K/S Shade Values by Wavelength for Typical 3.0 Gm/Lit Indigo Dye Set-Up

Home , Colorist, Ring dyeing, Sulfur dye

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.

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

by Richard Moore Holbert, Jr.

A dissertation submitted to the Graduate Faculty of North Carolina State University in partial fulfillment of the requirements for the Degree of Doctor of Philosophy

Fiber and Polymer Science

Raleigh, North Carolina

2011

APPROVED BY:

Warren Jasper Richard Gould

Jon Rust Peter Hauser Chair of Advisory Committee

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.

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 3.2.2 Analysis of Laboratory Preparation Time, Temperature, and Sodium Hydroxide Concentration Affect on %IOWY after One and Six Dip Indigo Dyeing Conditions 106 3.2.3 Analysis of Laboratory Preparation Time, Temperature, and Sodium Hydroxide Concentration Affect on Integ Shade Value after One and Six Dip Indigo Dyeing Conditions 114 3.2.4 Analysis of Laboratory Preparation Time, Temperature, and Sodium Hydroxide 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

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

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, cm2/sec x 10-10). 43 Table 1-5: Regression values for three parameter emphirical solution. 48 Table 1-6: Concentration of alkali system. 49 Table 1-7: Etters 1989 data set. 51 Table 1-8: Annis and Etters 1991 data set. 52 Table 1-9: Etters 1991 Equilibrium sorption of indigo on cotton obtained from different pHs in grams of dye per 100 grams of water(bath) or fiber. 54 Table 1-10: Dye concentrations required to yield equivalent shade at different pHs. 55 Table 1-11: % reflectance and corrected K/S values for different dyebath concentrations and pH. 56

2. Objectives of the Present Investigation

3. Experimental Methods and Procedures Table 3-1: Target dyed yarn sample weight for Methyl Pyrrolidinone extraction. 93 Table 3-2: Time, temperature, and sodium hydroxide concentration levels plus response variable for one dip of indigo. 99 Table 3-3: Time, temperature, and sodium hydroxide concentration levels plus response variable for six dips of indigo. 100 Table 3-4: ANOVA analysis results for laboratory preparation parameters on %Boil-off loss. 105 Table 3-5: ANOVA analysis results for laboratory preparation parameters on %IOWY for one dip of indigo. 111 Table 3-6: ANOVA analysis results for laboratory preparation parameters on %IOWY for six dips of indigo. 113 Table 3-7: ANOVA analysis results for laboratory preparation parameters on Integ for one dip of indigo. 118 Table 3-8: ANOVA analysis results for laboratory preparation parameters on Integ for six dips of indigo. 119 Table 3-9: ANOVA analysis results for laboratory preparation parameters on penetration factor from one dip of indigo. 123 Table 3-10: ANOVA analysis results for laboratory preparation parameters on 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

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 Table 5-13: ANOVA analysis results of empirical model to actual measured production yarn %IOWY. 259 Table 5-14: Calculated porosity value to fit Dye theory model %IOWY to production yarn results. 259 Table 5-15: ANOVA analysis results of dye theory model to actual measured production yarn %IOWY. 261 Table 5-16: ANOVA analysis results of empirical model to actual measured production yarn Integ. 262

vii

Table 5-17: ANOVA analysis results of dye theory model to actual measured production yarn Integ. 264 Table 5-18: ANOVA analysis results of dye theory model calculated porosity value to dye range speed. 265

6. Summary of Results, Discussions, and Recommendations Table 6-1: Empirical model performance review. 271 Table 6-2: Dye theory model performance review. 271

Appendix Table A-3-1: % Reflectance of mock dyed 100% cotton yarns used to calculate K/S. 282 Table A-3-3: %IOWY and Integ shade data from equilibrium sorption experiment. 283 Table A-4-1: Prime and replica raw data set. 284 Table A-4-2a: Convergence test - standard errors from empirical model %COWY parameter. 370 Table A-4-2b: Convergence test - standard errors from empirical model %IOWY parameter. 370 Table A-4-2c: Convergence test - standard errors from empirical model Integ parameter. 371 Table A-4-2d: Convergence test - standard errors from empirical model penetration level parameter. 371 Table A-5-1: Independent dye range raw data set. 396

viii

LIST OF FIGURES

1. Indigo Dyeing Principles: Review of Current Knowledge 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 2 Figure 1-25: Mt / M∞ as a function of Dt/r 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

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

2. Objectives of the Present Investigation

3. Experimental Methods and Procedures 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 Figure 3-11: Interaction profile for time, temperature, and sodium hydroxide concentration on %IOWY after one and six dips of indigo dye. 110

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, and sodium hydroxide concentration in laboratory preparation process. 114 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 Figure 3-20: Interaction profile for time, temperature, and sodium hydroxide concentration 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, and sodium hydroxide concentration in laboratory preparation process. 124 Figure 3-22: Penetration factor for six dips of indigo model as a function of time, temperature, and sodium hydroxide concentration in laboratory preparation process. 126 Figure 3-23: Optimized laboratory preparation parameters incorporating prediction profiles from %Boil-off loss and %IOWY from one dip of indigo dye. 128 Figure 3-24: Optimized laboratory preparation parameters incorporating prediction profiles from %Boil-off loss and %IOWY from six dips of indigo dye. 129 Figure 3-25: %IOWY from 6.3/1, 7.1/1, 8.0/1, and 12.0/1 OE yarns compared to Etters20 data under equilibrium sorption at pH 13 range. 133 Figure 3-26: %IOWY on 6.3/1, 7.1/1, 8.0/1, and 12.0/1 OE yarns compared to Etters20 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

4. Data Analysis from the Observational Study 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 various dye bath concentrations after six dips of indigo on 6.3/1 yarn. 168 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 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 set-up conditions. 234 Figure 4-44: Comparison of model predicted and actual oxidation rate. 236 Figure 4-45: Dye theory model oxidation rate functional relationship to dye range set-up conditions. 237

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 from production yarns. 260 Figure 5-15: Empirical model predicted Integ compared to actual measured values from production yarns. 262 Figure 5-16: Dye theory model predicted Integ compared to actual measured values from production yarns. 263 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

1. Indigo Dyeing Principles: Review of Current Knowledge 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 approximate solution of dye distribution when L is 1 to 20. 46

Equation 1-35: Etters empirical fit equation to calculate parameters c in three parameter approximate solution of dye distribution when L is 1 to 20. 47 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

2. Objectives of the Present Investigation

3. Experimental Methods and Procedures 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

4. Data Analysis from the Observational Study 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<0. 203 Equation 4-14: Dye bath concentration at the outside surface node. 203 Equation 4-15: Boundary condition at the center of the yarn due to symmetry. 204 Equation 4-16: Functional relationship of %IOWY at the surface related to Integ shade. 204 Equation 4-17: Relationship of surface %IOWY by Integ shade. 204 Equation 4-18: Nodal equation for center node. 206 Equation 4-19: Nodal equation for interior nodes. 206 Equation 4-20: Nodal equation for exterior node. 206 Equation 4-21: Expression for lambda and beta coefficients in the nodal equations. 206 Equation 4-22: Matrix example of all nodal equations in finite difference model. 207 Equation 4-23: Mogahzy's relationship for open end yarn radius as a function of yarn count. 207 Equation 4-24: Calculation of oxidized boundary layer as a function of wash reduction coefficient, and %COWY and %IOWY from the previous dip. 208 Equation 4-25: Determining the reduced boundary layer concentration and quantity after the nip process. 209 Equation 4-26: Explicit finite difference equation for oxygen distribution in the nodal mesh. 209 Equation 4-27: Rate of oxygen removal from the air stream. 209 Equation 4-28: Fraction of oxygen removed from the air stream as a function of total reduced dye present. 210 Equation 4-29: Boundary conditions for solving finite difference equations. 210 Equation 4-30: Equations used to track the convergence of reduced indigo dye into oxidized state. 211 Equation 4-31: Chemical reactions and intermediaries during the oxidation process. 212 Equation 4-32: Relationship for the grams of auxiliary chemicals per gram of indigo present. 212 Equation 4-33: Calculation of the %COWY based on total indigo amounts. 213 Equation 4-34: Dye theory model effective fiber diffusion coefficient. 222 Equation 4-35: Dye theory model prediction equation of effective yarn diffusion coefficient. 226 Equation 4-36: Dye theory model prediction equation wet pick-up. 230 Equation 4-37: Dye theory model prediction equation of wash reduction. 233 Equation 4-38: Dye theory model prediction equation of oxidation rate. 236

5. Empirical and Theoretical Dye Model simulation and validation

6. Summary of Results, Discussions, and Recommendations Equation 6-1: Equations to calculate %IOWY as a function of dye bath concentration and pH under equilibrium sorption conditions. 267 Equation 6-2: Expressions to relate penetration level of non-uniformly dyed yarns. 268

xvii

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 20th century, synthetic indigo gradually replaced natural dye worldwide. Over the last hundred plus years more indigo dye has been produced than any other single dye.

Even though indigo is classified as a vat dye, it does not perform like other vat dyes because it has little affinity for cotton. Compared to other vat dyes, indigo has inferior fastness properties. But these poor performance properties are indeed the very nature of the dye which makes it so popular. Due to the poor fastness properties, a desirable blue shade develops when indigo dyed denim is laundered repeatedly.

If indigo was introduced today, not many dyers or chemists would be interested. In fact, it might not even leave the lab compared to today’s requirements for commercializing a new dye. Zollinger noted in 198819, “Were it not for the persistence of the denim fashion, indigo would hardly be produced or used at all today.” This statement still rings true today. Given the extensive use of indigo in commercial dyeing applications, one would speculate the literature would be filled with fundamental experiments and knowledge of the use and driving properties of this important dye. At last, until recently this is not the case. It wasn’t until the end of the 1980’s when the Southeastern Section of the AATCC committee lead by investigations of J.N. Etters that significant research revealed the physico-chemical mechanisms of the sorption of indigo by cellulosic materials.

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

The majority of denim yarns dyed with indigo utilizes the 6-dip (or more) continuous rope dye range. A typical rope dye range will process 20 to 40 ropes of yarns at a time. The exact number will be predetermined by machine layout and subsequent slasher restrictions. 300-400 individual yarns make up a single rope. The final number of ropes will equate to 2 to 4 slasher sets. This characteristic allows the continuous rope dye range to produce uniformly dyed yarn at great production rates in a variety of shades.

Before the cotton yarns can be dyed with indigo, the cotton must be prepared. The pre- scouring process shown in figure 1-2 involves two main objectives. First the cotton is chemically cleaned with a penetrant, sequestering agent, and sodium hydroxide solution. Typical sodium hydroxide concentrations range from 10-25 g/l although higher levels (mercerization strength) are used to create unique dye characteristics. The main purpose is to remove natural waxes and oils from the cotton fibers. During this stage sulfur dyes are commonly added to enhance the final indigo dye shade. Multiple wash boxes follow the scour box to rinse contaminants from the yarns. The last benefit of the pre-scour section is to remove all excess air trapped in the yarns. Excess air in the yarns will prematurely oxidize the reducing agent and possibly indigo in the dye boxes causing the entire system to fall out of reduction.

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

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.

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

Since dye liquor is circulated through the dye boxes to maintain uniform concentrations, the indigo dye boxes can be modeled as one giant dye box. The conservation of mass principle for a control volume undergoing a process can be expressed as equation 1-1.

𝑁𝑒𝑡𝑐 ℎ𝑎𝑛𝑔𝑒 𝑎𝑖𝑛 𝑚 𝑠𝑠 𝑤𝑖𝑡ℎ𝑖𝑛𝐶 𝑉=𝑇𝑜𝑡𝑎𝑙𝑚 𝑎𝑠𝑠 𝑒𝑛𝑡𝑒𝑟𝑖𝑛𝑔−𝑇𝑜𝑡𝑎𝑙𝑚 𝑎𝑠𝑠 𝑙𝑒𝑎𝑣𝑖𝑛𝑔

Equation 1-1: First law of thermodynamics

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.

𝑁𝑎𝑆𝑂 +2𝑁𝑎𝑂𝐻⎯⎯⎯ 2𝐻 +2𝑁𝑎𝑆𝑂

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

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

The theoretical calculations of caustic and hydro in indigo stock mix are as follows. The molecular weight of indigo, hydro, and caustic are 262.26, 174.11, and 40.01 respectively. From the above two reactions 4 moles of 100% NaOH and 1 mole of 100% Na2S2O4 (Hydro) are required to completely reduce 1 mole of 100% indigo. In commercial operations, excess sodium hydroxide and

8 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

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.

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.

𝐻𝐼↔𝐻 +𝐻𝐼

Equation 1-4: First ionization of indigo dye

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

[][] 𝑘 = []

Equation 1-5: First associated equilibrium ionization constant

The second ionization step produces the even more soluble di-ionic form of indigo, I2- by equation 1- 6.

𝐻𝐼 ↔𝐻 +𝐼

Equation 1-6: Second ionization of indigo dye

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

[] 𝑘 = []

Equation 1-7: Second associated equilibrium ionization constant

The fractional distribution of each indigo dye form in figure 1-7 is governed by the pH and respective pKa values. The functional relationship for each form is given in equations 1-8.

𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝐹𝑜𝑟𝑚𝐼𝐼= ,𝑤ℎ𝑒𝑟𝑒 𝐴=(𝑝𝐻 − 𝑝𝐾 ) 𝑎𝑛𝑑 𝐵 = (2𝑝𝐻 −𝑝𝐾 −𝑝𝐾 ) [] 𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝐹𝑜𝑟𝑚𝐼𝐼𝐼= ,𝑤ℎ𝑒𝑟𝑒 𝐶=(𝑝𝐾 −𝑝𝐻) 𝑎𝑛𝑑 𝐷 = (𝑝𝐻 −𝑝𝐾 ) [] 𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛𝑎𝑙 𝐹𝑜𝑟𝑚𝐼𝑉= ,𝑤ℎ𝑒𝑟𝑒 𝐸=(𝑝𝐾 +𝑝𝐾 −2𝑝𝐻) 𝑎𝑛𝑑 𝐹 =(𝑝𝐾 −𝑝𝐻) []

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

A higher pKa value indictates weaker ionization. In fact, the autoprotolysis equilibrium of water has a pKa = 14.00. The relatively high value of 14 indicates only a few water molecules are ionized.8

In 1993 the actual pK1 and pK2 values for reduced indigo were unknown. Etters used the values found for tetra-, tri-, di-, and mono- sulphonic acid forms of indigo. He states when these data are extrapolated to the zero sulponic acid form, i.e. conventional reduced indigo, reasonable

25 estimates for pK1 and pK2 with 95% confidence limits are made. Etters' reported pKa estimates are: pK1 mean value is 7.97 (limits 7.19, 8.74) and pK2 mean value is 12.68 (limits 12.23, 13.08).

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

19 measured to be pK1 = 9.5 and pK2 = 12.7. By using these values it is possible to calculate the fractional amount of each reduced species of indigo in the dye bath for a given pH. Figure 1-8 illustrates the mono-ionic form dominates at pH of 11.0 while the di-ionic form reins superior at pH of 14.0. At traditional indigo pH dye ranges of 12.0 – 13.0, the mono-ionic to di-ionic form ratio is basically 50/50.

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.

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

Several alternative methods have been developed over the years to measure and monitor indigo and sodium hydrosulfite concentrations. Westbroek51 used an electrochemical method using multistep chronoamperometry. Photometric and spectrophotometric reflectance can be used to determine indigo concentrations by potentiometric titration. However the system doesn’t differentiate between unreduced indigo and leuco indigo in the dye bath. This is due to the oscillation of potential used to remove indigo particles from the electrode. By applying a -0.90 mV potential across the electrode, all indigo in the sample vessel is completely reduced to leuco indigo.

Sahin53 describes a laser diode spectrometer for monitoring indigo concentrations. A laser diode absorption spectrometer with monochromatic radiaton emmited at 635 nm to measure oxidized indigo absorption at the shoulder of a broad absorption peak. A linear calibration curve between 10 and 150 mg/l is shown in figure 1-11 which corresponds to indigo concentrations in the dye bath from 0.8 to 12 g/l (diluted with aerated water by a factor of 80). Typical dye bath indigo concentrations ranges are 1 to 3 g/l. Sahin claims no interference due to sulfur compounds present in dye bath which is a problem with electrochemical titration methods but no supporting evidence is provided.

