094 and 0.011 for one and six dips respectively. If the 1200+ 

70.00 

60.00 

50.00 

40.00 

30.00 

20.00 

10.00 

penetration factor value was removed, the resulting trend after one dip of indigo was flat with a R 2 

value of 0.049. Sodium hydroxide concentration doesn't have a major affect on penetration factor. 

0.00 

Penetration Factor (sex dips) 

120


1400.00 

1200.00 

1000.00 

800.00 

600.00 

400.00 

200.00 

0.00 

Effect of Sodium Hydroxide Concentration on Penetration 

Factor from One and Six Dips of Indigo 

R² = 0.011 

R² = 0.094 

0 2 4 6 8 10 12 14 16 



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 R 2 

value of 0.246. However, after six dips the general trend has a much stronger correlation as 

reflected in the R 2 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. 

70.00 

60.00 

50.00 

40.00 

30.00 

20.00 

10.00 

0.00 

Penetration Factor (six dips) 

121


1400.00 

1200.00 

1000.00 

800.00 

600.00 

400.00 

200.00 

0.00 

Effect of Temperture on Penetration Factor from One and Six 

Dips of Indigo 

R² = 0.729 

R² = 0.246 

70 75 80 85 90 95 100 



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. 

70.00 

60.00 

50.00 

40.00 

30.00 

20.00 

10.00 

0.00 

Penetration Factor (six dips) 

122

P.F. 

P.F. 

P.F. 

250 

200 

150 

100 

50 

250 

200 

150 

100 

50 

250 

200 

150 

100 

50 

P.F. Interaction Profile for One Dip P.F. Interaction Profile for Six Dips 


Time 

60 

55 

50 Time 

(min) 20 

40 

20 

40 

45 

40 

(min) 

20 

25 

30 

35 

40 

76 

100 

150 

76 

60 

55 

75 

Temperature 

(C) 100 

50 

45 

40 

102.5 

Temperature 

(C) 

80 

85 

90 

95 

100 

150 

0 

5 

10 

15 



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 R 2 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 

P.F. 

P.F. 

NaOH 

(g/l) 

60 

55 

50 

45 

40 

150 

150 

NaOH 

(g/l) 

P.F. 

20 

25 

30 

35 

40 

75 

85 

95 

20 

40 

105 

0 

5 

10 

20 

40 

75 

102.5 

15 


123

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. 

Penetration Factor Prediction Profile on One Dip of Indigo for Laboratory Preparation 


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 R 2 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. 

124

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. 

125

Penetration Factor Prediction Profile on Six Dips of Indigo for Laboratory Preparation 

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 

126

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 temperature 

value 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 no 

concentration 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. 

127

Prediction Optimized Profiler Prediction Profile on One Dip of Indigo for Laboratory Preparation Process 

Pred Formula Pred Formula % 

%IOWY By Dip # Boil-off Loss 

0.002823 0.030211 

Desirability 

0.363667 

0.03 

0.025 

0.02 

0.015 

0.02 

0.015 

0.01 

0.005 

0 

0 0.25 0.75 1 

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. 

20 

25 

30 

35 

40 

75 

80 

85 

90 

95 

100 

0 

5 

10 

30 

100 

11 

Time Time (min) Temperature (C) NaOH (g/l) 

15 

1 

1 

Dip # 

6 

0 

0.25 

0.5 

0.75 

1 

Desirability 

128

Prediction Optimized Profiler Prediction Profile on Six Dips of Indigo for Laboratory Preparation Process 

Pred Formula Pred Formula % 

%IOWY By Dip # Boil-off Loss 

0.021231 0.030211 

Desirability 

0.964286 

0.03 

0.025 

0.02 

0.015 

0.02 

0.015 

0.01 

0.005 

0 

0 0.25 0.75 1 

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. 

20 

25 

30 

35 

40 

75 

80 

85 

90 

95 

100 

30 

100 

11 

Time Time (min) Temperature (C) NaOH (g/l) 

Time: 30 minutes 

Temperature: 100°C 

Sodium hydroxide concentration: 12.7 g/l of 50% caustic soda 

0 

5 

10 

15 

1 

6 

Dip # 

6 

0 

0.25 

0.5 

0.75 

1 

Desirability 

129

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

Dyed Skeins 

In 1991 Etters 20 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 shade 

information 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 

130

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. 

131

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 4 

6.3 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 Etters 20 . 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 data 

range to encompass the range of current values. 

132

%IOWY (gm Indigo/100 gm cotton) 

Equilibrium Sorption Relationship at 13.1 to 13.3 pH 

100.00% 

10.00% 

1.00% 

0.10% 

0.01% 

Figure 3-25: %IOWY from 6.3/1, 7.1/1, 8.0/1, and 12.0/1 OE yarns compared to Etters 20 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 = 0.007303x 0.734588 

R² = 0.996 

0.01 0.1 1 10 

Dye Concentration (g/l) 

6.3 7.1 8 12 Etters 1991 

133

%IOWY (gm Indigo/100 gm cotton) 

Equilibrium Sorption Relationship at 11.0 to 11.2 pH 

100.00% 

10.00% 

1.00% 

0.10% 

0.01 0.1 1 10 


6.3 8 Etters 1991 

Figure 3-26: %IOWY on 6.3/1, 7.1/1, 8.0/1, and 12.0/1 OE yarns compared to Etters 20 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: %

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. 

Value of Componet A 

0.025 

0.02 

0.015 

0.01 

0.005 

0 

Coefficients of Equilibrium Sorption %IOWY Power 

Function 

11 11.5 12 12.5 13 13.5 

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. 

pH 

Component A Component B 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

0.1 

0 

Value of Component B 

135

Value of Componet A 

0.025 

0.02 

0.015 

0.01 

0.005 

0 

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. 

Coefficients of Equilibrium Sorption %IOWY Power 

Function

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. 

Calculated %IOWY (gm Indigo/100 gm cotton) 

100.00% 

10.00% 

1.00% 

0.10% 

0.01% 

Calculated Equilibrium Sorption Relationship at 

Various pH's 

0.01 0.1 1 10 


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) 

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

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. 

Integ 

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

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. 

Integ 

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

138

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. 

K/S at 660 nm 

40.0 

35.0 

30.0 

25.0 

20.0 

15.0 

10.0 

5.0 

0.0 

K/S at 660nm as a Function of %IOWY 

0.00 5.00 10.00 15.00 20.00 25.00 30.00 35.00 40.00 45.00 

%IOWY from Equilibrium Sorption 

6.3 7.1 8 12 

Poly. (6.3) Poly. (7.1) Poly. (8) Poly. (12) 

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

140

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, immersion 

dye 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 3.25 

pH 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 

141

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 3 9 

or 19683 trials to cover 3 levels on 9 parameters. As previously discussed, such an experiment isn't 

possible. 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. Specifically 

yarn 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% 

142

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. 

Scatterplot of Matrix Observational Study Dye Range Set-up Conditions and Interactions 

Speed m/min 

Indigo 

gm/lit 

Box pH 

Box mV 

38 

36 

34 

32 

30 

28 

26 

3 

2 

1 

13 

12 

11 

900 

800 

700 

8.63 11.37 

Dwell 

length m 

High value 

Middle value 

Low value 

26 29 3133 3537 

Speed m/min 

High value 

Middle value 

Low value 

1 2 

Indigo 

gm/lit g/l 

3 

High value 

Middle value 

Low value 

11 12 13 

Box pH 

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

High value 

Middle value 

Low value 

143

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. 

144

Standard Error of Indigo (g/l) 

4.5 

4 

3.5 

3 

2.5 

2 

1.5 

1 

0.5 

0 

0 5 10 15 20 25 

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. 

Additional Replicates Affect on Standard Error 

Number of Additional Replicates Added 

%COWY e-3 %IOWY e-4 Integ PL e-2 

145

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. 

Graph Builder 

%IOWY vs. Dip 

4.000% 

3.000% 

2.000% 

1.000% 

0.000% 

1 2 3 4 5 6 7 

Dip 

146

speciffic 

data sets are a presentedd. 

In figure 4-2, 

6.3/1 yarnn 

was dyed in three differeent 

indigo dyee 

bath 


wit th approximaately 

constantt 

speed, pH, aand 

mV. All three 

were 311.1 

meterrs/minute. 

The 

3.0 g/l dyeeing 

was 12.00 

pH and 789 mV with the 2.7 g/l at 11.88 

pH and 8000 

mV, 

and 2.3 

g/l at 11.9 pH and 805 mmV. 