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

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 Merritt29 demonstrated the effective use of ferrous sulfate/triethanolamine/sodium hydroxide or Fe/TEA/OH as the extraction solvent. Approximately 0.5 gram dyed sample is placed in flask then 100 ml of pre-prepared Fe/TEA/OH solution is added. (Fe/TEA/OH is prepared by adding 5 g/l ferrous sulfate, 50 g/l triethanolamine, and 10 g/l sodium hydroxide (pellets) to distilled water.) The extraction is carried out at 45° C for 90 minutes on a stirring hot plate. After 90 minutes the solution is cooled to room temperature, volume topped off to 100 ml, and absorbance measured at 406 nm. The solutions once again follow Beer’s law with dilutions made by additional reducing solution if needed.

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.

Surface of paint film

X dx I J

Substrate

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

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

𝑑𝐼 = −𝐾𝐼𝑑𝑥 − 𝑆𝐼𝑑𝑥 +𝑆𝐽𝑑𝑥=−(𝐾+𝑆)𝐼𝑑𝑥 + 𝑆𝐽𝑑𝑥

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

The upward flux (intensity J) is: - decreased by absorption = -KJdx - decreased by scattering = -SJdx - increased by backscatter = +SIdx

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

𝑑𝐽 = −𝐾𝐽𝑑𝑥 − 𝑆𝐽𝑑𝑥 +𝑆𝐼𝑑𝑥=−(𝐾+𝑆)𝐽𝑑𝑥 + 𝑆𝐼𝑑𝑥

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

Solution of these differential equations for an isotropically absorbing and scattering layer of infinite thickness leads to the widely used Kubelka-Munk equation, equation 1-11.9

/ 𝑅 =1+ − +2

Equation 1-11: Kubelka-Munk reflectance equation

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

( ) ( ) = − () ()

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

=𝑎∗𝐶

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

The definition of reflectance absorptivity coefficient requires uniform dye distribution in the cross section of the yarn. There is only one true reflectance absorptivity coefficient, “at”, for a given dye/fiber system. Etters has estimated that the value of “at” for dyeings in which indigo is uniformly distributed in the cross-section of the substrate is approximately 40 when the dye concentration is expressed as grams of indigo per 100 g of fiber.33

A useful description to represent an object's color was defined by the Committee of the Society of Dyers and Colourists in 1976 as the CIELAB system. This system defined three parameters that related the color value of an object. The L* represents the light to dark aspect, a* describes the

22 red to green color shift, and the b* term describes the yellow to blue relationship. These values are calculated using the equations in 1-16 that involve the tristimulus values which relate the measured reflectance wavelength values, average observer, and the standard light source. All calculations presented in this paper use a 10° observer and D65 standard light source. For more detailed review please reference book 9 in the bibliography section: Colour Physics for Industry.

𝐿∗ = 116 −16 𝑎∗ = 500[ − ] 𝑏∗ = 200[ − ]

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

∑ ∑ ∑ ̂ where = , 𝑌= , and 𝑍= ∑ ∑ ∑

Another method of expressing the overall color value from a sample is the Integ shade value, equation 1-17. In this calculation the K/S at each wavelength is scaled by the average observer and standard light source. The resulting Integ value increases in value as the overall color depth increases.

𝐼𝑛𝑡𝑒𝑔 = ∑ ∗E(𝑥 + 𝑦 +𝑧)

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

1.3.1.b Determination of Surface Reflectance, Rs

18 Etters summarized a method for the determination of Rs in 1991. To determine the Rs value, make successive linear regression analyses of K/Scorr versus concentration for various values

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

2 Etters plotted the R versus Rs values for blue, red, and yellow reactive dye on velour cotton in figure 1-13. It is revealed the R2 value for the blue dye is insensitive to surface reflectance with all the values being greater than 0.99. On the other hand, R2 for the red dye exhibits much greater

2 2 sensitivity to surface reflectance, with the maximum R occurring at an Rs of about 0.01. R for the yellow dye has only limited sensitivity to surface reflectance, with the R2 value reaching a maximum between 0.020 and 0.025. The most important point made in figure 1-13 is that, for the present series of dyes on the given velour substrate, the R2 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

The intercepts of the linear regression lines obtained in the analysis of K/Scorr versus concentration are given as a function of surface reflectance in figure 1-14. The zero intercept for the red and yellow dyes occur at about the same value of surface reflectance: 0.0166 and 0.0163. However the zero intercept for the blue dye occurs at a surface reflectance of 0.0128. Yellow dye is most sensitive to surface reflectance while the blue dye is the least.

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

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

1.5% for each dye. Plots of K/Scorr versus concentration in which both zero surface reflectance and the common value of 0.015 are given in figure 1-15. In each case the linearity is significantly improved by accounting for surface reflectance. The reflectance absorptivity coefficient (line slope) is increased in each case. Recall the R2 analysis indicated only small improvement by accounting for

Rs would be expected. Yet, the surface reflectance had a dramatic visual impact on the correlation of K/S versus concentration.

Corrected

Original

Corrected

Original

Corrected

Original

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

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.

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

14 12 10 8 6 4 2 % Indigo Pick-up Indigo % 0 1.5 5 10 20 30 45.5 61.2 80 88.2 50% NaOH Concentration (opg)

Mild Alkali Causticizing Mercerizing

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.

% Reflectance Values of Typical 6 Dip Indigo Dye Shade

3.5 3 2.5 2 1.5 1 % Reflectance 0.5 0 400 450 500 550 600 650 700 Wavelength (nm)

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 Values of Typical 6 Dip Indigo Dye Shade

60 50 40 30 20

K/S Corrected 10 0 400 450 500 550 600 650 700 Wavelength (nm)

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.

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

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

2 dyeing) can be expressed as Vi = π (r – pr) 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.

=𝑎∗𝐶 → =𝑎 → =𝑎 () ()

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

Where at in equation 1-18 is the true reflectance absorptivity coefficient for indigo that is distributed uniformly in the cross section of the yarn (p=1). Ca is the actual concentration of dye in the yarn cross section, and “p” is the fractional penetration of the yarn by the fixed dye.

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 Weisz3 and McGregor4.

1.4.1. Fundamental Sequence of Events during Dyeing

Etters28 defined four fundamental steps which outline the path of dye molecules from the bath to the fiber as illustrated in figure 1-21.

1. Diffusion of the dye in the external medium (usually water) toward the diffusional boundary layer at the fiber surface. 2. Diffusion of dye through the diffusional boundary layer that exists at the fiber surface. 3. Adsorption of the dye onto the fiber surface. 4. Diffusion of dye into the fiber interior by absorption.

Figure 1-21: Basic sequence of events in dyeing fibers.28

The rate of sorption of dye by textile materials is controlled by several fundamental physico- chemical parameters.

1. Denier of fiber, which is proportional to radius of the cylinder fiber. 2. Liquor ratio, the ratio of volume of dye bath to the volume of fiber mass. 3. Distribution coefficient or ratio of the equilibrium concentration of dye in both the application medium and the fiber. 4. Diffusion coefficient of the dye in both the application medium and the fiber. 5. Fundamental nature of the dyeing system: infinite or finite bath condition. 6. Thickness of the diffusional boundary layer at the fiber surface.

Rate of dyeing for a given system is inversely proportional to the denier of the fiber. As the denier of a given fiber increases, the surface area decreases for a given mass of fiber available for

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.

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.

𝐹=−𝐷∗

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

Here F is the rate of transfer per unit area of section, C the concentration of diffusing substance, D is the diffusion coefficient, and x the space coordinate measured normal to the section.

Using Fick’s first law, Fick’s second law for diffusion in one dimension can be derived as equation 1-20.

=𝐷

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

Furthermore, the equations can be expanded to multi-dimensions in cylindrical coordinate system to describe diffusion in cylinders.

= 𝑟∗𝐷 + + 𝑟∗𝐷

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

Here x = r cos θ and y = r sin θ, where r, θ, and z are cylindrical coordinates. Equation 1-21 can be solved by the method of separation of variables, method of Laplace transformation, or numerical solutions when the diffusion coefficient can be assumed constant.

Modeling the dye process by considering diffusion in long circular cylinders reduces the 3- dimensional equation to the following diffusion equation 1-22.

= 𝑟∗𝐷

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

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

𝐶=𝐶[1 − ∑ 𝐽(𝑟𝛼)/𝐽(𝑎𝛼)𝑒 ]+ ∑ 𝑒 𝐽(𝑟𝛼)/𝐽 (𝑎𝛼)∗

∫ 𝑟𝑓(𝑟)𝐽(𝑟𝛼)𝑑𝑟

Equation 1-23: Non-steady state solution to equation 1-21.2

Here αn ‘s are the positive roots of Jo which are the Bessel function of the first kind of order zero. If the concentration is initially uniform throughout the cylinder than equation 1-23 reduces to equation 1-24 and is graphically depicted in figure 1-22.

( ) =1− ∑ ()

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

Here the C is the concentration within the cylinder, C1 is the initial uniform concentration within the cylinder, and C0 is the constant surface concentration on the cylinder.

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

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

Other formal solutions to the partial differential equation have been developed. However there are certain limiting assumptions that must exist for the mathematical solutions to be valid.

1. It is assumed the diffusion coefficient is constant and not dependent on concentrations. 2. Equilibrium distribution coefficient of dye between fiber and dye bath is linear for a wide range of concentrations, i.e. linear sorption isotherms. 3. All fibers are morphologically stable, homogenous, and uniformly accessible endless cylinders. 4. No diffusional boundary layer exists in the dye bath and no “skin-core” effect exists in the fiber. This results in instantaneous equilibrium between dye on fiber surface and dye in the bath.

Given these assumptions Hill31 has developed a solution for infinite dye bath conditions in the absence of surface barrier effects, equation 1-25.

=1−∑ 𝑒

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

Here the βn’s are the positive transcendental Bessel roots given by J0 βn = 0 and is the fractional equilibrium uptake of dye at a given time Mt and at equilibrium 𝑀. An unfortunate limitation of Hill’s infinite bath equation is that all of the four assumptions previously mentioned must be present.

Newman31 developed an alternative solution for infinite dye bath conditions that does not require assumption #4. Namely, Newman’s solution is applicable in the presence of surface barrier effects. Due to this fact, Newman’s equation (equation 1-26) is particularly useful for diagnostic or analytical work.

∗ =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.

𝐿=

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

Here Dm and Ds are the diffusion coefficients of the diffusant in the external medium and polymer respectively, K is the equilibrium distribution coefficient of the diffusant between the external medium and the polymer, r is the radius of the cylinder, and δD is the thickness of the diffusional boundary layer.

The diffusional boundary layer is a mechanical characteristic that impedes sorption or desorption and is inversely proportional to the rate of flow of the external medium past the surface of the cylinder. When the rate of flow of the external medium is very high, the thickness of the diffusional boundary layer approaches zero and the value of “L” approaches infinity. As the value of

2 2 “L” approaches infinity, the βn /L drops out from Newman’s equation (equation 1-26) which then becomes equivalent to Hill’s equation (equation 1-25).

These solutions may not directly apply to indigo dyed cotton yarn due to several underlying assumptions. Namely the constant initial uniform concentration within the cylinder only applies before the first dip where C1=0. Also the diffusion coefficient may not remain constant through

40 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-Thakar31 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.

𝐷 ∗10 = . .

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

Here Uw is the viscosity of water in centipoises and Vm is the molal volume of the diffusing substance in ml per gram-mole. With the Ds value the “apparent diffusional boundary layer”, δD, can be determined.

1.4.3. Diffusional boundary Layer

The diffusional boundary layer, δD, potentially impedes dye uptake by the fiber. The thickness of diffusional boundary layer is proportional to the thickness of the hydrodynamic boundary layer and the thickness of the hydrodynamic boundary layer is inversely proportional to velocity of flow of the bath past the fiber surface. Figure 1-23 illustrates the effect of dye bath movement on fractional dye uptake. In case #4 of E=0 (infinite dye bath conditions), at low flow rate 50% uptake occurs at 0.4 dimensionless time units. Whereas 50% dye uptake occurs almost at 0.2 dimensionless time units at the higher flow rate.

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.

Table 1-4: Estimated diffusion coefficients for disperse Red 11 (D, cm2/sec x 10-10).31

Time (min) 15 opm (L=2) 30 opm (L=80) 90 opm (L=∞) 0.50 4.72 5.38 4.81 1.00 4.17 4.89 4.38 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.

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

1.4.4. Empirical Simplifications of Diffusion

The formal solution to Fick’s 2nd law of diffusion is a grueling task even for a superior mathematician. To simply the equations many empirical equations have been proposed over the years. Three such exponential equations were compared for the efficacy in simulating the functional relationship between , Dt/r2, and L that is found by formal use of Newman’s equation 1-26.31 The equations that were examined are one, two, and three parameter exponential equations. Vickerstaff suggested an empirical approximation using one parameter as shown in equation 1-29.31

=1−𝑒

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

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−𝑒

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

Etters developed a three parameter equation to express the functional relationship as shown in equation 1-31.31

=[1−𝑒 ]

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

Each of the three equations were fitted to data obtained by the use of formal solutions to Newman’s equation for the range of 0.05 to 0.95 at 0.05 intervals and associated values of Dt/r2 for values of L ranging from infinity to 1.0. The goodness of fit is expressed as adjusted R2. Etters’ three parameter equation provides the best fit of the three empirical exponential equations over a very wide range of L. Only at very low values of L does the two parameter equation perform as well.

For the three parameter equation to have empirical utility for a wide range of L values, it is necessary to express the parameters a, b, and c as a function of L. Etters derived the following expression for L at a range of 20 to infinity.

𝑃𝑉 =

Equation 1-32: Etters empirical fit equation to calculate parameters in three parameter approximate solution for dye distribution when L is 20 to infinity.31

Here PV equals a, b, or c in his three parameter equation for L range of 20 to infinity. parameter a: q0=5.530554, q1=160.58898, q2=-1750.616, q3=37.494042, q4=-374.48753 parameter b: q0=1.2479036, q1=27.400938, q2=88.43848, q3=33.90477, q4=52.505626 parameter c: q0=0.3798136, q1=12.004462, q2=-6.8204581, q3=11.003091, q4=5.3552691

For L range from 20 to 1, the three equations shown in equations 1-33, 1-34, and 1-35 accurately express the parameter values of a, b, and c which are utilized in equation 1-30.

𝑎=𝑞 + ln +𝑞 +𝑞

Equation 1-33: Etters empirical fit equation to calculate parameter a in three parameter approximate solution for dye distribution when L is 1 to 20.31

Here: q0=4.098044891, q1=3.024653177, q2=-2.49630292, q3=2.59232464

𝑏=𝑞 + +𝑞 ln +

Equation 1-34: Etters empirical fit equation to calculate parameter b in three parameter approximate solution for dye distribution when L is 1 to 20.31

Here: q0=1.179748591, q1=-0.14496394, q2=0.094386506, q3=0.001282442

𝑐=𝑞 + + +

Equation 1-35: Etters empirical fit equation to calculate parameter c in three parameter approximate solution for dye distribution when L is 1 to 20.31

Here: q0=0.916905399, q1=0.146475883, q2=-0.08873859, q3=-0.06737345

Etters supplied supporting evidence that the strength of the relationship is nearly as accurate as the formal equation of Newman and can be used with confidence as an analytical tool.31

Regression analysis is made according to the following equation for various values of c until, simply through trial and error, a value of c is found which results in the highest degree of linearization in a graphical plot of ln {-ln[1 – ( )1/c]} versus ln(Dt/r2) as shown in figure 1-25.

2 10 Figure 1-25: Mt / M∞ as a function of Dt/r for various values of E∞.

As shown in Figure 1-25, the above technique results in a series of nearly straight lines corresponding to various values of equilibrium bath exhaustion, E∞. The slope of each line defines the parameter b and the line intercept I (at Dt/r2=1) gives the parameter a, a=eI. Table 1-5 summarizes the regression values for a, b, and c for various E∞. For infinite dye bath conditions,

E∞= 0, table 1-5 gives the following values: a=5.3454, b=1.1299, and 1/c=2.3.

Table 1-5: Regression values for three parameter emphirical solution.10

E∞ a b 1/c 0.995 13.4067 0.1150 0.0625 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.

( ) 𝐷= [ )]

Equation 1-36: Etters relationship for apparent diffusion coefficient and three parameter estimates.31

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 Experiment15

The Southeastern Section Research Committee published a paper in 1989 investigating the effect of dye bath pH on color yield. This study used 8/1’s yarn knitted into tube form having 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

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.

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

Annis and Etter 1991 Experiment19

In May 1991 Annis and Etters published results from an experiment designed to investigate dye uptake and resulting color yield as influenced by dye bath pH. The same material, laboratory simulations of indigo dyeing, and analytical techniques used by the Southeastern Section of 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

Etters 1991 Experiment20

In December 1991, Etters published results from an experiment investigating the effect of pH and dye concentrations on fiber dye uptake under equilibrium conditions. 8/1’s cotton yarn knitted into tubes was dyed with indigo, sodium hydrosulfite, and sodium hydroxide or 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 Experiment27

To investigate shade sensitivity as a function of pH, Etters designed an experiment at two different pH levels and small permutations of pH were introduced. The experiment utilized 8/1’s denim yarn knitted into tubes with a flattened width of 4.5 cm and weight of 7.2 grams per 30 cm length.

The dye baths were three liters in total volume to ensure infinite dye bath conditions. Table 1-10 outlines the dye concentrations utilized in the experiment.

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.

Table 1-11: % reflectance and corrected K/S values for different dyebath concentrations and pH.27

Cb (g/l) pH %Rc K/S Cb (g/l) pH %Rc K/S 0.5 10.6 2.52 48 1.7 12.1 2.29 62.2 0.5 10.8 2.5 48.9 1.7 12.3 2.38 55.8 0.5 11 2.48 50 1.7 12.5 2.47 50.5 0.5 11.2 2.51 48.4 1.7 12.7 2.59 44.8 0.5 11.4 2.53 47.5 1.7 12.9 2.74 39.3 1 10.6 2.01 97 3.2 12.1 1.9 123.9 1 10.8 2 98.9 3.2 12.3 1.95 110.1 1 11 1.99 101 3.2 12.5 1.99 101 1 11.2 2 98.9 3.2 12.7 2.05 89.8 1 11.4 2.01 97 3.2 12.9 2.12 79.6 2.1 10.6 1.77 184.1 6.5 12.1 1.7 248.9 2.1 10.8 1.75 198.9 6.5 12.3 1.72 226.2 2.1 11 1.75 198.9 6.5 12.5 1.75 198.9 2.1 11.2 1.76 191.2 6.5 12.7 1.78 177.5 2.1 11.4 1.77 184.1 6.5 12.9 1.81 160.2

Chong 1995 Experiment29

The material used in the experiment was 16/1’s yarn woven in a 2x1 twill with 78x50 construction. One standard dipping consisted of immersing the material into a leuco indigo dye bath for 1 minute followed by immediate air oxidation for 3 minutes. 5 successive dips were chosen as the standard procedure. After dyeing, the material was thoroughly rinsed and soaped at boil for 10 minutes in a soaping bath containing 1.5 g/l of Lissapol NX. The standard dye bath consisted of the following formula.

Indigo dye – 2 g/l Sodium dithionite – 6 g/l Caustic soda – 5 g/l Sandozin NI – 0.2 g/l The reduction of indigo dye was carried out at 80° C for 10 minutes.

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

Xin 2000 Experiment46

In 2000 Xin, Chong, and Tu studied the effects of indigo, caustic, and hydro concentrations, immersion time, and number of indigo dips on the depth of shade. They used a 100% cotton 7/1’s open end yarn loosely knitted into fabric as the dyeing substrate. The fabric was boiled for 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.

𝐼𝑛𝑡𝑒𝑔 = ∑ ∗E(𝑥 + 𝑦 +𝑧)

Equation 1-37: Calculation of Integ as a function of K/S values, average observer, and standard light source.46

Here: E λ spectral power distribution of illuminant and (x λ + y λ + z λ) is the standard observer function. As the maximum absorption wavelength shifts to less than 660 nm for samples with high shade depth, the Integ value was used instead of the traditional K/S values.

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.

Effect of Oxidization Time on Depth of Shade

20 K/S

10 30 60 90 120 150 180 Oxidization Time (sec)

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

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

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

Chong29 also investigated the effect of increasing immersion time on color depth. In figure 1-29, an immersion time of 30 seconds appears to be adequate. Prolonged immersion time does not increase the color depth because the oxidized indigo on the material may be re-reduced by the reducing agents present and causes desorption of the indigo. These two separate experiments support each other’s conclusions.

Effect of Immersion Time on Depth of Shade

20 K/S

10 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 8th dip the change in depth of shade significantly decreases but does continue to darken. Also notice the cast shifts from greenish dark blue to redder less blue shade as the number of dips increase.

Figure 1-30: Relationship between number of dips and shade.46

Since the color depth of indigo dyed yarns relies on the progressive build-up of color through successive dipping and oxidation, the number of dips is the prime factor determining the final color yield. As shown in figure 1-31, the optimum color yield is achieved after about 10 dips. Chong29 and Xin46 independently confirm the results.

Figure 1-31: Chong's relationship between number of dips and uncorrected K/S.29

1.5.2.e Dye Bath Concentration Effect of Indigo Dye Uptake

The effect of dye concentration was studied by immersing knitted fabric into the simulated 5 dip method with varying dye bath concentrations by Xin46. The first graph in figure 1-32 illustrates a rapidly decreasing L* value with increasing dye concentrations until ~2 g/l, after which the level of decrease lightness slows down and tends to level off. The cast shift is displayed in the second graph of figure 1-32 with the shade shifting more red and yellow as dye concentration was increased. The final graph in figure 1-32 confirms the increasing depth of shade trend as indigo dye bath concentration was increased.

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

Chong29 examined the effect of indigo dye bath concentration on color yield as shown in figure 1-33. The affinity of indigo dye is very low, as is its build-up property. Hence increased color depth cannot be achieved solely by increasing the dye concentration. In fact the color yield remains fairly flat after 3 g/l.

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.

Figure 1-34: pH effect of shade with other parameters held constant.46

Although the maximum Integ shade in graph 3 of figure 1-34 reveal that color yield is much greater for a dyeing conducted at pH 11 then it is for a dyeing conducted at pH 13, a more detailed picture is given in figure 1-35. At a given indigo on weight of yarn concentration, the color yield will be greater at lower pH. Maximum color yield occurs in pH range of 10.5 to 11.5 and decreases as the dye bath pH is increased. It was suggested that it is owing to the higher affinity and lower solubility of the monophenolate form of indigo present at this pH range.

Figure 1-35: K/S shade vs % indigo on weight of yarn at various pH’s30.

Etters & Hou have noted ring dyeing of cotton yarn can be caused by a high strike rate of the dye for the cotton fiber in the yarn surface, i.e. the dye exhausts rapidly onto the fibers in the outer zones of the yarn at the expense of fibers in the yarn interior. Vickerstaff has observed that "… the diffusion rate cannot indicate the actual progress of dyeing in the initial stages, as this is determined by the affinity of the dye. If two dyes are present in a binary mixture, the dye which is first adsorbed by the fiber is that having the higher affinity, irrespective of their relative diffusion rates."

Affinity or substantivity of a dye for a fiber can be expressed in terms of an equilibrium distribution coefficient or K, the ratio of concentrations of dye in fiber to dye in dye bath at equilibrium. Relatively high values of distribution coefficient indicate relatively high substantivity or affinity of the dye for the fiber. Figure 1-36 illustrates the ratio of dye in denim yarn to dye in an infinite indigo dye bath as given from 5 dip laboratory dyeings conducted at pH 11 and 13. These values may be regarded as technical quantities since they were not obtained under equilibrium conditions. Both pH ranges exhibit a linear relationship, but the slope of the lower pH line is much steeper. This data suggest that either the “affinity” of the dye for the fiber is much higher at the

67 lower pH or the diffusion of the dye into the fiber is much more rapid at the lower pH. Either way the distribution coefficients are much higher at lower pH values than at higher pH values.

Figure 1-36: Non-equilibrium Concentration of dye in fiber (g/100g) vs concentration of dye in bath (g/100g).20

Equilibrium sorption isotherms for indigo on cotton fiber were obtained at two dye bath pH ranges (11.1-11.3) and (13.1-13.3) from 8 hour dyeings. These isotherms show a large difference in technical parameters such as dye uptake, yarn penetration, and color yield. To clarify this point, the equilibrium sorption data are plotted in figure 1-37. The indigo uptake is significantly higher for the dyeings at the lower pH. Furthermore, the isotherms are not linear as were the non-equilibrium isotherms given in figure 1-36. For the experimental conditions used, no obvious approach to a limiting fiber saturation value is evident for dyeings at either pH range. The previously observed pH effect on dye uptake appears to be caused by a real difference in apparent affinity.

Figure 1-37: Equilibrium isotherm for dye concentration in dye bath and fiber (g/100g).20

When figure 1-37 is reconfigured on a logarithmic scale, an excellent linear correlation between equilibrium concentration of dye in the fiber and dye in the dye bath is obtained as shown in figure 1-38. This indicates that equilibrium sorption in both pH’s are effectively described by the Freundlich isotherm20. A Freundlich isotherm is characterized by the power function or linear relationship on log by log scale.

Figure 1-38: Logarithmic plot of equilibrium isotherms for dye concentration.20

The mean technical distribution coefficient is calculated by dividing the indigo concentration in yarn by indigo concentration in dye bath. In figure 1-39 the relationship between dye bath pH and technical distribution coefficient, K, and the coefficient of variation of %CV are given. The technical distribution coefficient decreases with increasing pH and the %CV increases. This means substantivity associated with ring dyeing and color yield become more variable with increasing pH. Although this information is based on laboratory dyeings according to Etters30, the results from commercial dyeings tend to confirm the constancy of substantivity of indigo for denim yarn when dye bath pH is maintained within the range of 10.8 to 11.2.

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

2 expression derived by Etters, K/S = at[Cf/(2p – p )]; where at is the true value of the reflectance absorptivity coefficient, i.e., the value for uniform distribution of dye in the yarn cross-section, Cf is the concentration of dye in the yarn, and p is the fractional penetration of fixed dye in the yarn cross-section. This equation will hold approximately unless a severe concentration gradient exists within the dyed ring or colorant layer becomes translucent. The values of p have been roughly estimated by microscopy to be 0.65, 0.33, 0.20, and 0.20 for pH ranges 13, 12, 11, and 10 respectively33.

Etters' equation makes use of the true reflectance absorptivity coefficient. However in practical indigo dyeing processes true reflectance absorptivity coefficients must be replaced by apparent coefficients. The relationship between apparent reflectance absorptivity coefficient and dye bath pH is illustrated in figure 1-40. As the dye bath pH decreases from 13 to 11 there is more ring dyeing and an increasing apparent reflectance absorptivity coefficient. It has been found that between pH 10.8 and 11.2, the greatest color yield is achieved.

Figure 1-40: Apparent reflectance absorptivity coefficient vs pH.30

Figure 1-41 illustrates the apparent reflectance absorptivity coefficients of figure 1-40 plotted as a function of the technical distribution coefficients with additional data points added from other dye bath pH’s. As the distribution coefficient increases, the color yield also increases. It may be concluded from figure 1-41 that the yarn ring dyeing phenomenon is highly correlated with increasing substantivity and strike of indigo for cotton fiber that is associated with lower pH dye baths. The fact that the apparent reflectance absorptivity coefficients found in these 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

Etters15 proposed the effect of pH on distribution coefficient and apparent absorptivity coefficient is due to the ionized form of the dye molecule in the dye bath. The fraction of reduced indigo that exists as the mono-ionic form is given by equation 1-38.

𝑀𝑜𝑛𝑜𝑖𝑜𝑛𝑖𝑐 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 =

Equation 1-38: Mono-ionic fraction form of indigo dye as a function of pH.15

15 Here pK1 and pK2 are the pKa values associated with the two step ionization of reduced indigo . Mean values of mono-ionic form are plotted in figure 1-42 as a function of dye bath pH. It is noted above pH 11.5 the fraction of indigo that exists as a mono-anion begins to drop off rather severely and continues to decrease as pH increases. This is due to more of the mono-ionic form ionizing further to produce the more soluble di-ionic form. At dye bath pH of 12.7 about half of the indigo exists as mono-ionic and half has di-ionic form.

Figure 1-42: Relationship of Mono-ionic species of indigo and pH.30

The mean technical distribution coefficients are plotted as a function of the mean fraction of reduce indigo that exists as a mono-ionic form at various dye bath pH’s, figure 1-43. There is an exceptionally high linear correlation between the substantivity of indigo for cotton fiber and the fraction of indigo that exists in mono-ionic form. Etters15 concluded that the mono-ionic form of indigo has a much higher substantivity for cotton fiber then does the di-ionic form.

Figure 1-43: Relationship between mean technical distribution coefficient and fraction of indigo existing as mono-ionic form.30

Recall reduced indigo can exist in two forms: monophenolate ion or biphenolate ion. Shade depth for a given amount of fixed dye is shown to be highly correlated with the fractional amount of indigo that exists as a monophenolate ion in dye bath. The correlation is explained as an increased apparent affinity of the mono anion form. As the affinity increases, the strike rate of the dye for the yarn surfaces increases, leading to a more ring dyed yarn.

It is readily seen that the fractional amount of the mono-ionic form is maximum near the region of maximum reflectance absorptivity. By converting the apparent reflectance absorptivity into a fractional form and superimposing on top of the fractional amount of mono-ionic form as a function of pH, the relationship becomes clearer, figure 1-44. Only at low pH values does this

75 relationship break down. This can be explained by the superficial staining of the yarn by the acid leuco form (II). Based on these results, it is reasonable to postulate that the mono-ionic form is the principal species absorbed by the cotton. Or at least mono-ionic form has the highest apparent affinity for cotton.

Figure 1-44: Correlation of fractional distribution of apparent absorptivity coefficient and mono-ionic form of indigo as a function of pH.15

1.5.2.g Interrelationship of Dye Concentration and pH on Shade

Given the strong effect dye bath concentration and pH independently have on the resulting dye uptake, penetration, and shade; a more in-depth discussion is warranted. Figure 1-45 demonstrates the mean indigo concentration in the dye bath needed to produce a given shade depth (K/S) at various dye bath pH values. For example the indigo concentration required to produce a rather dark shade (K/S = 100) is about 3 g/l at pH 12.5. But only 1 g/l of indigo in dye bath is required to produce the same shade depth at pH 11.0. This is the result of dye distribution within the cross section of yarn.

Figure 1-45: Indigo concentration in dye bath required to produce a given shade depth at various pH’s from a 5 dip laboratory dyeing30.

When the dye uptake data is plotted vs. dye bath pH, the following relationship develops, figure 1-46. It is shown the maximum uptake at a particular pH depends on the concentration of dye in the dye bath. Maximum uptake occurs between pH 9.25 – 10.5. As the concentration of dye in the dye bath increases the maximum uptake occurs at lower and lower pH values within the specified range. It could be that all of the dye extracted from the knitted yarn tube was not in fact

“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.

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.

Figure 1-48: Corrected depth of shade as a linear function of indigo concentration in yarn and dyebath pH.15

Since less indigo dye bath concentration is required at lower pH values to achieve a desired shade, less indigo is washed off of the yarn at the conclusion of dyeing. In figure 1-49 the concentration of unfixed indigo has been estimated by Etters30 as a function of both concentrations of dye in the dye bath and dye bath pH. As the dye bath pH decreases, the amount of oxidized indigo that is trapped between the fibers in the denim yarn is decreased. Therefore, less dye is available to be washed off of the yarn.

Figure 1-49: Estimated concentration of unfixed indigo on yarn at corresponding dye bath concentration and pH.30

1.5.2.h Empirical indigo dye model

The Holy Grail for indigo dyers worldwide would be a dye model relating indigo on weight of yarn and shade to various controllable dye range parameters. This one equation has not yet been derived. But an empirical model based on a 5 dip laboratory experiment has been proposed by Etters21. In this model the dye bath indigo concentration and pH is used to predict the distribution coefficient, indigo on weight of yarn, and subsequently the final yarn shade.