All threee 

follow the ssame 

general build curve wwith 

large inccrease 

in %COWY 

from 1 to 2 dips. Addditional 

dips beyond 2 conntinued 

to inccrease 

the %CCOWY 

althouugh 

at 

a slowwer 

rate. Last t, the spacingg 

between dyee 

bath concentrations 

wass 

as expectedd 

with higher dye 

bath cconcentration 

n resulting in higher %COWWY 

while lower 

concentrattions 

resultedd 

in the lowerr 

%COWWY. 

To further explore the % %COWY and % %IOWY as thee 

number of dips increaseed, 

a couple oof 

Figure 4-2: Build curve e relationship foor 

%COWY as a ffunction 

of nummber 

of dips on 66.3/1 

yarn countt 

at similar speeed, 

pH, 

and redduction 

potential. 

Using the same s data seets 

a similar reelationship 

exxist 

for %IOWWY. 

Figure 4-33 

illustrates thhe 

%IOWWY 

build curve e as a function 

of number of dips basedd 

on the samee 

data points. . Notice the llinear 

relatioonship 

for %IOWY 

to number 

of dips. TThese 

curves illustrate witth 

increasing number of dips 

147

the % %IOWY lineary y increases. AAlso 

the higheer 

the dye batth 

concentrattion, 

the highher 

the %IOWWY. 

This same 

linear be ehavior is exhhibited 

by all data sets fromm 

all dye rangge 

set-up connditions. 

Whiile 

no 

previoous 

data has been published 

comparingg 

%IOWY andd 

the effects oof 

increasing dips, numberrous 

examples 

have bee en discussed relating shadde 

of the yarnn 

(K/S or Integg) 

to increasinng 

numbers oof 

dips. 

Refer to Xin 4 46 

Integ vs dipps 

curve in secction 

1-1. 

Figure 4-3: Build curve e relationship foor 

%IOWY as a fuunction 

of numbber 

of dips on 6.3/1 

yarn count at similar speedd, 

pH, 

and redduction 

potential. 

Since the %IOWY % increaased 

with eacch 

additional dip of indigo dye, one would 

expect the 

depthh 

of shade to increase as wwell. 

However, 

the relationnship 

does noot 

appear to bbe 

linear. Figgure 

4-4 illustrates 

the realationshipp 

between Integ 

shade valuue 

and number 

of indigo ddips 

from all ddata 

pointss. 

Even thoug gh the %IOWWY 

builds in a llinear 

nature, , the non-lineear 

nature of Integ shade 

versus 

the number r of dips is jusstified 

when cconsiderationn 

is given to nnon-linear 

relaationship 

between 

Integ and %IOWY under u equilibbrium 

sorptionn 

dye conditioons 

as well ass 

the possibility 

for variablle 

penettration 

levels from one dipp 

to the next. It should be noted the increase 

in dipss 

does not acctually 

148

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. 

Integ 

Graph Builder 

120 

100 

80 

60 

40 

20 

0 

Integ vs. Dip 

1 2 3 4 5 6 7 

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. 

Dip 

149

Figure 4-5: Integ shade e value as a function 

of numberr 

of dips on 6.3/ /1 yarn count att 

similar speed, pH, and reduction 

potenttial. 

Since %IOW WY caused thhe 

Integ shadee 

and %IOWYY 

by dips was linear, what caused Integ to 

be noon-linear 

func ction of numbber 

of dips? AAs 

previously shown in chaapter 

3, the Innteg 

shade haas 

a 

non-liinear 

relation nship to %IOWWY 

during equuilibrium 

sorpption. 

This coould 

explain tthe 

shape of 

curves 

in figure 4-5 5. The other possibility waas 

changes in penetration level as a funnction 

of nummber 

of dipps. 

The penet tration level aas 

a function of all data pooints 

is shownn 

in figure 4-66. 

Unlike the 

previoous 

relationsh hips, the peneetration 

level 

has a uniquee 

and unexpeected 

shape as 

the number 


dips wwas 

increased d. As the nummber 

of dips wwas 

increasedd 

the penetration 

level conntinued 

to 

decreease 

with redu ucing severityy. 

From dip 5 through 7 thhe 

penetratioon 

level remaiins 

relatively 

unchaanged. 

The decreased 

aveerage 

penetraation 

level witth 

each dip, ccould 

explain the non-lineaar 

relatioonship 

betwe een Integ andd 

dip as demoostrated 

in figure 

4-5. The penetration level decreassed 

with eeach 

addition nal dip due to additive proccess 

of layering 

dye not byy 

the dip proccess 

itself. 

150

Penetration level 

Graph Builder 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

0.2 

Penetration level vs. Dip 

1 2 3 4 5 6 7 

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. 

Dip 

151

Figure 4-7: Penetration 

level as a funcction 

of numberr 

of dips on 6.3/ /1 yarn count at similar speed, ppH, 

and reductioon 

potenttial. 

Besides the 

number of dips, the indiigo 

dye conceentration 

in thhe 

dye bath oof 

each dip shhould 

have a strong impa act on the ressponse 

variabbles. 

The nexxt 

series of graaphs 

investigaates 

the effecct 


indigoo 

dye bath co oncentration oon 

%COWY, % %IOWY, Integg, 

and penetraation 

level whhile 

considering 

the nuumber 

of dips s. Figure 4-8 shows the efffect 

of indigoo 

concentratioon 

on %COWWY 

when separated 

by one, 

three, and six dips. As iin 

figure 4-1, as the numbeer 

of dips increased 

so didd 

the %COWYY. 

Also aas 

in figure 4-2, 

as the indigo 

dye bath cconcentrationn 

increased, tthe 

%COWY inncreased. 

Thhe 

%COWWY 

build is fairly 

linear by indigo dye baath 

concentraation 

within eeach 

individuaal 

dip. 

152

%COWY 

Graph Builder 

14.00% 

12.00% 

10.00% 

8.00% 

6.00% 

4.00% 

2.00% 

%COWY vs Average Indigo (g/l) by Dip 

%COWY vs. Average Indigo (gm/lit) by Dip 

0.00% 

0.5 1 1.5 2 2.5 3 3.5 4 

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. 

(g/l) 

Average Indigo (gm/lit) 

Legend 

1 

3 

6 

1 

3 

6 

153

Measured %IOWY 

Graph Builder 

4.500% 

4.000% 

3.500% 

3.000% 

2.500% 

2.000% 

1.500% 

1.000% 

0.500% 

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 %IOWY 

and 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 (g/l) by Dip 

Measured %IOWY vs. Average Indigo (gm/lit) by 

Dip 

0.000% 

0.5 1 1.5 2 2.5 3 3.5 4 

(g/l) 


Legend 

1 

3 

6 

1 

3 

6 

154

Measured Integ 

Graph Builder 

120 

100 

80 

60 

40 

20 

Measured Integ vs Average Indigo (g/l) by Dip 

Measured Integ vs. Average Indigo (gm/lit) by Dip 

0 

0.5 1 1.5 2 2.5 3 3.5 4 


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. 

(g/l) 

Legend 

1 

3 

6 

1 

3 

6 

155


Graph Builder 

0.9 

0.8 

0.7 

0.6 

0.5 

0.4 

0.3 

Penetration Level vs Average Indigo (g/l) by Dip 

Penetration level vs. Average Indigo (gm/lit) by Dip 

0.2 

0.5 1 1.5 2 2.5 3 3.5 4 


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 

(g/l) 

Legend 

1 

3 

6 

1 

3 

6 

156

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 might 

expect. 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. 

157

%COWY 


Integ 


Graph Builder 

12.00% 

10.00% 

8.00% 

6.00% 

4.00% 

Yarn Count Affect on %COWY, %IOWY, Integ, and 

Penetration Level 

Yarn Count 

6.3 7.1 8 12 

2.00% 

4.00% 

3.50% 

3.00% 

2.50% 

2.00% 

1.50% 

1.00% 

0.50% 

100 

90 

80 

70 

60 

50 

40 

30 

0.6 

0.55 

0.5 

0.45 

0.4 

0.35 

0.3 

0.25 

0.2 

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 0.5 1 1.5 2 2.5 3 3.5 

Indigo gm/lit (g/l) 

Figure 4-12: Illustrates %COWY, %IOWY, Integ, and penetration level varies with yarn count and dye concentration after 

six dips. 

158

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. 