The empirical model is based on the Southeastern Section15 and Annis research19. The data obtained from both investigations is based on 5 dip, 15 second immersions of knitted denim yarn tubes as previously outlined. By analyzing these two data sets, Etters21 developed the following mathematical model.

The technical distribution coefficient, K, is defined in equation 1-39 to equal the concentration of dye in the fiber, Cf, divided by the concentration of dye in the dye bath, Cb. The concentrations are expressed in terms of grams of dye per 100 grams of fiber or water.

𝐾=

Equation 1-39: Definition of technical distribution coefficient.21

A regression analysis explains 86% of the variability of K in terms of the variability of pH and the relationship was defined in equation 1-40.

𝐾=𝑎+𝑏(𝑝𝐻)

Equation 1-40: Approximation for the technical distribution coefficient as a function of dye bath pH.21

Here the components are defined: a = 0.9623 and b = -0.000331.

Given the pH and dye concentration of the dye bath, one can calculate the technical distribution coefficient, K, and subsequently the dye concentration in the fiber, Cf.

The second part of the empirical model is based on the relationship between pH and the apparent reflectance absorptivity coefficient, a. Recall K/Scorr = a Cf. A regression analysis explains 94% of the variability of apparent reflectance absorptivity in terms of variability around pH. The empirical model for apparent reflectance absorptivity coefficient was defined by Etters in equation 1-41.

𝑎=𝑒

Equation 1-41: Empirical model of apparent reflectance absorptivity coefficient.21

Here i=-46.3280, b=6.4373, c=0.4733, d=-0.0905, and e=0.0030.

Given the dye bath pH one can calculate the apparent absorptivity coefficient, a. Using the calculated value for a and Cf, one can estimate the shade of the dyed fabric in terms of K/Scorr.

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.

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. Chong29 and Xin46 have demonstrated the significant effect immersion times less than 30 seconds have on the resulting shade. Any indigo dyer with immersion times different than 15 seconds must proceed cautiously when applying Etters’ relationships.

The vast majority of indigo dyed cotton experiments have been conducted with simulated 5 dip dye range set-up. While 5 dip dyeing may represent a significant amount of the denim yarn dyed, it is certainly not the only set-up. In fact the majority of denim shade spectrum produced falls within the 2 to 8 dip range. Once again, Chong29 and Xin46 have demonstrated the significant affect number of dyes has on the resulting shade. Since indigo dye uptake and/or degree of penetration

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.

2 Objectives of the Present Investigation

Although there is a long history of dyeing denim yarn with indigo, the process of dyeing with indigo still remains largely an art and not a science. - Zhou48

In an ideal world to investigate the effect of yarn count, number of dips, immersion time, dye bath pH, speed, and dye bath concentration on yarn uptake of dye and the resulting shade; a systematic design of experiment would be conducted. At last, this researcher has yet to find a denim manufacture willing to “blindly” produce a million+ yards of denim fabric that would be required for such an experiment. As a result, an indigo-cotton dye observational study is proposed that would gather key processing parameters and yarn samples during "actual indigo dyeing” process. It is hoped the resulting data and relationships provide more refined insight into the indigo-cotton dye system.

By processing yarn skeins through an actual indigo dye range it is put forth many of the issues surrounding laboratory experiments will be avoided. While certain dye parameters cannot be controlled by the experimenter, others can actually be more easily manipulated. Furthermore, careful selection of various production shades should yield adequate variation in the dyeing parameters to produce reliable results.

For each set of skeins processed, the following dye range set-up conditions were monitored.

1. Date and time skeins were processed. 2. Production shade number, dye range, and location. 3. Production yarn count and total number of ends per ball 4. Production indigo, caustic, and hydro feed rates to the dye range. 5. Dye range speed 6. Immersion time (dye dwell time) 7. Sky time (oxidation time) 8. Chemical checks made by the technician (g/l of indigo, mV potential, vatometer, pH, and % alkalinity. 9. Yarn count of skeins and the sequence of dye boxes that they were processed through.

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.

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.

%𝐵𝑜𝑖𝑙 𝑜𝑓𝑓 𝐿𝑜𝑠𝑠=

Equation 3-1: Calculation of %Boil off Loss.

Given the boil-off and dyed weight, the total percent chemical on weight of yarn (%COWY) was calculated according to equation 3-2. Note this was the total chemical amount on weight of yarn after dyeing. This number has fixed and unfixed indigo dye as well as residual sodium hydroxide and other salts resulting from oxidation.

%𝐶𝑂𝑊𝑌 =

Equation 3-2: Calculation of %COWY.

The skeins were washed in the laboratory using warm water of ~40°C. Washing of the yarn skeins was necessary to simulate dye range set-up and remove unfixed dye and chemical residuals from the yarn. Each skein was passed under running water until the water was clear of color. The final washed percent indigo on weight of yarn (%IOWYwash) was calculated by dividing the difference between Washed weight and Boil-off weight by the Boil-off weight, equation 3-3.

%𝐼𝑂𝑊𝑌 =

Equation 3-3: Calculation of %IOWYwash.

The final method used to determine %IOWY after the yarn skeins had been washed was Spectrophotometric Methyl Pyrrolidinone extraction. This method was ultimately chosen for later

91 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:

∗. %𝐼𝑂𝑊𝑌 = %

Equation 3-4: Calculation of %IOWY by Methyl Pyrrolidinone extraction.

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.

% %𝐼𝑂𝑊𝑌 = %

Equation 3-5: Calculation of %IOWY in terms of 100% Indigo paste from Methyl Pyrrolidinone extracts.

The next response variable was a calculation based on the actual shade of the dyed and washed yarn skein. The relationship K/S shade was expressed as a function of the % reflectance of the dyed sample minus the % reflectance of a mock sample at various wavelengths. The mock sample was the same yarns as the dyed sample processed the same way except without any actual indigo dye involved. Of course all mock dyed samples were created in the laboratory by padding dye bath chemicals minus the indigo on the yarn skeins. The mock dyed yarn % reflectance values are referenced in appendix section A-3-1. Higher values indicate a “darker” shade or in this case greater transfer of indigo during the dyeing process. Lower K/S values correspond to lighter shades with less dyed on weight of yarn and/or more penetration into the yarn structure. The equation for

K/S was given in equation 3-6. The %reflectance values were measured on a Hunterlab ColorQuest XE running on Gretag-Macbeth SLI-Form software.

( % ) ( % ) = − ∗ % ∗ %

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

To ensure accurate and repeatable shade measurements the yarn skeins were wrapped around a white plastic board 6 centimeters wide. By pulling the yarns tight during the wrapping process, the individual yarns were straight without any knots or twists and parallel to one another. The shade was measured with a 1 inch port on the spectrophotometer. The shade software automatically averages three individual readings. By moving the yarn skein between individual readings the average % reflectance was calculated. Furthermore each dyed yarn skein was measured on three separate occasions. The three separate readings were later averaged in Microsoft's Excel spreadsheet which resulted in the % reflectance values at each wavelength representing nine different readings.

To represent the total shade over many wavelengths in one number, the value of Integ has been developed. As pointed out by Xin46 the Integ value has greater importance when evaluating shade over a wide range of depths as the maximum absorption wavelength tends to shift at greater depths of shade. In equation 3-7, Eλ equals the spectral power distribution of the illuminant. The xλ

+ yλ + zλ function was the standard observer function. All shade evaluations were conducted using D65 illuminant with a 10° observer.

𝐼𝑛𝑡𝑒𝑔 = ∑ ∗E(𝑥 + 𝑦 +𝑧)

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

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 Values by Wavelength for Typical 3.0 gm/lit Indigo Dye Set-up 50.0 45.0 40.0 35.0 30.0 25.0 20.0 15.0 K/S shade value 10.0 5.0 0.0 400 450 500 550 600 650 700 Wavelength (nm)

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

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 and K/S Shade at 580nm and 660nm vs %IOWY 120.0

100.0

80.0

60.0

40.0

Integ or K/S Shade Value 20.0

0.0 0.000% 0.500% 1.000% 1.500% 2.000% 2.500% 3.000% 3.500% %IOWY

580nm 660nm Integ

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.

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.

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.

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 R2 value of 0.025. This low correlation was due to the high variability around the average value at each evaluated time and the relative low time dependence. This does not necessarily mean time doesn't play a significant role in %Boil-off loss but instead the affect of time could be over shadowed by other parameters.

Relationship of Time on %Boil-off Loss during Laboratory Preparation 4.00%

3.50%

3.00%

2.50%

2.00%

1.50% %Boil-off Loss

1.00% R² = 0.025 0.50%

0.00% 20 25 30 35 40 Time (minutes)

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

The effect of sodium hydroxide concentration in the boil off box is illustrated in figure 3-4. As with time, sodium hydroxide concentration causes a slight increase in %Boil-off loss as the concentration was increased. Unlike time, sodium hydroxide appears to reach a plateau at ~11 g/l.

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 R2 value of 0.148. Again the low correlation was due the high variability of %Boil-off loss at various levels of sodium hydroxide concentration.

Relationship of Sodium Hydroxide Concentration on %Boil-off Loss during Laboratory Preparation 4.00% 3.50% 3.00% 2.50% 2.00% 1.50% %Boil-off Loss 1.00% R² = 0.148 0.50% 0.00% 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 R2 value was 0.687 which indicates a fairly strong single parameter correlation. Furthermore, the degree of change was rather large with 1.25% at 76°C and increasing to 2.75% at 100°C. This means the %Boil-off loss more than doubles over the range of temperatures evaluated.

102

Relationship of Temperature on %Boil-off Loss during Laboratory Preparation 4.00% 3.50% 3.00% 2.50% 2.00% 1.50% %Boil-off Loss 1.00% R² = 0.687 0.50% 0.00% 70 75 80 85 90 95 100 Temperature (C)

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.

103

Interaction Profiles%Boil-off Loss Interaction Profile 0.04 40 40 0.03 20 20 Time Time 0.02 % Boil- off Loss (min) 0.01

0.04 Temperature 100 0.03 100 Temperature 0.02 % Boil- off Loss 76 (C) 76 0.01 0.04

15 NaOH 0.03 15 0 0 NaOH 0.02 % Boil- off Loss (g/l) 0.01 0 5 20 25 30 35 40 80 85 90 95 10 15 100 Figure 3-6: Interaction profile for time, temperature, and sodium hydroxide concentration on %boil-off loss during laboratory preparation process

The interaction profile does however illustrate that time and sodium hydroxide concentration independently can play a major role in %Boil-off loss even though the R2 values from figures 3-3 and 3-4 were very low. For example, the lower left hand graph of %Boil-of loss as a function of time and sodium hydroxide concentration shows a change in time and sodium hydroxide concentration causes a linear change in %Boil-off loss. Specifically, as the sodium hydroxide concentration was held constant at 0 g/l, the increase in time causes a linear increase in %Boil-off loss. The upper right hand graph shows that as time was held constant an increase in sodium hydroxide concentration causes a non-linear increase in %Boil-off loss. Graphical depictions of single parameter affects on %Boil-off loss highlight these detailed changes in the overall variation of the experiment. A more rigorous analysis was needed to determine the significance of each parameters affect on %Boil-loss.

An ANOVA analysis of time, temperature, and sodium hydroxide concentration on %boil-off revealed the statistically significant parameters as well as created a model to predict %Boil-off loss as a function of those parameters. Table 3-4 summarizes the ANOVA analysis results after removing

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 R2 value for second order trend curve was higher than a linear trend line. The summary of fit produces a R2 of 0.89 for this model compared to the actual data points. Furthermore the analysis of variance calculates a P-value less than 0.0001 for this model. Both values indicate high correlation and significance for the model compared to actual data points.

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

The model was constructed using the estimates from the parameter estimates section in table 3-4, equation 3-9.

%𝐵𝑜𝑖𝑙 − 𝑜𝑓𝑓𝐿𝑜𝑠𝑠 =−1.634𝑒 ∗(𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒−88.03) + 7.41𝑒 ∗𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒+ −6.683𝑒 ∗(𝑁𝑎𝑂𝐻−7.64) + 4.69𝑒 ∗ 𝑁𝑎𝑂𝐻 + 1.942𝑒 ∗ 𝑡𝑖𝑚𝑒 − 0.05178

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

105

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.

%Boil-off Loss Prediction Profile for Laboratory Preparation Process % Boil- off Loss off ±0.00233 0.030211 0 5 20 25 30 35 40 75 80 85 90 95 10 15 100

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

3.2.2 Analysis of Laboratory Preparation Time, Temperature, and Sodium Hydroxide Concentration Affect on %IOWY after One and Six Dip Indigo Dyeing Conditions

The %IOWY after one and six dips of indigo as a function of time was illustrated in figure 3-8. Inspection of one dip dyeing represented by X's and solid trend line, showed poor correlation which is statistically supported by the low second order polynomial R2 value of 0.046. While the correlation coefficient was obviously very low the general trend was an increasing %IOWY value

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 R2 value of 0.034. As with one dip, the %IOWY after six dips as a function of time appears to reach a critical value at 32 minutes. Further increases in time result in slightly lower %IOWY. While the effect of time appears to have more importance at one dip, the same effect can be seen after six dips. The time affect was highly variable, particularly after one dip, and thus difficult to draw immediate conclusions on the role time plays in the laboratory preparation procedure.

Effect of Time on %IOWY from One and Six Dips of Indigo 0.400% 2.500% R² = 0.034 0.350% 2.000% 0.300%

0.250% 1.500% R² = 0.046 0.200% 0.150% 1.000% %IOWY (six dips) %IOWY (one dip) 0.100% 0.500% 0.050% 0.000% 0.000% 20 25 30 35 40 Time (minutes) 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 R2 value of 0.086. Increasing sodium hydroxide concentration resulted in increasing %IOWY until 9 g/l. Further increases in concentration resulted in decreased %IOWY as

107 illustrated in figure 3-9. For six dips the best curve fit was described as essentially constant with a R2 value of 0.037. Again, the poor correlation was due to high variability in the data points and limited effect sodium hydroxide concentration during the laboratory preparation process played in %IOWY.

Effect of Sodium Hydroxide Concentration on %IOWY from One and Six Dips of Indigo 0.400% 2.500% R² = 0.037 0.350% 2.000% 0.300%

0.250% 1.500% R² = 0.086 0.200% 0.150% 1.000% %IOWY (six dips) %IOWY (one dip) 0.100% 0.500% 0.050% 0.000% 0.000% 0 2 4 6 8 10121416 Sodium Hydroxide Concentration (g/l) One Dip Six Dips

Figure 3-9: Relationship of sodium hydroxide concentration during laboratory preparation on %IOWY from one and six dips of indigo dye

The effect of temperature during laboratory preparation had a major impact on %IOWY. After one dip of indigo the best curve fit was by a second order polynomial with a R2 value of 0.708. After six dips of indigo the second order polynomial R2 value was 0.743. The same general trend was seen after one and six dips of indigo. Under both dyeing conditions as the temperature was increased from 76°C, the %IOWY increased. The maximum %IOWY occurred at 94°C as shown in figure 3-10. Furthermore, the change in %IOWY appears to flatten out at 94°C. The data points indicate temperatures higher then 95°C do not produce a true change in %IOWY. Also notice the

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

Effect of Temperture on %IOWY from One and Six Dips of Indigo 0.400% 2.500% R² = 0.743 0.350% 2.000% 0.300% R² = 0.708 0.250% 1.500% 0.200% 0.150% 1.000% %IOWY (six dips) %IOWY (one dip) 0.100% 0.500% 0.050% 0.000% 0.000% 70 75 80 85 90 95 100 Temperature (°C) One Dip Six Dips

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.

109

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

(min) (min)

(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.

%𝐼𝑂𝑊𝑌 = −7.312𝑒 ∗(𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒−88.29) + 8.425𝑒 ∗ 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 + 1.0𝑒 ∗ 𝑡𝑖𝑚𝑒 + 2.345𝑒 ∗ 𝑁𝑎𝑂𝐻 − 0.05075

Equation 3-10: %IOWY as a function of time, temperature, and sodium hydroxide concentration after one dip of indigo.

This equation was used to build the prediction profiler graphs shown in figure 3-12. These curves finally illustrate the significance of temperature during laboratory preparation on %IOWY. They also show the low dependence of %IOWY on time and sodium hydroxide concentration. The 95% confidence intervals were also calculated and plotted as blue dotted curves. The best overall combination yields confidence intervals of ±0.0896% with a mean value of 0.2946% indigo on weight of yarn.

111

%IOWY Prediction Profile on One Dip of Indigo for Laboratory Preparation Process %IOWY 0.002946 ±0.000895 0 5 20 25 30 35 40 75 80 85 90 95 10 15 100

Time (min) Temperature (C) NaOH (g/l) Figure 3-12: %IOWY for one dip of indigo model as a function of time, temperature, and sodium hydroxide concentration in laboratory preparation process

A full ANOVA analysis was conducted on %IOWY after six dips of indigo by time, sodium hydroxide concentration, and temperature during laboratory preparation. The results are presented in table 3-6. Just like one dip of indigo the parameter estimates indicate the first and second order term of temperature were statistically significant with P-values of ≤0.0001 and 0.0148 respectively for six dips of indigo. Time and sodium hydroxide concentration were left in the model calculations even though each was determined to be insignificant. The summary of fit for the model was calculated to be R2 of 0.76 and the analysis of variance had a P-value of 0.0006. Both indicate the model was a good fit and statistically significant compared to the data used to create the model.

112

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

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

%𝐼𝑂𝑊𝑌 = −1.386𝑒 ∗(𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒−87.78) + 1.901𝑒 ∗ 𝑡𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒 + 2.64𝑒 ∗ 𝑡𝑖𝑚𝑒 + 3.081𝑒 ∗ 𝑁𝑎𝑂𝐻 + 0.0032114

Equation 3-11: %IOWY as a function of time, temperature, and sodium hydroxide concentration after six dips of indigo.

This equation was also graphically represented in figure 3-13. These curves finally illustrate the significance of temperature on %IOWY. They also show the low dependence of %IOWY on time and sodium hydroxide concentration. The 95% confidence intervals are at minimum value when time equals 30 minutes based on the blue dotted confidence curves. The best overall combination yields confidence intervals of ±0.1654% with a mean value of 2.143% IOWY. While the magnitude of confidence intervals for six dips of indigo is two times greater than one dip, the mean %IOWY at six dips is almost ten times greater than one dip. Therefore, the overall confidence after six dips of indigo is actually greater than after one dip of indigo.

113

%IOWY Prediction Profile on Six Dips of Indigo for Laboratory Preparation Process %IOWY 0.021429 ±0.001654 0 5 20 25 30 35 40 75 80 85 90 95 10 15 100

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

Figure 3-13: %IOWY for six dips of indigo model as a function of time, temperature, and sodium hydroxide concentration in laboratory preparation process

3.2.3 Analysis of Laboratory Preparation Time, Temperature, and Sodium Hydroxide Concentration Affect on Integ Shade Value after One and Six Dip Indigo Dyeing Conditions

The general trend for time's effect on Integ shade value from both one and six dip dyeings is shown in figure 3-14. After one dip of indigo, increasing boil-off time caused the Integ shade value to increase which indicates the indigo color became darker. The trend has an overall R2 value of 0.245 which indicated a poor overall correlation. The general trend is for constant Integ shade value from 20 minutes till 30 minutes. At 30 minutes a high degree of variability exists in Integ shade value. Further increases in time result in increased Integ shade values.

During six dips of indigo dyeing, time had the opposite effect on Integ shade value as reflected in figure 3-14. As the time increased the Integ shade value decreased indicating the indigo color becomes lighter. The trend has an overall R2 value of 0.021 which indicates a very poor overall correlation. Over the entire time span the Integ shade value ranged from 91 at 37 minutes to 101 at 30 minutes. This is a change of 10 Integ shade value units or less than 10%. The general trend for Integ as a function of time after six dips of indigo dyeing is that of constant value. Neither the one

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

Effect of Time on Integ from One and Six Dips of Indigo 105.0 34.0 R² = 0.021 100.0 32.0

30.0 95.0

28.0 90.0 26.0 Integ (six dips) Integ (one dip) 85.0 24.0 R² = 0.245 80.0 22.0

20.0 75.0 20 25 30 35 40 Time (minutes) One Dip Six Dips

Figure 3-14: Relationship of laboratory preparation time on Integ shade value from one and six dips of indigo dye

Next sodium hydroxide concentration during laboratory preparation was evaluated after one and six dips of indigo. Both dyeing conditions exhibited a plateau as the sodium hydroxide concentration was increased. Figure 3-15 shows the apex is approximately 6 g/l for one dip and 11 g/l for six dips. Continued increasing concentration levels beyond these values resulted in decreasing Integ values for both dip conditions. However, both dyeing conditions exhibited poor correlation as reflected in the R2 values of 0.187 and 0.182 for one and six dips respectively. The poor correlation can be explained by the relatively small change in Integ values over a wide range of concentrations coupled with the high variability associated with each concentration. At 7.5 g/l concentration the variability of Integ shade value dramatically increased compared to lower

115 concentrations. As the concentration is further increased the variability appears to reduce while the overall Integ shade value also decreased.

Effect of Sodium Hydroxide Concentration on Integ from One and Six Dips of Indigo 105.0 34.0 R² = 0.182 100.0 32.0

30.0 95.0

28.0 90.0 26.0 Integ (six dips) Integ (one dip) 85.0 24.0 R² = 0.187 80.0 22.0

20.0 75.0 0 2 4 6 8 10121416 Sodium Hydroxide Concentration (g/l) One Dip Six Dips

Figure 3-15: Relationship of sodium hydroxide concentration during laboratory preparation on Integ shade value after one and six dips of indigo dye

Unlike previous %IOWY analysis, temperature doesn't play a major role in Integ shade value variation. After one dip of indigo, the general trend was increased Integ shade as the temperature was increased from 88°C to 100°C. However the changes in Integ shade values were small and the overall R2 correlation was low at 0.122 as shown in figure 3-16. After six dips of indigo the general trend was decreased Integ shade as the temperature was increased from 88°C to 100°C. However, the changes in Integ shade values were small and the overall R2 correlation was low at 0.015 as shown in figure 3-16. At 88°C the variability increased considerably under both one and six dip dyeing conditions and appears to decrease as the temperature is increased. Like the other two parameters, temperature has a high degree of variability so a detailed ANOVA analysis was needed to confirm insignificance.

116

Effect of Temperture on Integ from One and Six Dips of Indigo 105.0 34.0 100.0 32.0 R² = 0.015 30.0 95.0

28.0 90.0 26.0 Integ (six dips) Integ (one dip) R² = 0.122 85.0 24.0 80.0 22.0

20.0 75.0 70 75 80 85 90 95 100 Temperature (°C) One Dip Six Dips

Figure 3-16: Relationship of temperature during laboratory preparation on Integ shade value after one and six dips of indigo dye

The full ANOVA analysis involving first and second order plus interactions of parameters was shown in table 3-7 for one dip indigo dyeing condition. The P-values calculated in parameter estimates shown no statistically significant effect for all values except the intercept which of course was meaningless. This conclusion was further supported by relatively low R2 in the summary of fit and high P-value in analysis of variance results. As a result, the Integ shade value from one dip of indigo was not used to optimize the laboratory preparation procedure.

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 R2 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

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

Since time, temperature, and sodium hydroxide concentration were determined to have insignificant effect on Integ shade value and penetration factor is a function of Integ shade value and %IOWY, this researcher expects the penetration factor to have the same relationship as the inverse of %IOWY. For completeness, the full analysis was presented. First, notice a high degree of variability in the penetration factor presented in figure 3-17 after one dip of indigo. The extremely low levels of %IOWY at shorter times produced high penetration factor values. With all data points the R2 correlation was very low at 0.088. If the single point at 1200+ penetration factor was removed, the function was flat with R2 of 0.057. Time doesn't appear to affect penetration factor after one dip of indigo.

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 R2 correlation was very low at 0.03 and is basically constant over all times.

Effect of Time on Penetration Factor from One and Six Dips of Indigo 1400.00 70.00

1200.00 60.00 R² = 0.03 1000.00 50.00

800.00 40.00

600.00 30.00

400.00 20.00 R² = 0.088 200.00 10.00 Penetration Factor (one dip) Penetration Factor (sex dips) 0.00 0.00 20 25 30 35 40 Time (minutes) One Dip Six Dips

Figure 3-17: Relationship of time during laboratory preparation on penetration factor after one and six dips of indigo dye

The same observations can be made in regards to sodium hydroxide concentration influence on penetration factor after one and six dips of indigo. Very poor correlation exists as illustrated in figure 3-18 with R2 values of 0.094 and 0.011 for one and six dips respectively. If the 1200+ penetration factor value was removed, the resulting trend after one dip of indigo was flat with a R2 value of 0.049. Sodium hydroxide concentration doesn't have a major affect on penetration factor.

120

Effect of Sodium Hydroxide Concentration on Penetration Factor from One and Six Dips of Indigo 1400.00 70.00

1200.00 60.00 R² = 0.011 1000.00 50.00

800.00 40.00

600.00 30.00

400.00 20.00

R² = 0.094 Penetration Factor (six dips) Penetration Factor (one dip) 200.00 10.00

0.00 0.00 0 2 4 6 8 10121416 Sodium Hydroxide Concentration (g/l) One Dip Six Dips

Figure 3-18: Relationship of sodium hydroxide concentration during laboratory preparation on penetration factor after one and six dips of indigo dye

The temperature effect on penetration factor after one and six dips of indigo was discussed. Under both indigo dyeing conditions the penetration factor decreased as the temperature was increased, figure 3-19. This was the opposite trend as shown for %IOWY as a function of temperature, refer back to figure 3-10. After one dip the general trend in figure 3-19 isn't as pronounced due to the greater variation in penetration factor values which was reflected in the R2 value of 0.246. However, after six dips the general trend has a much stronger correlation as reflected in the R2 value of 0.729. Both dyeing conditions exhibit reduce variation as the temperature is increased. The penetration factor reaches the minimum value at approximately 95°C and does not vary further as temperature continues to increase.

121

Effect of Temperture on Penetration Factor from One and Six Dips of Indigo 1400.00 70.00

1200.00 60.00

1000.00 R² = 0.729 50.00

800.00 40.00

600.00 30.00

400.00 20.00 Penetration Factor (six dips)

Penetration Factor (one dip) 200.00 10.00 R² = 0.246 0.00 0.00 70 75 80 85 90 95 100 Temperature (°C) One Dip Six Dips

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.

122

P.F. Interaction Profile for One Dip P.F. Interaction Profile for Six Dips Interaction Profiles Interaction Profiles 60 250

200 Time 55 Time 150 Time 50 Time 20 20 P.F. 40 40 P.F. 40 40 100 (min) 20 20 45 (min) 50 40

Temperature 60 Temperature 250 76 76 75 75 200 55 150 Temperature 50 Temperature 102.5

P.F. P.F. 102.5 100 100 (C) 100 45 (C) 50 40 60 250 200 NaOH 55 NaOH 150 NaOH 50 15 NaOH

P.F. P.F. 0 150 15 45 150 100 0 (g/l) (g/l) 50 40 0 5 0 5 20 25 30 35 40 80 85 90 95 10 15 20 25 30 35 40 75 85 95 10 15 100 105 Figure 3-20: Interaction profile for time, temperature, and sodium hydroxide concentration on penetration factor after one and six dips of indigo dye

The full ANOVA analysis results after one dip of indigo were shown in table 3-9. The parameter estimates with statistical significance was determined to be first and second order temperature represented by P-values of 0.0021 and 0.0293 respectively. The R2 of 0.68 and P-value of 0.0050 for the complete model indicate reasonable agreement that was statistically significant to the actual data points. While the overall agreement was lower than for %IOWY, this was somewhat expected given the greater degree of variability especially with the 1200+ penetration value.

Table 3-9: ANOVA analysis results for laboratory preparation parameters on penetration factor from one dip of indigo

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

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

Figure 3-21: Penetration factor for one dip of indigo model as a function of time, temperature, and sodium hydroxide concentration in laboratory preparation process

The full ANOVA analysis results after six dips of indigo were shown in table 3-10. The parameter estimates with statistical significance was determined to be first and second order temperature represented by P-values of 0.0001 and 0.0171 respectively. The R2 of 0.75 and P-value of 0.0007 for the complete model indicated reasonable agreement that was statistically significant to the actual data points. However, the overall agreement was less than previous %IOWY analysis.

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

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

Figure 3-22: Penetration factor for six dips of indigo model as a function of time, temperature, and sodium hydroxide concentration in laboratory preparation process

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

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

% 0.03 0.025 0.02

0.030211 0.015 Boil-off Loss red Formula P # 0.02 0.015 0.01

0.002823 0.005 IOWY By Dip By IOWY Pred Formula 0 % 1 0.75 0.363667 0.25 Desirability 0 0 5 1 6 0 1 20 25 30 35 40 75 80 85 90 95 10 15 0.5 100 0.25 0.75 30 100 11 1 TimeTime (min) TemperatureTemperature (C) NaOHNaOH (g/l) Dip # Desirability 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.

128

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

% 0.03 0.025 0.02

0.030211 0.015 Boil-off Loss red Formula P # 0.02 0.015 0.01

0.021231 0.005 IOWY By Dip By IOWY Pred Formula 0 % 1 0.75 0.964286 0.25 Desirability 0 0 5 1 6 0 1 20 25 30 35 40 75 80 85 90 95 10 15 0.5 100 0.25 0.75 30 100 11 6 TimeTime (min) TemperatureTemperature (C) NaOHNaOH (g/l) Dip # Desirability Figure 3-24: Optimized laboratory preparation parameters incorporating prediction profiles from %Boil-off loss and %IOWY from six dips of indigo dye

Additional observations made during the experiment were controlling the temperature of the solution was the most difficult of the three factors. The time and sodium hydroxide concentration were the easiest. Temperature levels of 100°C were easily maintained at atmospheric conditions by just maintaining a slow boil in the preparation bath. Combining the above comments with the results from the analysis of one and six dip indigo dyed skeins yields the following optimum laboratory preparation procedure. These specific laboratory preparation parameters were used on all following trials.

Time: 30 minutes

Temperature: 100°C

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

129

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

In 1991 Etters20 published equilibrium sorption curves for %IOWY as a function of dye bath concentration and pH. Unfortunately this data did not contain shade information. With the 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 Etters20. Namely the %IOWY follows a Freundlich isotherm or power relationship between %IOWY and dye bath concentration at different dye bath pH values. Also note the %IOWY was independent of the yarn count. In figure 3-25 the equilibrium sorption data at pH ranges 13.1 to 13.3 were illustrated. The "X" marks were Etter's 1991 data points. The other points were 6.3/1, 7.1/1, 8.0/1, and 12.0/1 yarn count data from current equilibrium sorption experiment. The curve fit was Etter's 1991 data points extended above and below the original data range to encompass the range of current values.

132

Equilibrium Sorption Relationship at 13.1 to 13.3 pH 100.00%

10.00%

1.00% y = 0.007303x0.734588 R² = 0.996 0.10%

0.01% %IOWY (gm Indigo/100 gm cotton) (gm Indigo/100 %IOWY 0.01 0.1 1 10 Dye Concentration (g/l)

6.3 7.1 8 12 Etters 1991

Figure 3-25: %IOWY from 6.3/1, 7.1/1, 8.0/1, and 12.0/1 OE yarns compared to Etters20 data under equilibrium sorption at pH 13 range.

The same relationship was illustrated in figure 3-26 for pH ranges of 11.0 to 11.2. Once again the current experimental results mirror Etter's 1991 data. Both sets of data are almost perfectly modeled by a power function.

133

Equilibrium Sorption Relationship at 11.0 to 11.2 pH 100.00%

10.00%

y = 0.019156x0.583135 R² = 0.992 1.00%

%IOWY (gm Indigo/100 gm cotton) (gm Indigo/100 %IOWY 0.10% 0.01 0.1 1 10 Dye Concentration (g/l)

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 Etters20 data under equilibrium sorption at pH 11 range.

By combining all current equilibrium sorption data with Etter's 1991 data, a general relationship between dye bath concentration and pH affect on total %IOWY was revealed. The power functions at various pH values were summarized in equation 3-13 in the general form.