159

%COWY 


Integ 


Graph Builder 

Speed Affect on %COWY, %IOWY, Integ, and Penetration Level 

Speed (m/min) 

26.52 - 31.09 31.09 - 34.75 34.75 - 36.58 

12.00% 

11.00% 

10.00% 

9.00% 

8.00% 

7.00% 

6.00% 

5.00% 

4.00% 

3.00% 

2.00% 

3.50% 

3.00% 

2.50% 

2.00% 

1.50% 

1.00% 

0.50% 

100 

90 

80 

70 

60 

50 

40 

30 

0.5 

0.45 

0.4 

0.35 

0.3 

0.25 

0.2 

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 

Indigo gm/lit 

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. 

(g/l) 

160

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. 

161

%COWY 


Integ 


Graph Builder 

pH Affect on %COWY, %IOWY, Integ, and Penetration Level 

Box pH 

10.96 - 11.6 11.6 - 11.86 11.86 - 12.588 

12.00% 

11.00% 

10.00% 

9.00% 

8.00% 

7.00% 

6.00% 

5.00% 

4.00% 

3.00% 

2.00% 

3.50% 

3.00% 

2.50% 

2.00% 

1.50% 

1.00% 

0.50% 

100 

90 

80 

70 

60 

50 

40 

30 

0.5 

0.45 

0.4 

0.35 

0.3 

0.25 

0.2 

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 

(g/l) 

Indigo gm/lit 

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

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. 

163

%COWY 


Integ 


Graph Builder 

Reduction Potential Affect on %COWY, %IOWY, Integ, and 


12.00% 

10.00% 

8.00% 

6.00% 

4.00% 

2.00% 

3.50% 

3.00% 

2.50% 

2.00% 

1.50% 

1.00% 

0.50% 

100 

90 

80 

70 

60 

50 

40 

30 

0.5 

0.45 

0.4 

0.35 

0.3 

0.25 

726 - 786 

Box mV 

786 - 851 851 - 891 

0.2 

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 

(g/l) 

Indigo gm/lit 

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. 

164

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. 

165

%COWY 


Integ 


Graph Builder 

12.00% 

10.00% 

8.00% 

6.00% 

4.00% 

2.00% 

3.50% 

3.00% 

2.50% 

2.00% 

1.50% 

1.00% 

0.50% 

100 

90 

80 

70 

60 

50 

40 

30 

0.5 

0.45 

0.4 

0.35 

0.3 

0.25 

Dwell Length Affect on %COWY, %IOWY, Integ, and 


0.2 

0.5 1 1.5 2 2.5 3 3.5 

Dwell length 

8.63 11.37 

0.5 1 1.5 2 2.5 3 3.5 

Indigo gm/lit 

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. 

(g/l) 

(m) 

166

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 to 

conventional 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. 

167

%COWY 


Integ 


Graph Builder 

12.00% 

10.00% 

8.00% 

6.00% 

4.00% 

2.00% 

3.50% 

3.00% 

2.50% 

2.00% 

1.50% 

1.00% 

0.50% 

100 

90 

80 

70 

60 

50 

40 

30 

0.5 

0.45 

0.4 

0.35 

0.3 

0.25 

Dwell Time Affect on %COWY, %IOWY, Integ, and 


14.03 - 16.7 

Dwell time 

16.7 - 19.6 19.6 - 25.7 

0.2 

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 

Indigo gm/lit 

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. 

(g/l) 

(sec) 

168

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. 

(g/l) 

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. 

169

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 more 

importantly 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. 

170

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 

171

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. 

Average Normalized Standard Error 

for all Significant Parameters 

1.2 

1.15 

1.1 

1.05 

1 

0.95 

0.9 

0.85 

0.8 

Convergence Test for Empirical %COWY Model 

0 5 10 15 20 25 

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 R 2 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. 

172

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

173

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. 

1: 0.0 

⎡ 

⎡ 

2: 0.1642 

⎤ 

⎢ 

⎢ ⎥ 

⎢ 

⎢ 

3: 0.3126 

⎥ 

%

Actual %COWY 

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. 

175

%COWY 

0.086371 

[0.08272, 0.09018] 

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. 

%COWY Prediction Profile for Dye Range Set-up Conditions 

6 

8 

10 

12 

14 

1 

3 

4.2.2 %IOWY Empirical Model Generation 

5 

7 

26 

The same process was repeated for the %IOWY using the prime data set as the initial 

starting point for the ANOVA analysis. The R 2 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 

29 

32 

35 

1 

2 

(g/l) 

3 

11 

12 

176

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 

177

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. 



1.2 

1.15 

1.1 

1.05 

1 

0.95 

0.9 

0.85 

0.8 

Convergence Test for Empirical %IOWY Model 

0 5 10 15 20 25 

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 pH 

parameter was removed from the model and the ANOVA analysis repeated. 

178

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 R 2 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. 

179

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. 

180

1: 0.0 

⎡ 

2: 0.6057 

⎤ 

⎢ ⎥ 

⎢ 

3: 1.0341 

⎥ 

%

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 (Xin 46 ) 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. 

Measured 


0.01993 

[0.01934, 0.02054] 

%IOWY Prediction Profile for Dye Range Set-up Conditions 

7 

8 

9 

10 

11 

12 

1 

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

3 

5 

7 

26 

28 

30 

32 

34 

36 

1 

2 

(g/l) 

3 

182

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 R 2 was 0.96 with an F ratio of 1049. 

This was determined to be statistically significant. The initial parameter standard errors are listed in 

parameter 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. 

183

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. 



1.2 

1.15 

1.1 

1.05 

1 

0.95 

0.9 

0.85 

0.8 

Convergence Test for Empirical Integ Model 

0 5 10 15 20 25 

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 R 2 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 

184

ecome 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. 

185

1: 0.0 

⎡ 

2: 0.6763 

⎤ 

⎢ ⎥ 

⎢ 

3: 1.0511 

⎥ 

Integ = exp[4.0128 +

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 Xin 46 and Chong 29 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. 

Measured 

Integ 

84.19798 

[81.3518, 87.1437] 

Integ Prediction Profile for Dye Range Set-up Conditions 

7 

9 

11 

1 

3 

5 

7 

26 

28 

30 

32 

34 

36 

Figure 4-27: Prediction profile for Integ shade values as a function of each dye range set-up conditions. 

1 

2 

(g/l) 

3 

11 

12 

187

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 R 2 

correlation coefficient of 0.48 but deemed significant due to F ratio of 32.6 and P-value for the 

model 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. 

188

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 

189

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. 



1.2 

1.1 

1 

0.9 

0.8 

0.7 

0.6 

Convergence Test for Empirical Penetration Level 

Model 

0 5 10 15 20 25 


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. 

190

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. 

191

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 a 

function of dye range set-up conditions is provided as equation 4-4. 

192

1: 0.0 

⎡ 

2: 0.0433 

⎤ 

⎢ 

⎥ 

⎢ 

3: 0.0098 

⎥ 

Penetration Level = −0.4789 +

Actual Penetration 

Level 

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. 

194

Actual 


0.310253 

±0.017625 

Penetration Level Prediction Profile for Dye Range Set-up Conditions 

7 

9 

11 

1 

3 

5 

7 

26 

Figure 4-30: Prediction profile of empirical model penetration level as a function of dye range set-up parameters. 

29 

32 

35 

1 

2 

(g/l) 

3 

11 

12 

195

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 the 

general 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 

196

eduction, 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. Ozisik 59 

presented a method that calculates the diffusion coefficient by use of equation 4-5.

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 be 

approximated. 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% argon 8 . 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/m 3 or g/l 8 . 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 cm 2 /sec 60 . 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 

198

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 was 

regulated 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 or 

was 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. 

199

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 (cm 2 /sec). The coefficient describes the rate at which a material diffuses 

through a unit area.

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 of 

F(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. 

 

 

∆ 

= 

∗ 

 

 

∆

the equilibrium sorption experiments discussed in chapter 3.3, equation 4-11. Second, the fraction 

of the maximum possible %IOWY was calculated based on Cranks 2 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. 

%

the equilibrium sorption experiments discussed in chapter 3.3, equation 4-11. Second, the fraction 

of the maximum possible %IOWY was calculated based on Cranks 2 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. 

%

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

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. 

nodes 

C0 

C1 

∆r 

0 1 2 m-1 m m+1 M-1 M 

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

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. 

nodes 

C0 

C1 

∆r 

0 1 2 m-1 m m+1 M-1 M 

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

1+2

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.























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. 

∆

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, I R , produces the following chemical reactions.

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. 

%

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 

214

angee 

speed. Both h of these casses 

do not acttually 

exist in real world. FFor 

this example 

the real 

oxidattion 

rate occu urred betweeen 

1.0 e-3 andd 

1.0 oxidatioon 

rate units. 