At each pH: %𝐼𝑂𝑊𝑌 = 𝐶𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡𝐴 ∗ 𝐷𝑦𝑒𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 11.2 pH: %𝐼𝑂𝑊𝑌 = 0.019156 ∗ 𝐷𝑦𝑒𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛. 12.8 pH: %𝐼𝑂𝑊𝑌 = 0.010734 ∗ 𝐷𝑦𝑒𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛. 13.2 pH: %𝐼𝑂𝑊𝑌 = 0.007448 ∗ 𝐷𝑦𝑒𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛.

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

134

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.

Coefficients of Equilibrium Sorption %IOWY Power Function 0.025 0.8 0.7 0.02 0.6 0.015 0.5 0.4 0.01 0.3 0.2 0.005 Value of A Componet 0.1 B Value of Component 0 0 11 11.5 12 12.5 13 13.5 pH

Component A Component B

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.

135

Coefficients of Equilibrium Sorption %IOWY Power Function 0.025 0.8 0.7 0.02 y = -0.244296x + 0.816158 0.6 0.015 R² = 0.999384 0.5 0.4 0.01 0.3 0.2 0.005 y = 0.016492x + 0.003465 Value of A Componet R² = 0.999981 0.1 B Value of Component 0 0 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Value of Monophenolate Indigo Dye Fraction as a Function of pH

Component A Component B

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.

𝑀𝑜𝑛𝑜𝑝ℎ𝑒𝑛𝑜𝑙𝑎𝑡𝑒𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛 = .. 𝐶𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡𝐴 = 0.016492 ∗ 𝑀𝑜𝑛𝑜𝑝ℎ𝑒𝑛𝑜𝑙𝑎𝑡𝑒𝐹𝑟𝑎𝑐𝑖𝑜𝑛 +0.003465

𝐶𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡𝐵 = −0.244296 ∗ 𝑀𝑜𝑛𝑜𝑝ℎ𝑒𝑛𝑜𝑙𝑎𝑡𝑒𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛 +0.816158

%𝐼𝑂𝑊𝑌 = 𝐶𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡𝐴 ∗ 𝐷𝑦𝑒𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛

Equation 3-14: General relationships between indigo dye bath concentration and pH to resulting %IOWY under equilibrium sorption.

136

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 Equilibrium Sorption Relationship at Various pH's 100.00%

10.00%

1.00%

0.10%

0.01% 0.01 0.1 1 10

Calculated %IOWY (gm Indigo/100 gm cotton) Calculated %IOWY (gm Indigo/100 Dye Concentration (g/l)

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

𝐼𝑛𝑡𝑒𝑔 = 45.60937 + (592.19421 ∗ %𝐼𝑂𝑊𝑌) − (9928.5539 ∗ (%𝐼𝑂𝑊𝑌 − 0.045773)) + (1.83538𝑒 ∗ (%𝐼𝑂𝑊𝑌 − 0.045773)) − (1.52245𝑒 ∗ (%𝐼𝑂𝑊𝑌 − 0.045773)) + (4.27080𝑒 ∗ (%𝐼𝑂𝑊𝑌 − 0.045773))

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

The inverse relationship was actually required in order to calculate the penetration level. Switching the independent and dependent variables produced the relationship for calculating the %IOWY on the outside surface as a function of Integ shade value. The relationship is displayed in figure 3-31 and resulting equation listed as equation 3-16.

%IOWY on Outside Surface

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

%𝐼𝑂𝑊𝑌 = −0.02646 + (9.5386𝑒 ∗𝐼𝑛𝑡𝑒𝑔) + (1.3593𝑒 ∗ (𝐼𝑛𝑡𝑒𝑔 − 55.2088) ) + (3.909𝑒 ∗ (𝐼𝑛𝑡𝑒𝑔 − 55.2088)) + (2.4244𝑒 ∗ (𝐼𝑛𝑡𝑒𝑔 − 55.2088)) + (6.4303𝑒 ∗ (𝐼𝑛𝑡𝑒𝑔 − )55.2088 )

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

139

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 660nm as a Function of %IOWY 40.0 35.0 30.0 25.0 20.0 15.0 K/S at 660 nm 10.0 5.0 0.0 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 39 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.

ScatterplotScatterplot ofMatrix Observational Study Dye Range Set-up Conditions and Interactions

38 High value 36 34 Middle value 32 30

Speed m/min Low value 28 26 3 High value

2 Middle value gm/lit Indigo

1 Low value

13 High value

12 Middle value Box pH Box Low value 11 High value 900

Middle value 800 Box mV Box Low value 700 8.63 11.37 26 29 3133 3537 1 2 3 11 12 13 Dwell Indigo length m Speed m/min gm/litg/l Box pH Figure 3-33: Range of observational study dye range set-up conditions and interactions.

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

Additional Replicates Affect on Standard Error 4.5 4 3.5 3 2.5 2 1.5 1 0.5 Standard Error of Indigo (g/l) 0 0 5 10 15 20 25 Number of Additional Replicates Added

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

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.

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.

Graph Builder %IOWY vs. Dip

4.000%

3.000%

2.000%

1.000%

0.000%

1234567

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

146

To further explore the %COWY and %IOWY as the number of dips increased, a couple of specific data sets are presented. In figure 4-2, 6.3/1 yarn was dyed in three different indigo dye bath concentrations with approximately constant speed, pH, and mV. All three were 31.1 meters/minute. The 3.0 g/l dyeing was 12.0 pH and 789 mV with the 2.7 g/l at 11.8 pH and 800 mV, and 2.3 g/l at 11.9 pH and 805 mV. All three follow the same general build curve with large increase in %COWY from 1 to 2 dips. Additional dips beyond 2 continued to increase the %COWY although at a slower rate. Last, the spacing between dye bath concentrations was as expected with higher dye bath concentration resulting in higher %COWY while lower concentrations resulted in the lower %COWY.

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.

Using the same data sets a similar relationship exist for %IOWY. Figure 4-3 illustrates the %IOWY build curve as a function of number of dips based on the same data points. Notice the linear relationship for %IOWY to number of dips. These curves illustrate with increasing number of dips

147 the %IOWY lineary increases. Also the higher the dye bath concentration, the higher the %IOWY. This same linear behavior is exhibited by all data sets from all dye range set-up conditions. While no previous data has been published comparing %IOWY and the effects of increasing dips, numberous examples have been discussed relating shade of the yarn (K/S or Integ) to increasing numbers of dips. Refer to Xin46 Integ vs dips curve in section 1-1.

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.

Since the %IOWY increased with each additional dip of indigo dye, one would expect the depth of shade to increase as well. However, the relationship does not appear to be linear. Figure 4-4 illustrates the realationship between Integ shade value and number of indigo dips from all data points. Even though the %IOWY builds in a linear nature, the non-linear nature of Integ shade versus the number of dips is justified when consideration is given to non-linear relationship between Integ and %IOWY under equilibrium sorption dye conditions as well as the possibility for variable penetration levels from one dip to the next. It should be noted the increase in dips does not actually

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.

Graph Builder Integ vs. Dip 120

100

60 Integ

0 1234567

Dip

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

To further investigate Integ variation as it relates to number of dips, once again three specific dye conditions were used. These specific dye conditions are graphed in figure 4-5. Clearly, the Integ shade value builds in a non-linear fashion as the number of dips is increased. The depth of shade also maintains the effect of indigo dye box concentration: the higher the dye concentration, the darker the shade while lighter indigo dye bath concentrations resulted in lighter shades.

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.

Since %IOWY caused the Integ shade and %IOWY by dips was linear, what caused Integ to be non-linear function of number of dips? As previously shown in chapter 3, the Integ shade has a non-linear relationship to %IOWY during equilibrium sorption. This could explain the shape of curves in figure 4-5. The other possibility was changes in penetration level as a function of number of dips. The penetration level as a function of all data points is shown in figure 4-6. Unlike the previous relationships, the penetration level has a unique and unexpected shape as the number of dips was increased. As the number of dips was increased the penetration level continued to decrease with reducing severity. From dip 5 through 7 the penetration level remains relatively unchanged. The decreased average penetration level with each dip, could explain the non-linear relationship between Integ and dip as demostrated in figure 4-5. The penetration level decreased with each additional dip due to additive process of layering dye not by the dip process itself.

150

Graph Builder Penetration level vs. Dip 0.9

0.8

0.7

0.6

0.5 Penetration level Penetration 0.4

0.3

0.2 1234567

Dip 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.

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.

Besides the number of dips, the indigo dye concentration in the dye bath of each dip should have a strong impact on the response variables. The next series of graphs investigates the effect of indigo dye bath concentration on %COWY, %IOWY, Integ, and penetration level while considering the number of dips. Figure 4-8 shows the effect of indigo concentration on %COWY when separated by one, three, and six dips. As in figure 4-1, as the number of dips increased so did the %COWY. Also as in figure 4-2, as the indigo dye bath concentration increased, the %COWY increased. The %COWY build is fairly linear by indigo dye bath concentration within each individual dip.

152

Graph Builder %COWY vs Average Indigo (g/l) by Dip %COWY vs. Average Indigo (gm/lit) by Dip 14.00% Legend

12.00% 1 3

10.00% 6

1 8.00% 3

%COWY 6.00%

4.00%

2.00%

0.00% 0.5 1 1.5 2 2.5 3 3.5 4

Average Indigo (gm/lit)(g/l) 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.

153

Graph Builder Measured %IOWY vs Average Indigo (g/l) by Dip Measured %IOWY vs. Average Indigo (gm/lit) by Dip 4.500% Legend

4.000% 1

3.500% 3 6 3.000% 1

2.500% 3

6 2.000%

Measured %IOWY 1.500%

1.000%

0.500%

0.000% 0.5 1 1.5 2 2.5 3 3.5 4 (g/l) Average Indigo (gm/lit) 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.

154

Graph Builder Measured Integ vs Average Indigo (g/l) by Dip Measured Integ vs. Average Indigo (gm/lit) by Dip 120 Legend

1 100 3

80 1

60 6 Measured Integ 40

0 0.5 1 1.5 2 2.5 3 3.5 4

Average Indigo (gm/lit)(g/l) 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.

155

Graph Builder Penetration Level vs Average Indigo (g/l) by Dip Penetration level vs. Average Indigo (gm/lit) by Dip 0.9 Legend

0.8 1 3

0.7 6

1 0.6 3

6 0.5 Penetration level

0.4

0.3

0.2 0.5 1 1.5 2 2.5 3 3.5 4

Average Indigo (gm/lit)(g/l) 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

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

Graph Builder Yarn Count Affect on %COWY, %IOWY, Integ, and Penetration Level Yarn Count 6.3 7.1 8 12

12.00%

10.00%

8.00%

%COWY 6.00%

4.00%

2.00% 4.00% 3.50% 3.00% 2.50%

%IOWY 2.00% 1.50% 1.00% 0.50% 100 90 80 70 Integ 60 50 40 30 0.6 0.55 0.5 0.45 0.4 0.35

Penetration level 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 (g/l) Indigo gm/lit

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

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%

%COWY 6.00% 5.00% 4.00% 3.00% 2.00% 3.50% 3.00% 2.50% 2.00% %IOWY 1.50% 1.00% 0.50% 100 90 80 70 Integ 60 50 40 30 0.5 0.45 0.4 0.35 0.3 Penetration level 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(g/l)

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

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

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%

Indigo gm/lit(g/l)

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

Graph Builder Reduction Potential Affect on %COWY, %IOWY, Integ, and Penetration Level Box mV 726 - 786 786 - 851 851 - 891

12.00%

10.00%

8.00%

%COWY 6.00%

4.00%

2.00% 3.50% 3.00% 2.50% 2.00% %IOWY 1.50% 1.00% 0.50% 100 90 80 70 Integ 60 50 40 30 0.5 0.45 0.4 0.35 0.3 Penetration level 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 4-15: 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

Graph Builder Dwell Length Affect on %COWY, %IOWY, Integ, and Penetration Level Dwell length (m) 8.63 11.37

12.00%

10.00%

8.00%

%COWY 6.00%

4.00%

2.00% 3.50% 3.00% 2.50% 2.00% %IOWY 1.50% 1.00% 0.50% 100 90 80 70 Integ 60 50 40 30 0.5 0.45 0.4 0.35 0.3 Penetration level 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 (g/l) 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.

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

Graph Builder Dwell Time Affect on %COWY, %IOWY, Integ, and Penetration Level Dwell time (sec) 14.03 - 16.7 16.7 - 19.6 19.6 - 25.7

12.00%

10.00%

8.00%

%COWY 6.00%

4.00%

2.00% 3.50% 3.00% 2.50% 2.00% %IOWY 1.50% 1.00% 0.50% 100 90 80 70 Integ 60 50 40 30 0.5 0.45 0.4 0.35 0.3 Penetration level 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(g/l)

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.

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.

Convergence Test for Empirical %COWY Model

1.2 1.15 1.1 1.05 1 0.95 0.9

for all Significant Parameters 0.85

Average Normalized Standard Error Average Normalized 0.8 0 5 10 15 20 25

Number of Additional Replicates Added

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

Now the final empirical %COWY model was generated based on all available data points. The final R2 correlation coefficient was 0.88 with an F ratio of 380 as shown in table 4-2. For completeness the final parameter estimates and standard errors are also shown. The final model maintained the same statistically significant parameters as the prime data set model as demonstrated in the effect tests. No new statistically significant terms surfaced.

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 ⎢ ⎢ ⎥ %𝐶𝑂𝑊𝑌 =𝑒𝑥𝑝 ⎢−0.6590 + (0.03819 ∗ 𝑌𝑎𝑟𝑛 𝐶𝑜𝑢𝑛𝑡) + 𝑀𝑎𝑡𝑐ℎ(𝐷𝑖𝑝) ⎢4: 0.4205⎥ + (2.8376𝑒 ∗ ⎢ ⎢5: 0.4862⎥ ⎢ ⎢6: 0.5410⎥ ⎣ ⎣7: 0.5830⎦ 𝑆𝑝𝑒𝑒𝑑) + 0.8576 ∗ log 𝐷𝑦𝑒 𝐵𝑎𝑡ℎ( ) − (0.2874 ∗ 𝑝𝐻) − (6.5040𝑒 ∗ (𝑆𝑝𝑒𝑒𝑑) −33.1 ) − ⎤ ⎥ ⎥ 2.5018𝑒 ∗(𝑝𝐻 − 11.83) ∗ (𝑆𝑝𝑒𝑒𝑑) −33.1 ⎥ ⎥ ⎥ ⎦

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

To better illustrate the relationship between actual %COWY and the predicted value from the empirical model the two values were plotted against each other in figure 4-20. There is obviously a strong relationship with the predicted versus actual following a linear 1 to 1 relationship. There are however a few points were the predicted %COWY is in the range of 4% to 6% but the actual values are in the 8% to 12% range. However, overall the %COWY model performed well.

174

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 Prediction Profile for Dye Range Set-up Conditions %COWY 0.086371 [0.08272, 0.09018] 6 8 1 3 5 7 1 2 3 10 12 14 26 29 32 35 11 12

(g/l)

Figure 4-21: %COWY prediction profile for dye range set-up condition affect on %COWY from the empirical model.

The graph in the second column from figure 4-21 confirms the number of dips has a non- linear impact on the %COWY. The shape of this curve is very similar to the curve in figure 4-1 when the %COWY versus dips was discussed. Also, the dye range speed was determined to be statistically significant but by the second order term. As the middle column graph illustrates, as the speed is increased the %COWY increases until a limit is reached at approximately 33 m/min. The original graphical analysis did not detect this relationship. The graph in the fourth column identifies a strong relationship between the dye bath indigo concentration and the %COWY. Logically, as the dye bath concentration is increased the %COWY also increases. In the final coumn graph of figure 4-21, as the pH of the dye bath is increased the %COWY decreases. Recall this same relationship was detected in figure 4-14.

4.2.2 %IOWY Empirical Model Generation

The same process was repeated for the %IOWY using the prime data set as the initial starting point for the ANOVA analysis. The R2 correlation coefficient was determined to be 0.97 with an F ratio of 1585 as shown in table 4-3. This was determined to be the best possible model fit using all dye range set-up conditions, second order terms, and interactions. The parameter estimates listed in table 4-3 produce the initial standard errors for each significant parameter. Note the dye bath pH was determined to be statistically insignificant with a P-value of 0.1449. However, this

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.