Figure 4-32: Fiber diffu usion coefficientts 

for each yarnn 

count as the oxxidation 

rate changes. 

The same graph was creeated 

for yarn 

diffusion cooefficients 

as a function off 

oxidation rate 

in 

figuree 

4-33. Here e the yarn difffusion 

coefficcients 

have a different behhavior 

as the ooxidation 

ratee 

was 

decreeased. 

As the oxidation ratte 

was decreaased 

from higgh 

values, thee 

variation in yarn diffusionn 

across 

the yarn counts 

became greater. At 11.0 

e-2 oxidattion 

rate units 

the variatioon 

in yarn difffusion 

was aat 

a maximum m. Further redductions 

in oxxidation 

rate caused the vaariation 

betwween 

yarn couunts 

to deccrease 

and th he magnitudee 

of the yarn ddiffusion 

coeffficient 

shifted 

lower. 

215

Figure 4-33: Yarn diffu usion coefficientts 

for each yarn count as a function 

of oxidation 

rate. 

The variati ion in calculated 

wet pick-up 

values as a function off 

oxidation ratte 

was 

investtigated. 

As ill lustrated in fiigure 

4-34, ass 

the oxidatioon 

rate was deecreased 

fromm 

high valuess 

the 

variattion 

between yarn counts increased. AAt 

approximattely 

1.0 e-2 oxxidation 

rate units the meaan 

value of wet pick-u up shifts higher 

regardlesss 

of yarn counnt. 

The shifts in yarn diffussion 

and wet pick- 

up at low oxidation n rates were caused by lacck 

of indigo oxidation 

during 

the allotteed 

oxidation ttime. 

Again this phenom menon doesn't 

occur in thee 

real world. 

216

Figure 4-34: Wet pick- -up variation witthin 

yarn countss 

as a function oof 

oxidation ratee. 

By incorpo orating these properties toogether 

the optimum 

oxidation 

rate thaat 

minimizes the 

error in fiber diffus sion, yarn difffusion, 

and wwet 

pick-up was 

determineed. 

First, the standard 

deviattion 

for fiber diffusion, yarrn 

diffusion, aand 

wet pick-up 

at each oxxidation 

rate was calculateed. 

Next, these standa ard deviationss 

were normaalized 

by the average standdard 

deviatioon 

for each 

coeffiicient. 

Then, the normalized 

standard ddeviations 

weere 

combinedd 

to produce a single errorr 

measurement 

relationship. 

Whhen 

this valuee 

reached a mminimum 

the optimum oxiddation 

rate had 

been determined. The normalized 

standard deviations foor 

each dye coefficient 

andd 

the combined 

relatioonship 

are displayed 

in figgure 

4-35. Staarting 

with ann 

extremely loow 

oxidation rate the 

combbined 

normalized 

standard deviations wwere 

high. As the oxidationn 

rate was inccreased 

the 

combbined 

normalized 

standard deviations began 

to decreease. 

In this particular exaample, 

the 

optimmum 

oxidation n rate was 0.0064 

oxidationn 

rate units. FFurther 

increaases 

in oxidattion 

rate caussed 

the coombined 

norm malized standdard 

deviation 

to increase slightly in value 

with furthher 

increases 

resultting 

in constant 

combined normalized sstandard 

deviiations 

due too 

instantaneoously 

fast indigo 

217

oxidattion. 

Due to the nature off 

the oxidatioon 

profile all ooxidation 

ratee 

optimizationn 

began at the 

low 

end oof 

the spectrum 

with increaasing 

oxidatioon 

rate until tthe 

minimumm 

combined normalized 

standard 

deviation n was reachedd. 

Figure 4-35: Standard deviations as a function of oxiddation 

rate. 

4.3.2 Algorithm to Calculate thee 

Dye Coefficients 

The operat tor would inpput 

the speciffic 

dye range set-up condittions 

such as speed, indigoo 

dye 

bath cconcentration 

n, etc and thee 

final target vvalues 

for %CCOWY, 

%IOWWY, 

and Integ sshade 

by yarnn 

countt 

and dip. Firs st the fiber diiffusion 

coeffficient, 

yarn ddiffusion 

coeffficient, 

and wwet 

pick-up was 

calcullated 

based on o the yarn coount 

and assuumed 

initial wwash 

reductioon, 

wet pick-uup, 

and oxidattion 

rate. Then the wash 

reduction coefficient annd 

wet pick-uup 

were optimmized 

to mainntain 

constant 

values 

across all dy ye dips and yaarn 

counts. TThen 

the oxiddation 

rate waas 

adjusted until 

the minimmum 

combbined 

normalized 

standard deviation occcurred 

at eacch 

dip. After all calculationns 

and 

218

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 1 

second 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. 

219

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 and 

in 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 R 2 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. 

220

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. 

221

Actual Fiber Diffusion 

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. 

1: 0.0 

⎡ 

2: −0.3903 

⎤ 

⎢ 

⎥ 

⎢ 

3: 0.2868 

⎥

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. 

Predicted Fiber Diffusion 

2.209e-9 

[1.89e-9, 2.58e-9] 

Effective Fiber Diffusion Coefficient Prediction Profile for Dye Range Set-up 

1 

2 

3 

4 

5 

6 

7 

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

1 

2 

(g/l) 

3 

11 

12 

223

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 coefficients 

was expected. As shown in table 4-12 the adjusted R 2 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. 

224

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. 

225

Comparison of Actual Yarn Diffusion by Dye Theory Model 

0.000011 

0.00001 

0.000009 

0.000008 

0.000007 

0.000006 

0.000005 

0.000004 

0.000003 

0.000002 

0.000001 

0 

0 0.000001 0.000003 0.000005 0.000007 0.000009 0.000011 

Predicted Yarn Diffusion Coefficient 

Actual Yarn Diffusion 

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

1: 0.0 

⎡ 

2: −0.0516 

⎤ 

⎢ 

⎥ 

⎢ 

3: −0.4549 

⎥

ecomes 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. 

Effective Yarn Diffusion Coefficient Prediction Profile for Dye Range Set-up Conditions 

Predicted Yarn Diffusion 

3.172e-6 

[2.85e-6, 3.53e-6] 

1 

3 

5 

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. 

7 

1 

2 

(g/l) 

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 

3 

11 

12 

14 

16 

18 

20 

22 

227

ath 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 dye 

bath. 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 R 2 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. 

228

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. 

229

Actual 

Wet Pick-up 

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

Wet pick-up 

0.031492 

±0.002685 

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. 

Wet Pick-up Coefficient Prediction Profile for Dye Range Set-up Conditions 

40 

50 

60 

70 

1 

2 

(g/l) 

3 

0 

0.000001 

0.000002 

0.000003 

0.000004 

0.000005 

0.000006 

0.000007 

0.000008 

231

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. 

232

Actual Wash Reduction 

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

concentration effect on wash reduction maybe related to the definition of %COWY as previously 

discussed. 

Wash % 

0.110581 

±0.006796 

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. 

Wash Reduction Coefficient Prediction Profile for Dye Range Set-up Conditions 

27 

29 

31 

33 

35 

37 

14 

15 

16 

17 

18 

19 

20 

21 

800 

900 

1 

2 

(g/l) 

3 

234

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. 

235

Actual Oxidization Rate 

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

1: 0.0 

⎡ 

2: −0.4686 

⎤ 

⎢ 

⎥ 

⎢ 

3: −0.6932 

⎥

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. 

Predicted Oxidization Rate 

0.086658 

[0.07606, 0.09873] 

Oxidation Rate Coefficient Prediction Profile for Dye Range Set-up Conditions 

1 

3 

5 

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. 

7 

27 

29 

31 

33 

35 

37 

60 

Enter dye range parameters 

Calculate 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 

70 

700 

800 

900 

237

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 

238

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 sets 

used 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 # of Speed Dwell Oxidation Dye Bath Dye Dye Dye NaOH 

Shade # Dips (m/min) Time (sec) Time (sec) (g/l) pH mV (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 

239

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 R 2 = 0.91 and deemed 

highly significant with F ratio of 651 as shown in table 5-2. The predicted versus actual graph, figure 

5-1, 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. 

%COWY Actual 

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

240

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

Following the same analysis method the dye theory model %COWY was compared to actual 

measured values. The results weren't as well correlated as the empirical model. The resulting R 2 

correlation coefficient is 0.74 with an F ratio of 179 as shown in table 5-3. Furthermore, the slope 

was 0.76 with an intercept of 0.72%. This indicates the dye theory model over predicts the true 

%COWY at high values. This is graphically represented in figure 5-2 where a 10% predicted %COWY 

corresponds to an 8% actual value. 