Convergence Test for Empirical %IOWY Model

1.2 1.15 1.1 1.05 1 0.95 0.9 0.85

for all Significant Parameters 0.8

Average Normalized Standard Error Average Normalized 0 5 10 15 20 25 Number of Additional Replicates Added

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 R2 correlation coefficient was determined to be 0.97 with an F ratio of 2597 from table 4-5. These two coefficients indicate the model is a very strong fit to the data. Also listed under the parameter estimate section is the final standard error for each parameter.

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 ⎢ ⎥ %𝐼𝑂𝑊𝑌 = exp[−6.0772 + 𝑀𝑎𝑡𝑐ℎ(𝐷𝑖𝑝) ⎢4: 1.3031 ⎥ + 4.4823e ∗ 𝑌𝑎𝑟𝑛 𝐶𝑜𝑢𝑛𝑡 −1.5847e ∗ ⎢5: 1.5257 ⎥ ⎢6: 1.7062 ⎥ ⎣7: 1.8717⎦ 𝑆𝑝𝑒𝑒𝑑 + 0.8713 ∗log 𝐷𝑦𝑒 𝐵𝑎𝑡ℎ ]

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

To better illustrate the relationship between actual %IOWY and the predicted value from the empirical model the two values were plotted against each other in figure 4-23. There is obviously a strong relationship with the predicted versus actual following a linear 1 to 1 relationship.

Actual %IOWY

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

181

A prediction profile graph was created for the empirical model %IOWY as a function of each dye range set-up condition. As shown in figure 4-24, increasing yarn count causes the %IOWY to increase. This relationship was observed during the graphical analysis section and hasn't been documented by others. Just as demonstrated by other experiments (Xin46) and illustrated in the graphical analysis section, increasing the number of dips causes the %IOWY to increase in a nearly linear fashion. This relationship is highlighted in the second column graph of figure 4-24. The third column graph shows increasing speed was determined to cause the %IOWY to decrease. This was originally observed in the graphical analysis section and hasn't been documented by others. In the final column of figure 4-24, increasing the indigo concentration in the dye bath causes the %IOWY to increase. This relationship has been well documented in previous experiments.

%IOWY Prediction Profile for Dye Range Set-up Conditions %IOWY 0.01993 Measured [0.01934, 0.02054] 7 8 9 1 3 5 7 1 2 3 10 11 12 26 28 30 32 34 36

(g/l)

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

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 R2 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.

Convergence Test for Empirical Integ Model

1.2 1.15 1.1 1.05 1 0.95 0.9 0.85 0.8 for all Significant Parameters

Average Normalized Standard Error Average Normalized 0 5 10 15 20 25 Number of Additional Replicates Added

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

The final empirical Integ model based on dye range set-up parameters was generated. The correlation coefficient R2 value of 0.96 and F ratio of 1610 from table 4-7 indicated the overall model improved from the prime data set. The final parameter standard errors are displayed in the parameter estimates section of table 4-7. During the ANOVA analysis other dye range set-up condition first order, second order, and interaction effects were evaluated and determined to not

184 become statistically significant. The final P-value for each parameter is listed in effect tests section of table 4-7.

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

The final Integ equation was determined based on the parameter estimates from table 4-7. The empirical model Integ prediction equation based on dye range set-up conditions is listed in equation 4-3.

185

1: 0.0 ⎡2: 0.6763 ⎤ ⎢ ⎥ 3: 1.0511 ⎢ ⎥ Integ = exp[4.0128 + 𝑀𝑎𝑡𝑐ℎ(𝐷𝑖𝑝) ⎢4: 1.2771 ⎥ + 1.0585e ∗ 𝑌𝑎𝑟𝑛 𝐶𝑜𝑢𝑛𝑡 −8.6794e ∗ ⎢5: 1.4299 ⎥ ⎢6: 1.5344 ⎥ ⎣7: 1.6367⎦ 𝑆𝑝𝑒𝑒𝑑 + 0.7791 ∗log 𝐷𝑦𝑒 𝐵𝑎𝑡ℎ − 0.1271 ∗ 𝑝𝐻]

Equation 4-3: Empirical model Integ as a function of dye range set-up conditions.

The comparison between actual Integ shade values and empirical model predicted are shown in figure 4-26. Overall the model fit is fairly uniform. However, notice at the higher predicted Integ values the relationship falls off the 1 to 1 line. Second, there is a group of data points at 40, 80, 110, and 140 predicted Integ units completely off line with the actual values.

Actual Integ

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

186

The prediction profile for each dye range set-up condition effect on predicted Integ shade value from the empirical model is shown in figure 4-27. Just as seen in the graphical analysis section as the yarn count is increased the Integ value increased. Increasing depth of shade as a function of yarn count has not been previously published. Just as Xin46 and Chong29 have demonstrated, as the number of dips was increased the resulting Integ shade value also increased. As previously discussed in the graphical section, increases in speed caused the Integ values to decrease. Again, this hasn't been previously discussed in the literature. As the dye bath concentration was increased the predicted Integ shade value also increased. This again is a well established relationship in published literature and confirmed here. In the last column of figure 4-27, as the dye bath pH values increase the Integ shade values decrease. This mirrors Etter's detailed experiments on pH sensitivity of the resulting shade of the yarn.

Integ Prediction Profile for Dye Range Set-up Conditions Integ 84.19798 Measured [81.3518, 87.1437] 7 9 1 3 5 7 1 2 3 11 26 28 30 32 34 36 11 12

(g/l)

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

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 R2 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.

Convergence Test for Empirical Penetration Level Model 1.2

1.1

0.9

0.8

0.7

for all Significant Parameters 0.6

Average Normalized Standard Error Average Normalized 0 5 10 15 20 25 Number of Additional Replicates Added

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 + 𝑀𝑎𝑡𝑐ℎ(𝐷𝑖𝑝) ⎢4: −0.0398 ⎥ + 1.4097e ∗𝑌𝑎𝑟𝑛 𝐶𝑜𝑢𝑛𝑡− ⎢5: −0.0736 ⎥ ⎢6: −0.1044 ⎥ ⎣7: −0.1214⎦ 8.6054e ∗ 𝑆𝑝𝑒𝑒𝑑 − 3.5665e ∗Dye Bath + 7.6393𝑒 ∗ 𝑝𝐻 + 9.3778𝑒 ∗ (𝑆𝑝𝑒𝑒𝑑 − 33.1)

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

The comparison between actual and predicted penetration level for all data points is illustrated in figure 4-29. The poor correlation highlighted in the ANOVA analysis is graphically apparent. However, the overall trend does follow the general 1 to 1 line. One possible reason for this error lies in using the ANOVA analysis to calculate and model the penetration level directly. An alternative method would be to use the calculated %IOWY and Integ shade values from the prediction models. The Integ would be converted into %IOWY from equilibrium sorption then the penetration level directly calculated. This may yield a better correlation and will be investigated shortly.

193

Level Actual Penetration

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

Penetration Level Prediction Profile for Dye Range Set-up Conditions Actual 0.310253 ±0.017625 Penetration Level 7 9 1 3 5 7 1 2 3 11 26 29 32 35 11 12

(g/l)

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

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.

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 reduction, diffusion of oxygen through the yarn structure, and oxidation rate. The observational study produced three known values for each yarn, dip, and dye range set-up. Specifically the three known values were %COWY, %IOWY, and Integ shade. To overcome the deficiency in number of known values, several assumptions were made.

First the diffusion of dye in the external medium and diffusion of dye through the boundary layer were grouped together as one unknown coefficient called the effective yarn diffusion coefficient, Dy. This coefficient controlled the dye bath concentration within the yarn structure that was available to dye into the fiber. It was not the actual diffusion coefficient of indigo dye through the dye bath. The influence of this parameter determined the effective dye bath concentration within the yarn structure which affected the %COWY, %IOWY, and indigo distribution within the yarn.

The diffusion coefficient for indigo dye in the water solution is not directly known. However, a value can be assumed based on other equations and theoretical work. Ozisik59 presented a method that calculates the diffusion coefficient by use of equation 4-5.

/ () 𝐷 =7.4𝑒 ∗ .

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

ε = Association factor for solvent, H20, = 2.6. M = Molecular weight of solvent, H20, = 18.02. T = Temperature in Kelvin = 293K. μ = Viscosity of solvent = 1 cP (centipoise). V = Molal volume of solute A as liquid at its normal boiling point = 165 cm3/g mol.

After performing the calculations the indigo dye diffusion coefficient in dye bath was determined to be 6.934e-6 cm2/sec. While this value is not exact, it does provide a starting point for optimization calculations that iteratively seek the effective yarn diffusion coefficient final value.

Second, the adsorption of dye onto the fiber surface and the diffusion of dye into the fiber surface were grouped together to created the effective fiber diffusion coefficient, Df. The coefficient

197 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%

8 oxygen, and 1.3% argon . The corresponding mole fractions are 0.78 N2, 0.21 O2, and 0.0096 Ar at one atmosphere pressure. The density of air at room temperature (20° C) and one atmosphere pressure is 1.21 kg/m3 or g/l8. Therefore the initial concentration of oxygen in the air is 0.21 * 1.21 g/l = 0.2541 g/l. Since air is mostly composed of oxygen and nitrogen, the mixture can be modeled as a binary system. The diffusion of oxygen through nitrogen at room temperature (20° C) and one atmosphere pressure has been determined to be 0.219 cm2/sec60. This value was used during the oxidation process.

In order to manipulate the remaining five unknown coefficients, calculations were expanded to incorporate several dips of indigo across multiple yarn counts. The following relationships were utilized to construct an iterative process to goal seek the optimum value for each unknown coefficient.

1. The effective fiber diffusion coefficient, Df, was assumed constant regardless of yarn count and only dependent on the specific dye range set-up and indigo dip analyzed. 2. The effective yarn diffusion coefficient, Dy, was assumed constant regardless of yarn count and only dependent on the specific dye range set-up and indigo dip analyzed. 3. The wash reduction coefficient was constant regardless of yarn count and dips. The dip assumption applied only to the interior dips not first or last dip since these nip pressures were higher than the interior dips. This coefficient only depended on dye range set-up. 4. The wet pick-up coefficient was constant regardless of yarn count and dips. Constant wet pick-up only applied to the interior dips for the same reason as wash reduction. 5. The oxidation rate was assumed constant for each yarn count and dip process. It only depended on the dye range set-up parameters.

Using the above assumptions the following relationships were identified. The effective fiber diffusion coefficient was governed by the final Integ shade of the yarn. By converting the Integ shade into %IOWY from equilibrium sorption, the outside or visible surface indigo concentration was

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 (cm2/sec). The coefficient describes the rate at which a material diffuses through a unit area.

𝐹= −𝐷

=𝐷

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

When expanding Fick's laws to cylinders it is customary to neglect material transport along the yarn length or z axis and assumes no differential material transport occurs around the circumference of the yarn. The remaining direction is radial or along the yarn's radius. This was considered the primary route for material transport and Fick's laws are rewritten into equation 4-7.

= 𝑟 𝐷 −𝐹(𝐶,𝑟)

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

Here C is defined to represent the dye bath concentration in grams/liter, t is the time in seconds, r is

2 the radius in centimeters, Dy is the yarn diffusion coefficient in cm /sec, and F(C,r) is the grams per liter of indigo in the dye bath removed per time into the cotton fibers. This last term behaves

200 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.

= ∗ + + 𝐷 ∗𝐶 −2𝐶 +𝐶 +𝐶 −2𝐶 + ∆ ∆ ∆ ∆ 𝐶 − [𝐹(𝐶,𝑟)]

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

The superscript “j” was used to represent the current time while “j+1” equals next time step. The subscript “i” represents the current node while “i-1” and “i+1” represents the previous and next node respectively.

The dye removal term, F(C,r), was defined by the amount of dye that leaves the dye stream and transfers to the cotton fiber per time. The amount of dye in grams leaving the dye bath at each node is defined by the affinity of the dye molecule for cotton fiber surface. This dye will form a boundary layer around the fibers as long as the affinity is faster than the diffusion of dye from the surface into the fiber interior. Since the exact boundary layer thickness is unknown, the affinity of dye for cotton fiber and subsequent diffusion from boundary layer into fiber was grouped together.

The resulting expression was the relative or effective fiber diffusion coefficient, Df.

By setting the amount of dye leaving the dye stream at each node equal to the amount of dye transferred to the fiber, the F(C,r) term was defined. This relationship was modeled by incorporating two different aspects. First, the maximum possible %IOWY was calculated based on

201 the equilibrium sorption experiments discussed in chapter 3.3, equation 4-11. Second, the fraction of the maximum possible %IOWY was calculated based on Cranks2 theoretical analysis solution for infinite dye bath conditions, equation 4-10. Incorporating these two expressions together in equation 4-9 resulted in the final relationship of %IOWY at each node.

%𝐼𝑂𝑊𝑌 = %𝐼𝑂𝑊𝑌 ∗

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

∆ / ∆ ∆ / =1− ∑ 𝑒 ≈ / − − /

Equation 4-10: Crank's expression for the fractional relationship of dye pick-up.2

Where 𝛿's are the positive roots of 𝐽(𝑎∗𝛿) =0 and introduced Df to represent the fiber diffusion coefficient, units of cm2/sec, into the fibers where α is the cotton fiber radius in centimeters. The effective fiber radius of 0.0009 cm was used from Hudson56.

%𝐼𝑂𝑊𝑌 =𝐶𝑜𝑚𝑝𝐴∗(𝑅𝐵𝐿 )

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

It follows that the grams of indigo removed from the dye stream were related to the %IOWY at each node by converting the %IOWY into grams. Recognizing the %IOWY was actually grams of indigo per gram of cotton, the grams of indigo was calculated by multiplying the %IOWY by the number of grams of cotton at each node. Now the results from equation 4-9 was linked with the F(C,r) term by equation 4-12. Since the fraction of maximum possible %IOWY was non-linearly dependent on the step time, ∆t, the solution for dye stream concentration is no longer explicit in nature. Therefore, the greatest time step that ensured stability must be deteremined.

202

∗% 𝐹(𝐶,𝑟) =

Equation 4-12: Functional relationship between indigo leaving the dye bath stream and dye diffused into the cotton fiber.

The boundary conditions needed to solve the finite difference model consists of initial time conditions, dye concentration conditions at the interior node, and dye conditions at the exterior node. The initial boundary conditions at t<0 are listed in equation 4-13.

𝐶(𝑟) = 0 𝑎𝑡 𝑟 ≤ 𝑟𝑎𝑑𝑖𝑢𝑠 𝑎𝑛𝑑𝑡<0

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

Obviously the dye concentration within the yarn is zero prior to the first indigo dye box. During multiple dip applications, this assumes all indigo dye has been either extracted by the nip or fully oxidized and therefore immobile for continued yarn or fiber diffusion.

Next the dye bath concentration at the outside node was defined by boundary condition in equation 4-14.

𝐶(𝑟) = 𝐷𝑦𝑒 𝐵𝑎𝑡ℎ 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑎𝑡𝑖𝑜𝑛 𝑎𝑡 𝑟 =𝑦𝑎𝑟𝑛𝑟𝑎𝑑𝑖𝑢𝑠𝑎𝑛𝑑𝑡≥0

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

This condition assumes dye stream concentration at the outside node is equal to dye bath concentration and all other chemical additives as soon as yarn enters the dye bath and maintained during the entire dip process. Given the relatively rough yarn surface, due to irregular shape from uneven yarn thickness and wrapper fibers, micro turbulent flow develops instead of conventional

203 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 𝑎𝑡 𝑟=0 𝑎𝑛𝑑 𝑡>0

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

Prior to indigo dye box #1, the yarns are free of any indigo dye. Also the calculated %IOWY distribution from a dip was used in additive nature for each subsequent dip. This will simulate the additive nature of multiple dip indigo dyeing and expressed in equation 4-16.