241

%COWY Actual 

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 

242

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 R 2 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. 

%IOWY Actual 

Figure 5-3: Empirical model predicted %IOWY compared to actual measured values. 

243

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. 

244


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 

245

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 R 2 of 0.97 with an F ratio 

of 2108. Both of these calculations indicate extremely strong empirical model fit to the actual 

measured values. The slope of the model fit was 1.084 which means the model underestimates the 

actual Integ shade values by 8.4%. 

Integ Actual 

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

246

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 R 2 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. 

247

Integ Actual 

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 

248

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 model 

correlation coefficient was R 2 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. 

Penetration Level Actual 

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

249

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 R 2 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. 

250

Dye Theory Model Compared to Canadian Dye Range Actual Penetration Level 


0.6 

0.5 

0.4 

0.3 

0.2 

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 

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 

251

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 theory 

model 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 poor 

performance 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 

252

is actuually 

closer to o the observaational 

curve. This indicatees 

the dye theeory 

model bbetter 

predicts 

the 

penettration 

level than t the emppirical 

model. 

Figure 5-9: Indigo build d profile for Cannadian 

dye rangge 

set-up on 4433 

shade with 29 m/min, 1.26 g/ l dye bath 

concenntration 

and 12. 2 pH. 

By constru ucting similar build profile curves for the 

other Canadian 

dye rangge 

set-ups a 

similaar 

relationship p developed. Figure 5-10 was construccted 

from 32 mm/min, 

1.66 gg/l, 

and 11.8 pH 

dye seet-up 

and figu ure 5-11 fromm 

32 m/min, 22.09 

g/l, and 112.1 

pH. In fiigure 

5-10 booth 

models slightly 

underr 

predict the %IOWY % and tthe 

resulting IInteg 

shade. However, thee 

dye theory models buildd 

profile 

better matc ches the obseervational 

meeasured 

profille 

even thouggh 

both modeels 

predict moore 

penettionrat 

than measured. m Inn 

figure 5-11, the empirical 

model slighttly 

under estimates 

the %IOWY 

and Innteg 

values while w the dye ttheory 

model 

slightly overr 

estimates thhe 

%IOWY but 

underestimmates 

the Innteg. 

In this dye d range set-up, 

both models 

over estimate 

penetrration 

level byy 

basically thee 

same degree. 

253

Figure 5-10: Indigo build 

profile for Caanadian 

dye rannge 


shade with 322 

m/min, 1.66 gg/l 

dye bath 


and 11. 8 pH. 

Figure 5-11: Indigo build 

profile for Caanadian 

dye rannge 


shade with 322 

m/min, 2.09 gg/l 

dye bath 


and 12. 1 pH. 

254

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 R 2 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. 

Empirical Model Indirect Penetration Level Comparison on Canadian Dye Range 

0.6 


0.5 

0.4 

0.3 

0.2 

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 

Figure 5-12: Empirical model predicted indirect penetration level compared to actual measured values. 

255

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 dwell 

length. 

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

Reference # of Speed Dwell Oxidation Dye Bath Dye Dye Dwell 

Shade # Dips (m/min) Time (sec) Time (sec) (g/l) pH mV Length, m 

1134 1 to 7 31.1 16.7 69.5 2.994 11.98 789 8.63 

1157 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 Production Actual Actual Empirical Empirical Dye Theory Dye Theory 

Shade # Yarn Count %IOWY Integ %IOWY Integ %IOWY 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% 76.2 

1169 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 dye 

theory 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 

257

esearched 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. 

258

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 Production Actual Actual Dye Theory Dye Theory Porosity 

Shade # Yarn Count %IOWY Integ %IOWY Integ 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 

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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. 

260

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. 

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Integ Actual 

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. 

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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. 

Integ Actual 

Figure 5-16: Dye theory model predicted Integ compared to actual measured values from production yarns. 

263

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 R 2 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. 

264

Theoretical Porosity 

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 

265

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. 

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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 but 

there 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.

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. 

%

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't 

linear 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, 

269

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. 

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Table 6-1: Empirical model performance review 

Response Correlation Coef, R 2 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, R 2 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 

271

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 R 2 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 

272

ath 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. 

273

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278

APPENDIX 

279

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 

 

 

= (−%

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.

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. 

282

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 4 

7.1 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 1 

12 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 6 

12 19.2293 13.43 5.86% 75.8 5 

12 29.95 13.2 8.53% 87.5 4 

283

Section A-4-1: Observational Study Raw Data -Dye Range Parameters 

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

Shade 

Dye Bath 

ID 

Dwell 

(gpl 

Dye Dye Bath Dwell 

Nip 

Speed Time Oxidation 100% Dye Bath Alkalinity Length Oxidation Pressures 

(m/min) (sec) Time (sec) Indigo) Bath pH (mV) (gpl) (m) Length (m) (psi) 

1160 36.6 14.1 59.1 0.891 11.66 745 3.16 8.63 36.03 70 

Yarn Skein Response Variables 

Yarn Dye 

Greige Boil Off Dyed Washed 

Total Surface 

Penetration 

Count route Dips Weight Weight Weight Weight %COWY %IOWY %IOWY Integ 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 

Wavelength 

(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 

284

Table A-4-1: Continued 

Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1160 36.576 14.1 59.1 0.891 11.66 745 3.16 8.63 36.03 70 


Yarn Dye 


Total Surface 

Penetration 


12 1 only 1 6.1529 5.9725 6.0856 5.9596 1.894% 0.145% 0.188% 6.4 0.80 

12 1--2 2 6.1463 5.9698 6.109 5.9689 2.332% 0.264% 0.405% 12.1 0.56 

12 1--3 3 6.5291 6.3408 6.5588 6.3577 3.438% 0.447% 0.731% 19.9 0.56 

12 1--4 4 6.3526 6.1746 6.3433 6.1902 2.732% 0.538% 0.949% 24.7 0.47 


Wavelength 


400 22.62 16.46 11.88 10.47 

420 28.00 21.35 15.73 14.13 

440 27.21 20.23 14.68 13.00 

460 24.70 17.72 12.61 10.98 

480 22.66 15.68 10.93 9.35 

500 20.73 13.97 9.61 8.13 

520 18.42 11.99 8.00 6.61 

540 15.56 9.71 6.40 5.21 

560 13.96 8.48 5.46 4.43 

580 12.35 7.26 4.60 3.72 

600 10.63 6.04 3.85 3.11 

620 9.30 5.15 3.32 2.70 

640 7.88 4.28 2.81 2.30 

660 6.98 3.88 2.64 2.19 

680 9.11 5.09 3.35 2.76 

700 18.00 11.73 8.00 6.56 

285


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1160 36.576 14.1 59.1 0.764 11.91 762 2.5 8.63 36.03 70 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

286


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1160 36.576 14.1 59.1 0.764 11.91 762 2.5 8.63 36.03 60.00 


Yarn Dye 


Total Surface 

Penetration 


7.1 1 only 1 6.7962 6.556 6.6875 6.5431 2.006% 0.161% 0.253% 8.2 0.64 

7.1 1--2 2 6.8133 6.562 6.7048 6.5562 2.176% 0.302% 0.470% 13.7 0.64 

7.1 1--3 3 6.9451 6.69 6.8819 6.6933 2.868% 0.469% 0.821% 21.9 0.57 

7.1 1--4 4 6.8598 6.615 6.7976 6.6334 2.760% 0.653% 1.264% 31.4 0.52 


Wavelength 


400 19.66 15.27 11.17 8.59 

420 24.53 19.96 15.01 11.61 

440 23.68 18.91 13.99 10.65 

460 21.37 16.51 11.95 8.96 

480 19.47 14.56 10.27 7.51 

500 17.73 12.94 9.00 6.45 

520 15.62 11.03 7.40 5.19 

540 13.10 8.87 5.90 4.10 

560 11.64 7.66 5.00 3.48 

580 10.20 6.47 4.20 2.95 

600 8.70 5.34 3.48 2.50 

620 7.56 4.54 2.99 2.21 

640 6.42 3.77 2.54 1.98 

660 5.74 3.43 2.35 1.90 

680 7.58 4.56 3.06 2.39 

700 15.32 10.79 7.31 5.37 

287


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1160 36.576 14.1 59.1 0.764 11.91 762 2.5 8.63 36.03 60.00 


Yarn Dye 


Total Surface 

Penetration 


8 1 only 1 6.0312 5.8294 5.9189 5.7961 1.535% 0.163% 0.210% 7.0 0.78 

8 1--2 2 6.0612 5.8525 5.9722 5.8303 2.045% 0.310% 0.418% 12.4 0.74 

8 1--3 3 6.0001 5.7917 5.9468 5.7817 2.678% 0.480% 0.743% 20.1 0.65 

8 1--4 4 6.1102 5.9038 6.0451 5.8998 2.393% 0.660% 1.208% 30.3 0.55 


Wavelength 


400 21.30 16.02 11.81 8.99 

420 26.56 20.89 15.77 12.26 

440 25.92 19.87 14.71 11.25 

460 23.58 17.42 12.61 9.44 

480 21.62 15.46 10.89 7.95 

500 19.78 13.77 9.57 6.82 

520 17.51 11.82 7.94 5.49 

540 14.74 9.57 6.36 4.31 

560 13.11 8.32 5.40 3.64 

580 11.51 7.09 4.55 3.06 

600 9.80 5.88 3.77 2.56 

620 8.50 4.99 3.24 2.23 

640 7.18 4.15 2.75 1.96 

660 6.36 3.74 2.55 1.84 

680 8.46 4.97 3.28 2.34 

700 17.06 11.45 7.80 5.47 

288


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1160 36.576 14.1 59.1 0.764 11.91 762 2.5 8.63 36.03 60.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

289


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1162 31.0896 16.7 69.5 1.066 11.76 743 3.42 8.63 36.03 70.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


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 


Wavelength 


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 

290


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1162 31.0896 16.7 69.5 1.066 11.76 743 3.42 8.63 36.03 70.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

291


Shade 

Dye Bath 

ID 

Dwell 

(gpl Dye Dye Dye Bath Dwell 

Nip 

Speed Time Oxidation 100% Bath Bath Alkalinity Length Oxidation Pressures 

(m/min) (sec) Time (sec) Indigo) pH (mV) (gpl) (m) Length (m) (psi) 

1162 31.0896 16.7 69.5 1.129 11.7 747 3.62 8.63 36.03 70.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

292


Shade 

Dye Bath 

ID 

Dwell 


Nip 



1162 31.0896 16.7 69.5 1.129 11.7 747 3.62 8.63 36.03 70.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

293


Shade 

Dye Bath 

ID 

Dwell 


Nip 



T3675 34.75 14.7 62.2 1.932 11.5 836 4.82 8.63 36.03 70.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

294


Shade 

Dye Bath 

ID 

Dwell 


Nip 



T3675 34.75 14.7 62.2 1.932 11.5 836 4.82 8.63 36.03 70.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

295


Shade 

Dye Bath 

ID 

Dwell 


Nip 



T3675 34.75 14.7 62.2 1.932 11.5 836 4.82 8.63 36.03 70.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

296


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



4257 31.09 16.7 69.5 2.084 11.62 847 4.71 8.63 36.03 70.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

297


Shade 

Dye Bath 

ID 

Dwell 


Nip 



1169 31.09 16.7 69.5 2.34 11.6 888 6.27 8.63 36.03 70.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

298


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1134 31.09 16.7 69.5 2.314 11.89 805 5.17 8.63 36.03 70.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

299


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1134 31.09 16.7 69.5 2.314 11.89 805 5.17 8.63 36.03 70.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

300


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1134 31.09 16.7 69.5 2.314 11.89 805 5.17 8.63 36.03 70.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

301


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1134 31.09 16.7 69.5 2.314 11.89 805 5.17 8.63 39.40 70.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

302


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



t3688 32.92 15.8 65.7 2.417 11.82 867 4.93 8.63 39.40 70.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

303


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1156 36.58 14.1 59.1 2.572 11.72 797 5.55 8.63 39.40 70.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

304


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1156 36.58 14.1 59.1 2.572 11.72 797 5.55 8.63 39.40 70.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

305


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1156 36.58 14.1 59.1 2.572 11.72 797 5.55 8.63 39.40 70.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

306


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1156 36.58 14.1 59.1 2.572 11.72 797 5.55 8.63 39.40 70.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

307


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1156 36.58 14.1 59.1 2.572 11.72 797 5.55 8.63 39.40 70.00 


Yarn Dye 


Total Surface 

Penetration 


8 2 only 1 5.9864 5.791 6.123 5.7978 5.73% 0.438% 0.820% 20.9 0.53 

8 2,2 2 6.1299 5.9379 6.3578 5.9582 7.07% 0.804% 1.480% 40.0 0.54 

8 2,2-3 3 5.9995 5.8051 6.2847 5.847 8.26% 1.153% 2.411% 53.0 0.48 

8 2,2-4 4 6.0744 5.8782 6.3371 5.9483 7.81% 1.555% 3.695% 65.0 0.42 

8 2,2-5 5 6.0165 5.8274 6.318782 5.9211 8.43% 2.071% 5.329% 76.2 0.39 


Wavelength 


400 11.80 7.27 5.67 4.49 3.61 

420 15.89 9.96 7.47 5.78 4.50 

440 14.70 8.86 6.52 4.99 3.83 

460 12.48 7.27 5.28 4.01 3.08 

480 10.71 5.94 4.26 3.25 2.49 

500 9.40 5.05 3.61 2.75 2.16 

520 7.75 4.04 2.91 2.23 1.79 

540 6.19 3.19 2.34 1.83 1.54 

560 5.24 2.73 2.03 1.64 1.43 

580 4.36 2.32 1.78 1.49 1.33 

600 3.60 1.99 1.61 1.39 1.29 

620 3.05 1.78 1.47 1.33 1.26 

640 2.62 1.66 1.45 1.36 1.34 

660 2.51 1.67 1.51 1.47 1.48 

680 3.31 2.10 1.82 1.73 1.71 

700 7.83 4.36 3.43 2.90 2.54 

308


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1156 36.58 14.1 59.1 2.572 11.72 797 5.55 8.63 39.40 70.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

309


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1157 32.92 15.9 65.7 2.497 12.41 847 3.67 8.63 39.40 70.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

310


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1157 32.92 15.9 65.7 2.497 12.41 847 3.67 8.63 39.40 70.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

311


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1157 32.92 15.9 65.7 2.497 12.41 847 3.67 8.63 39.40 70.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

312


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



X3254 27.43 18.9 78.8 2.614 12.29 778 2.85 8.63 39.40 70.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

313


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1156 36.58 14.1 59.1 2.716 11.94 836 6.06 8.63 39.40 70.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

314


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1156 36.58 14.1 59.1 2.716 11.94 836 6.06 8.63 39.40 70.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

315


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1156 36.58 14.1 59.1 2.716 11.94 836 6.06 8.63 39.40 70.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

316


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1134 31.09 16.7 69.5 2.994 11.98 789 6.6 8.63 39.40 70.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

317


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1134 31.09 16.7 69.5 2.994 11.98 789 6.6 8.63 39.40 70.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

318


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1134 31.09 16.7 69.5 3.133 12.54 801 6.16 8.63 39.40 70.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

319


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1134 31.09 16.7 69.5 3.133 12.54 801 6.16 8.63 39.40 70.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

320


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



t3735 34.75 19.6 63.9 0.761 11.08 722 2.13 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 

1--5,4- 

6 8.3191 7.9783 8.3805 8.0502 5.04% 1.167% 3.321% 61.9 0.35 

6.3 5 7 8.1713 7.8316 8.2105 7.9057 4.84% 1.358% 3.884% 66.5 0.35 


Wavelength 


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 

321


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1110 32.92 20.7 67.5 0.733 12.23 813 2.79 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 

1--2,1- 

3 6.854 6.62 6.746 6.6079 1.90% 0.365% 0.763% 18.3 0.48 

7.1 2 4 6.9343 6.7022 6.8375 6.6915 2.02% 0.446% 0.875% 23.5 0.51 


Wavelength 


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 

322


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1110 32.92 20.7 67.5 0.733 12.23 813 2.79 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 

1--2,1- 

3 6.1363 5.9296 6.0544 5.9254 2.10% 0.369% 0.726% 16.6 0.51 

8 2 4 6.1302 5.9119 6.0437 5.9109 2.23% 0.455% 0.864% 23.0 0.53 


Wavelength 


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 

323


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1110 32.92 20.7 67.5 0.733 12.23 813 2.79 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 

1--2,1- 

3 3.9594 3.8156 3.9091 3.819 2.45% 0.417% 0.756% 17.9 0.55 

12 2 

1--2,1- 

4 4.0246 3.8837 3.9877 3.8952 2.68% 0.583% 0.930% 25.8 0.63 

12 2,1 

1-2,1- 

5 3.9455 3.805 3.9101 3.8191 2.76% 0.670% 1.041% 29.8 0.64 

12 2,1-2 

1-2,1- 

6 3.8618 3.7262 3.8285 3.747 2.75% 0.821% 1.271% 35.9 0.65 

12 2,1-2,1 7 3.8127 3.6766 3.7908 3.6985 3.11% 0.964% 1.530% 40.9 0.63 


Wavelength 


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 

324


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



t3706 34.75 19.6 63.9 0.94 11.48 861 2.22 11.37 40.50 40.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

325


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



t3706 34.75 19.6 63.9 0.94 11.48 861 2.22 11.37 40.50 40.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

326


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1142 34.75 19.6 63.9 0.946 11.49 742 3.4 11.37 40.50 40.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

327


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1142 34.75 19.6 63.9 0.946 11.49 742 3.4 11.37 40.50 40.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

328


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1126 34.75 19.6 63.9 1.051 11.38 792 3.32 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

329


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1126 34.75 19.6 63.9 1.051 11.38 792 3.32 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

330


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1126B 34.75 19.6 63.9 1.157 11.05 817 1.56 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

331


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1126B 34.75 19.6 63.9 1.157 11.05 817 1.56 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

332


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1126 34.75 19.6 63.9 1.117 11.55 771 2.79 11.37 40.50 40.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

333


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1126 34.75 19.6 63.9 1.117 11.55 771 2.79 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

334


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1126A 34.75 19.6 63.9 1.174 10.98 826 1.57 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

335


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



t3738 34.75 19.6 63.9 1.409 11.36 874 2.35 11.37 40.50 40.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

336


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1099 32.92 20.7 67.5 1.827 11.71 867 3.11 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

337


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1099 32.92 20.7 67.5 1.738 11.71 873 3.07 11.37 40.50 40.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

338


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1099 32.92 20.7 67.5 1.827 11.71 867 3.11 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

339


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1099 32.92 20.7 67.5 1.615 11.61 863 3.12 11.37 40.50 40.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

340


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



x3319 27.43 25 81 1.848 12.19 801 2.55 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

341


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



x3319 27.43 25 81 1.848 12.19 801 2.55 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

342


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



q1910 34.75 19.4 63.9 1.831 11.54 875 4.56 11.37 40.50 40.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

343


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



q1910 34.75 19.4 63.9 1.831 11.54 875 4.56 11.37 40.50 40.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

344


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



q1910 34.75 19.4 63.9 1.831 11.54 875 4.56 11.37 40.50 40.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

345


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



q1910 34.75 19.4 63.9 1.831 11.54 875 4.56 11.37 40.50 40.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

346


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



x3313 32.92 20.7 67.5 1.762 12.31 795 3.12 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

347


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



x3313 32.92 20.7 67.5 1.762 12.31 795 3.12 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

348


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



x3313 32.92 20.7 67.5 1.762 12.31 795 3.12 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


8 1 only 1 5.8101 5.6212 5.8169 5.6029 3.48% 0.396% 0.766% 18.4 0.52 

8 1--2 2 5.7765 5.64 5.8693 5.6401 4.07% 0.698% 1.187% 33.9 0.59 

8 1--3 3 5.726 5.5375 5.8057 5.5472 4.84% 1.055% 2.052% 48.7 0.51 

8 1--4 4 5.8234 5.6296 5.946 5.6582 5.62% 1.445% 3.132% 60.2 0.46 


Wavelength 


400 12.33 7.92 6.04 4.84 

420 16.40 10.81 8.08 6.22 

440 15.36 9.87 7.07 5.37 

460 13.21 8.23 5.74 4.33 

480 11.52 6.85 4.67 3.52 

500 10.20 5.89 3.96 2.99 

520 8.56 4.74 3.17 2.43 

540 6.92 3.77 2.55 1.99 

560 5.90 3.23 2.20 1.77 

580 4.95 2.74 1.93 1.60 

600 4.11 2.35 1.72 1.48 

620 3.53 2.11 1.61 1.44 

640 2.99 1.90 1.53 1.43 

660 2.83 1.91 1.60 1.53 

680 3.64 2.39 1.90 1.77 

700 8.47 5.08 3.64 3.03 

349


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



x3313 32.92 20.7 67.5 1.762 12.31 795 3.12 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

350


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



4223 32.92 20.7 67.5 2.07 12.49 907 3.75 11.37 40.50 40.00 


Yarn 


Total Surface 

Penetration 

Count Dye route Dips Weight Weight Weight Weight %COWY %IOWY %IOWY Integ Level 

6.3 1 only 1 7.0745 6.9739 7.1606 6.8906 2.68% 0.333% 0.694% 15.3 0.48 

6.3 1--2 2 7.0767 6.9669 7.2175 6.8938 3.60% 0.630% 0.992% 28.1 0.63 

6.3 1-2,2 3 7.0788 6.9842 7.2548 6.9179 3.87% 0.961% 1.379% 38.1 0.70 

6.3 1-2,2,2 4 7.0893 6.985 7.2603 6.9307 3.94% 1.094% 1.784% 45.0 0.61 

6.3 1-2,2,2,2 5 7.0793 6.9933 7.2746 6.9562 4.02% 1.461% 2.491% 53.8 0.59 

6.3 1-2,2,2,2,2 

1- 

6 7.025 6.916 7.252 6.9043 4.86% 1.551% 2.859% 57.6 0.54 

6.3 2,2,2,2,2,2 7 7.0844 6.9686 7.3252 6.9766 5.12% 1.828% 3.468% 63.2 0.53 


Wavelength 


400 14.19 9.39 7.44 6.35 5.36 4.82 4.33 

420 18.75 12.78 10.13 8.53 6.96 6.13 5.46 

440 17.70 11.80 9.17 7.60 6.17 5.43 4.81 

460 15.32 9.95 7.61 6.26 5.06 4.48 3.95 

480 13.40 8.41 6.26 5.11 4.13 3.67 3.25 

500 11.89 7.26 5.33 4.33 3.51 3.14 2.78 

520 10.04 5.85 4.26 3.48 2.83 2.57 2.29 

540 8.09 4.64 3.37 2.79 2.30 2.13 1.92 

560 6.96 3.91 2.87 2.40 2.00 1.87 1.72 

580 5.82 3.27 2.44 2.09 1.77 1.69 1.57 

600 4.79 2.74 2.09 1.85 1.61 1.56 1.46 

620 4.05 2.37 1.85 1.68 1.49 1.47 1.39 

640 3.42 2.08 1.68 1.59 1.44 1.45 1.39 

660 3.20 2.00 1.66 1.56 1.42 1.45 1.40 

680 4.27 2.59 2.04 1.85 1.61 1.59 1.51 

700 10.09 6.04 4.43 3.67 3.08 2.84 2.56 

351


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



4223 32.92 20.7 67.5 2.07 12.49 907 3.75 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


7.1 1 only 1 6.475 6.3967 6.5935 6.3195 3.08% 0.343% 0.701% 15.6 0.49 

7.1 1--2 2 6.5846 6.5142 6.7445 6.4489 3.54% 0.640% 0.977% 27.6 0.66 


Wavelength 


400 14.36 9.79 

420 18.81 13.24 

440 17.73 12.20 

460 15.32 10.24 

480 13.35 8.63 

500 11.81 7.46 

520 10.00 6.02 

540 8.04 4.77 

560 6.88 4.01 

580 5.73 3.33 

600 4.71 2.78 

620 3.98 2.39 

640 3.36 2.10 

660 3.17 2.01 

680 4.25 2.62 

700 10.14 6.19 

352


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



4223 32.92 20.7 67.5 2.07 12.49 907 3.75 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

353


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



4223 32.92 20.7 67.5 2.07 12.49 907 3.75 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

354


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



x3313 32.92 20.7 67.5 1.93 12.33 800 3.26 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

355


Shade 

Dye Bath 

ID 

Dwell 


Nip 



4223 32.92 20.67 67.5 2.011 12.7 924 4.12 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

356


Shade 

Dye Bath 

ID 

Dwell 


Nip 



4223 32.92 20.67 67.5 2.011 12.7 924 4.12 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

357


Shade 

Dye Bath 

ID 

Dwell 


Nip 



4223 32.92 20.67 67.5 2.011 12.7 924 4.12 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

358


Shade 

Dye Bath 

ID 

Dwell 


Nip 



4223 32.92 20.67 67.5 2.011 12.7 924 4.12 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

359


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



t3663 34.75 19.6 63.9 2.053 11.84 865 4.29 11.37 40.50 40.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

360


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1472 34.75 19.6 63.9 2.259 11.85 858 4.17 11.37 40.50 40.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

361


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1472 34.75 19.6 63.9 2.158 11.88 846 4.4 11.37 40.50 40.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

362


Shade 

Dye Bath 

ID 

Dwell 


Nip 



x3626 31.09 21.7 71.5 2.283 11.8 783 4.48 11.37 40.50 40.00 


Yarn 

Count 

Dye 

route Dips 

Greige 

Weight 

Boil Off 

Weight 

Dyed 

Weight 

Washed 

Weight %COWY 

Total 


Surface 


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 


Wavelength 


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 

363


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



x3626 31.09 21.7 71.5 2.134 11.76 789 4.58 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

364


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1139 28.35 24.1 78.4 2.261 11.69 810 5.09 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 

1-3,2- 

5 8.2123 7.8902 8.3684 7.9789 6.06% 1.624% 4.320% 69.7 0.38 

6.3 3,2 

1-3,2- 

6 8.2672 7.9373 8.4549 8.057 6.52% 1.986% 5.539% 77.4 0.36 

6.3 3,2-3 7 8.2995 7.9644 8.5276 8.1316 7.07% 2.410% 7.229% 85.5 0.33 


Wavelength 


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 1.32 

580 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 

365


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



x3669 31.09 21.7 71.5 2.277 11.92 880 5.14 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

366


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1139 28.35 24.1 78.4 2.307 11.77 822 5.62 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 

1-3,1- 

6 6.9719 6.7815 7.243 6.9018 6.81% 1.839% 5.282% 75.9 0.35 

7.1 3,3 7 7.2627 7.0641 7.5541 7.204 6.94% 2.036% 6.052% 80.1 0.34 


Wavelength 


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 

367


Shade 

Dye Bath 

ID 

Dwell 


Nip 



1134 26.52 25.7 83.8 3.228 11.4 873 6.15 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

368


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



1134 29.26 23.5 75.9 3.497 11.62 897 5.13 11.37 40.50 40.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

369

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 0.014312 

2 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 0.010561 

17 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 0.018978 

2 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 0.016531 

17 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 

370

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 0.020554 

2 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 0.017759 

17 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^2 

0 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 0.000371 

15 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 

371

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 

#include 

#include 

#include 

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; 

372

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

if (yarn_count == 3) oFile = fopen ("yarninput3.txt", "rb" ); 

if (yarn_count == 4) oFile = fopen ("yarninput4.txt", "rb" ); 

if (oFile==NULL) {fputs ("File error",stderr); exit (1);} 

while (input[0][0] != current_dip) 

{ 

for (z=0; z

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

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]

} 

} 

} 

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]; 

for (ctx = 0; ctx

BB[ctx][ctx]=1.0 + (-2.0*lamda); 

} 

for (ctx = 1; ctx

for (i = 0; i < rows; i++) 

{ 

if (AAinvt[i][i] == 0) 

{ 

pivot = 0; 

j = i + 1; 

while ((pivot == 0) && (j = 0; j--) 

{ 


for ( k = (j+1); k < rows; k++) 

{ 


} 


} 


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 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 

379

{ 

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]

printf("%e\t%e\t%e\n", IOWYsurface_ratio, IOWYtotal_ratio, COWYtotal_ratio); 

if (current_dip > 1) 

{ 

Df = Df * IOWYsurface_ratio; 

Dy = Dy * IOWYtotal_ratio; 

wetpickup = wetpickup * COWYtotal_ratio; 

} 

else 

{ 

Dy = Dy * IOWYtotal_ratio; 

Df = Df * IOWYsurface_ratio; 

wetpickup = wetpickup * COWYtotal_ratio; 

} 

} // Close Dy & Df convergence loop 

// Save IOWY & COWY amount and distribution 

for (ctx = 0; ctx

if (wash

for (ctx = 1; ctx

COWY_save[cty][ctx], Integ_save[cty][ctx]); 

} 

} 

cty = 1; 

for (ctz = 1; ctz

for (ctz = 1; ctz

Section A-4-3b: Computer program to calculate %COWY, %IOWY, and Integ shade values given the 

input dye range set-up conditions. 

#include 

#include 

#include 

#include 

int main () 

{ 

FILE * pFile; 

FILE * oFile; 

FILE * o2File; 



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; 

386

yarn_count = 1; 

for (cty = 1; cty

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/lit 

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]; 

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)); 



} 


{ 




} 


{ 




} 


{ 




} 


{ 




} 

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; 

388

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

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

} 

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]); 

} 

} 

} 

Cj1[rows-1] = AAinvt[rows-1][rows] / AAinvt[rows-1][rows-1]; 

for (j = (rows-2); j >= 0; j--) 

{ 


for ( k = (j+1); k < rows; k++) 

{ 


} 


} 


{ 

IOWY[0] = IOWY[0] + IOWYstep[0]; 

} 


{ 

{ 

IOWY[ctx] = IOWY[ctx] + IOWYstep[ctx]; 

} 

} 

IOWY[rows] = IOWY[rows] + IOWYstep[rows]; 

for (ctx = 0; ctx

X[ctx]=0.0; 

Xrbl[ctx]=0.0; 

Xiowy[ctx]=0.0; 

for(cty = 0; cty

for (cty = 0; cty

{ 

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 

{ 

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]

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 

for (ctx = 0; ctx

Section A-5-1: Observational Study Raw Data -Dye Range Parameters 

Table A-5-1: Independent indigo dye range raw data set 

Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



443 29.00 20.1 73.6 1.262 12.18 813 2.58 9.70 38.90 95.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

396


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



443 29.00 20.1 73.6 1.262 12.18 813 2.58 9.70 38.90 95.00 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

397


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



443 29.00 20.10 73.60 1.196 12.06 807 2.51 9.70 38.90 95 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

398


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



418 32.00 18.20 66.70 1.658 11.83 814 3.29 9.70 38.90 95 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

399


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



402 28.00 20.80 76.30 1.986 12.24 841 3.53 9.70 38.90 95 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

400


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



402 28.00 20.80 76.30 1.986 12.24 841 3.53 9.70 38.90 95 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

401


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



402 28.00 20.80 76.30 1.986 12.24 841 3.53 9.70 38.90 95 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

402


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



471 32.00 18.20 66.70 2.094 12.12 838 3.42 9.70 38.90 95 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

403


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



471 32.00 18.20 66.70 2.094 12.12 838 3.42 9.70 38.90 95 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

404


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



471 32.00 18.20 66.70 2.094 12.12 838 3.42 9.70 38.90 95 


Yarn Dye 


Total Surface 

Penetration 


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 


Wavelength 


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 

405


Shade 

Dye Bath 

ID 

Dwell 

(gpl 


Nip 



401 28.00 20.80 76.30 2.211 12.11 820 3.72 9.70 38.90 95 


Yarn Dye 


Total Surface 

Penetration 


8 1 only 1 9.3795 9.0347 9.4691 9.0311 3.76% 0.422% 0.827% 21.2 0.51 

8 1--2 2 9.3241 8.9773 9.5306 9.013 5.10% 0.751% 1.481% 40.1 0.51 

8 1--3 3 9.2045 8.8731 9.4807 8.9362 5.78% 1.178% 2.841% 57.5 0.41 

8 1--4 4 9.2051 8.8685 9.492 8.967 5.96% 1.573% 4.330% 69.8 0.36 

8 1--6 6 9.1474 8.8177 9.5895 8.9952 7.67% 2.379% 7.711% 87.4 0.31 


Wavelength 


400 11.81 7.38 5.31 4.17 2.97 

420 15.74 9.97 6.80 5.25 3.55 

440 14.62 8.94 5.97 4.56 3.08 

460 12.45 7.41 4.89 3.74 2.58 

480 10.69 6.06 3.96 3.04 2.13 

500 9.34 5.15 3.36 2.60 1.87 

520 7.73 4.11 2.71 2.12 1.58 

540 6.14 3.24 2.16 1.73 1.36 

560 5.19 2.75 1.88 1.55 1.28 

580 4.29 2.32 1.66 1.41 1.21 

600 3.53 1.97 1.48 1.30 1.16 

620 2.99 1.75 1.36 1.23 1.13 

640 2.57 1.62 1.34 1.24 1.16 

660 2.48 1.66 1.44 1.36 1.30 

680 3.24 2.06 1.71 1.58 1.48 

700 7.82 4.44 3.24 2.70 2.15 

406

Coefficients of Equilibrium Sorption %IOWY Power Function - Digital ...

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