%𝐼𝑂𝑊𝑌 𝑎𝑡 𝑠𝑢𝑟𝑓𝑎𝑐𝑒 𝑜𝑓( 𝑦𝑎𝑟𝑛=𝑓𝑢𝑛𝑐𝑡𝑖𝑜𝑛 𝐼𝑛𝑡𝑒𝑔 𝑠ℎ𝑎𝑑𝑒)𝑎𝑓𝑡𝑒𝑟 𝑒𝑎𝑐ℎ 𝑑𝑖𝑝

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

To determine the distribution of indigo dye within the yarn, the amount of indigo on the surface was assumed to equal the corresponding amount of dye from uniformly dyed yarns. The relationship developed in chapter 3.3 for Integ shade value will be utilized. Given the Integ shade value, the corresponding %IOWY on the surface of the yarn was calculated by relationship in equation 4-16 and utilizing expression in equation 4-17.

%𝐼𝑂𝑊𝑌 = −2.6465𝑒 + 9.5386𝑒 ∗ 𝐼𝑛𝑡𝑒𝑔 + 1.3593𝑒 ∗ (𝐼𝑛𝑡𝑒𝑔 − 55.2088) + 3.9090𝑒 ∗ (𝐼𝑛𝑡𝑒𝑔 − )55.2088 + 2.4244𝑒 ∗ (𝐼𝑛𝑡𝑒𝑔 − 55.2088) + 6.4303𝑒 ∗ (𝐼𝑛𝑡𝑒𝑔 − )55.2088

%𝐼𝑂𝑊𝑌 = %𝐼𝑂𝑊𝑌 ∗

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

204

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.

∆r/2

Cm r ∆r

∆r C2

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

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

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 𝐶 =𝐶 and 𝐶 =𝐶:

205

𝐶 (𝛽−𝛾−𝛽−𝛾) + 𝐶 (1+2𝛾) = 𝐶(−𝛽−𝛾+𝛽−𝛾) +𝐶 (1−2𝛾) − 𝐹(𝐶 ,𝑟)

𝐶 (1+2𝛾) = 𝐶 (1−2𝛾) − 𝐹(𝐶 ,𝑟)

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

𝐶 (−𝛽 − 𝛾) +𝐶 (1 + 2𝛾) + 𝐶 (𝛽 − 𝛾) =𝐶 (𝛽 + 𝛾) +𝐶 (1 − 2𝛾) + 𝐶 (−𝛽 + 𝛾) − 𝐹(𝐶 ,𝑟)

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

Node = M - 1 where 𝐶 and 𝐶 = dye bath concentration:

𝐶(1+2𝛾) +𝐶(𝛽−𝛾) =𝐶(1−2𝛾) +𝐶(−𝛽 + 𝛾) +2∗𝐶(𝛽 + 𝛾) − 𝐹(𝐶 ,𝑟)

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

All three nodal equations utilized a simplified expression for lambda and beta as detailed in equation 4-21.

∆ ∆ 𝛾= ,β = ∆ ∆

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

2 Here the Dy coefficient is assumed to be a constant value, cm /sec. Re-arranging and grouping the following M simultaneous equations were written in matrix form, equation 4-22.

206

1+2𝛾 −2𝛾 0 0… ⎡𝐶 ⎤ ⎡ ⎤ 𝛽−𝛾 1+2𝛾 −𝛽−𝛾 0… ⎢𝐶 ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 0………0⎥ … = ⎢ … 0 𝛽−𝛾 1+2𝛾 −𝛽−𝛾⎥ ⎢𝐶 ⎥ ⎢ ⎥ ⎣ …0 0𝛽−𝛾1+2𝛾⎦ ⎣𝐶⎦ 1 − 2𝛾 2𝛾 0… ⎡ 𝐶 ⎤ ⎡ −𝐹(𝐶 ,𝑟) ⎤ ⎡ ⎤ −𝛽 + 𝛾 1 − 2𝛾 𝛽 +𝛾0… ⎢ 𝐶 ⎥ ⎢ −𝐹(𝐶 ,𝑟) ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ 0………0⎥ … + … ⎢ …0−𝛽+𝛾1−2𝛾𝛽+𝛾⎥ ⎢𝐶 ⎥ ⎢ −𝐹(𝐶 ,𝑟 ) ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ …00−𝛽+𝛾1−2𝛾⎦ ⎣𝐶⎦ ⎣−𝐹(𝐶,𝑟)+2∗𝐶(𝛽 + 𝛾)⎦

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

To utilize the lambda and beta equations from equation 4-21, the effective yarn radius was determined from Mogahzy's relationship for yarn count (English cotton count)57. Equation 4-22 was the equation to calculate the effective yarn radius at a given open end spun yarn count. With the effective yarn radius, the ∆r value was calculated by dividing the radius by the number of nodes minus one.

. . 𝑦𝑎𝑟𝑛 𝑟𝑎𝑑𝑖𝑢𝑠 (𝑐𝑚)= √

Equation 4-23: Mogahzy's relationship for open end yarn radius as a function of yarn count.57

Additionally the yarn porosity value was determined. This property was defined to be the area of the fiber in a nodal shell per total area of yarn at that nodal shell. Nabovati58 reported typical yarn porosity values in the range of 0.69 to 0.95. Given the 100% cotton yarns are dyed in a zero tension state, the porosity value of 0.65 was assumed for all calculations since this was the absolute low end of published values.

Solution for the future dye concentration within the yarn from the algebraic equations in 4- 22 was conducted by Guess-Jordan elimination method executed in purpose written software

207 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.

𝑂𝐵𝐿(𝑔𝑚) = 𝑊𝑎𝑠ℎ 𝑅𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 ∗ (%𝐶𝑂𝑊𝑌 − %𝐼𝑂𝑊𝑌) ∗ 𝐶𝑜𝑡𝑡𝑜𝑛( )

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

Next, the wet pick-up caused by the squeeze of nip rolls after the dip process was investigated. Wet pick-up is defined to cause a fraction of excess reduced dye bath liquor between the fibers to be extracted. The excess reduced dye was called the Reduced Boundary Layer or RBL and two forms must be tracked. The concentration of the RBL so future %IOWY calculations could be determined and the number of grams of reduced dye for oxidation tracking. The concentration of the RBL is simply the concentration of the dye bath at each node after the nip process, since squeezing the yarns and reducing the quantity of excess dye doesn't change the concentration. This is summarized in equation 4-25. Second, the quantity of reduced dye must be tracked. Here the grams were calculated by multiplying the dye bath concentration by the available liter space between the fibers at each node and then multiplying by the wet pick-up coefficient.

208

𝑅𝐵𝐿 =𝐷𝑦𝑒 𝐵𝑎𝑡ℎ( ) 𝑅𝐵𝐿(𝑔𝑚) =𝐷𝑦𝑒 𝐵𝑎𝑡ℎ ∗𝐿𝑖𝑡𝑒𝑟 ∗ 𝑊𝑒𝑡 𝑃𝑖𝑐𝑘𝑢𝑝

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

4.3.1.c The Oxidation Process

The movement and concentration of oxygen in the yarn structure was modeled exactly the same as the dye bath liquor. The same nodal mesh was utilized. The difference was oxygen concentration was determined at each time step instead of dye bath concentration. This was expressed in grams of oxygen (O2) per liter. The equations and boundary conditions are listed in equations 4-26 to 4-28.

= ∗ + + 𝐷𝑂 ∗𝑂 −2𝑂 +𝑂 +𝑂 −2𝑂 + ∆ ∆ ∆ ∆ 𝑂 − [𝑂𝑥(𝑂, 𝑟)]

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

Here DOy was the oxygen diffusion coefficient.

𝑂𝑥(𝑂,) 𝑟 = 𝑋 ∗𝑂

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

Here Xi was defined to be the fraction of oxygen removed from the air stream.

209

(% ∗( )) 𝑋 = ∗ ∗ ∗∆

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

The initial oxygen concentration is assumed zero at the start of the oxidation process. The outside node oxygen concentration was set equal to the air concentration and maintained during the entire oxidation process. Also like the dye bath concentration, oxygen concentration was symmetrical about the center or core of the yarn.

𝑂(𝑟) = 0 𝑎𝑡 𝑟 ≤ 𝑟𝑎𝑑𝑖𝑢𝑠 𝑎𝑛𝑑𝑡<0

𝑂(𝑟) = 𝐴𝑖𝑟 𝑐𝑜𝑛𝑐𝑒𝑛𝑡𝑎𝑡𝑖𝑜𝑛 𝑎𝑡 𝑟 = 𝑦𝑎𝑟𝑛 𝑟𝑎𝑑𝑖𝑢𝑠𝑎𝑛𝑑𝑡≥0

=0 𝑎𝑡 𝑟=0 𝑎𝑛𝑑 𝑡>0

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

The oxidation rate, OR, is an unknown coefficient defined to be the grams of reduced indigo per gram of oxygen per second consumed during the oxidation process and has units of 1/sec. The values of Xi can range from zero to one. A value greater than one means either the oxidation rate, grams of reduced indigo, and/or time step were high compared to the grams of available oxygen. In this situation all of the available oxygen was consumed by the reduced indigo but more wasn't consumed than available. This assumption now makes the total finite difference model implicit instead of full explicit since the Xi value was dependent on the ∆t value. Therefore, many more time steps were used in the calculations to produce a stable solution.

After each oxidation rate time step the grams of oxygen and impact on reduced indigo are tracked. First the grams of oxygen removed from the air stream were calculated based on reduced boundary layer and the %IOWY that required oxidizing. Then the total change in grams per liter of

210 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.

∆𝑅𝐵𝐿𝑔𝑚 = −%𝐼𝑂𝑊𝑌 ∗𝐶𝑜𝑡𝑡𝑜𝑛 −𝑂𝑥𝑖𝑑𝑎𝑡𝑖𝑜𝑛 𝑅𝑎𝑡𝑒∗𝑂 ∗𝐿𝑖𝑡𝑒𝑟 ∗∆𝑡

∆ ∆𝑅𝐵𝐿 =

∆𝑂𝐵𝐿𝑔𝑚 = 𝑂𝑥𝑖𝑑𝑎𝑡𝑖𝑜𝑛 𝑅𝑎𝑡𝑒∗𝑂 ∗𝐿𝑖𝑡𝑒𝑟 ∗∆𝑡

%𝐼𝑂𝑊𝑌 = %𝐼𝑂𝑊𝑌 ∗

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

Last the %COWY calculation must be defined. This value represents the unfixed indigo and residual sodium hydroxide and sodium sulfate from the dyeing process that has not been washed off the fiber surface. The measured value of this parameter will depend on three main constitutes.

1. The indigo dye, sodium hydroxide, and sodium dithionite concentration in the dye bath. 2. The net pick-up of chemicals during the dip and nip process. 3. The fixation rate of the dye.

The indigo dye concentration is a measured value based on empirical correlations discussed during the %T measurements. On the other hand, the total alkalinity measurement doesn't directly relate to just the sodium hydroxide concentration. Likewise, the mV reduction potential doesn't

211 directly measure only sodium dithionite concentration. As a result, only one component of item #1 is a direct measurement of concentration in the dye bath. Additionally, the actual wet pick-up of chemicals during the dip and nip process was an unknown property which was approximated by the wet pick-up coefficient. The fixation rate of indigo dye was unknown and the main property under investigation. Due to these shortcomings an approximation was developed. The amount of residual chemicals on weight of yarn will be a direct function of the amount of indigo on weight of yarn. This functional relationship was developed by analyzing the indigo reduction/oxidation process.

The oxidation of reduced indigo, IR, produces the following chemical reactions.

𝐼 +𝑂 +𝐻0 ⎯⎯⎯ 𝐼 +2𝑁𝑎𝑂𝐻+2𝑁𝑎𝑆𝑂

2𝑁𝑎𝑆𝑂 +𝑂 ⎯⎯⎯ 2𝑁𝑎𝑆𝑂

Equation 4-31: Chemical reactions and intermediaries during the oxidation process.

From equation 4-31, for every mole of reduced indigo that is oxidized, 2 moles of sodium hydroxide and 2 moles of sodium sulfate or Glauber salt were produced. By converting the mole fractions by the molecular weight a relationship of grams of each chemical per gram of indigo was generated a shown in equation 4-32.

∗ . . =2∗ = .

Equation 4-32: Relationship for the grams of auxiliary chemicals per gram of indigo present.

Adding these two together and 1.0 for the grams of indigo itself resulted in a value of 2.3884 grams of total chemicals per gram of indigo. The total %COWY at each node was calculated based on the

212 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.

%𝐶𝑂𝑊𝑌 = 2.3884 ∗ [(%𝐼𝑂𝑊𝑌 ∗ 𝐶𝑜𝑡𝑡𝑜𝑛 )+ 𝑅𝐵𝐿𝑔𝑚 +𝑂𝐵𝐿𝑔𝑚]

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

Equation 4-33 assumes the only residual chemicals on weight of yarn were derived from the oxidation of reduced indigo and no other residual chemicals exist. This obviously isn't the situation under real world dyeing conditions where excess sodium hydroxide and sodium dithionite are feed to the dye range. However, it was directly related to the amount of indigo on weight of yarn and varies linearly with indigo amount. Due to this assumption calculated values for the wet pick-up and wash reduction will not be absolute numbers. Instead, the wet pick-up and/or wash reduction coefficient may scale greater or less than reality to make the calculated %COWY match the measured value. How these scale will depend on the actual concentration of sodium hydroxide and sodium sulfate in the dye bath. Since the amount of these components is usually related to the indigo concentration, it is expected wet pick-up and wash reduction coefficients will depend on indigo dye bath concentration.

213

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 range speed. Both of these cases do not actually exist in real world. For this example the real oxidation rate occurred between 1.0 e-3 and 1.0 oxidation rate units.

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

The same graph was created for yarn diffusion coefficients as a function of oxidation rate in figure 4-33. Here the yarn diffusion coefficients have a different behavior as the oxidation rate was decreased. As the oxidation rate was decreased from high values, the variation in yarn diffusion across the yarn counts became greater. At 1.0 e-2 oxidation rate units the variation in yarn diffusion was at a maximum. Further reductions in oxidation rate caused the variation between yarn counts to decrease and the magnitude of the yarn diffusion coefficient shifted lower.

215

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

The variation in calculated wet pick-up values as a function of oxidation rate was investigated. As illustrated in figure 4-34, as the oxidation rate was decreased from high values the variation between yarn counts increased. At approximately 1.0 e-2 oxidation rate units the mean value of wet pick-up shifts higher regardless of yarn count. The shifts in yarn diffusion and wet pick- up at low oxidation rates were caused by lack of indigo oxidation during the allotted oxidation time. Again this phenomenon doesn't occur in the real world.

216

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

By incorporating these properties together the optimum oxidation rate that minimizes the error in fiber diffusion, yarn diffusion, and wet pick-up was determined. First, the standard deviation for fiber diffusion, yarn diffusion, and wet pick-up at each oxidation rate was calculated. Next, these standard deviations were normalized by the average standard deviation for each coefficient. Then, the normalized standard deviations were combined to produce a single error measurement relationship. When this value reached a minimum the optimum oxidation rate had been determined. The normalized standard deviations for each dye coefficient and the combined relationship are displayed in figure 4-35. Starting with an extremely low oxidation rate the combined normalized standard deviations were high. As the oxidation rate was increased the combined normalized standard deviations began to decrease. In this particular example, the optimum oxidation rate was 0.064 oxidation rate units. Further increases in oxidation rate caused the combined normalized standard deviation to increase slightly in value with further increases resulting in constant combined normalized standard deviations due to instantaneously fast indigo

217 oxidation. Due to the nature of the oxidation profile all oxidation rate optimization began at the low end of the spectrum with increasing oxidation rate until the minimum combined normalized standard deviation was reached.

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

4.3.2 Algorithm to Calculate the Dye Coefficients

The operator would input the specific dye range set-up conditions such as speed, indigo dye bath concentration, etc and the final target values for %COWY, %IOWY, and Integ shade by yarn count and dip. First the fiber diffusion coefficient, yarn diffusion coefficient, and wet pick-up was calculated based on the yarn count and assumed initial wash reduction, wet pick-up, and oxidation rate. Then the wash reduction coefficient and wet pick-up were optimized to maintain constant values across all dye dips and yarn counts. Then the oxidation rate was adjusted until the minimum combined normalized standard deviation occurred at each dip. After all calculations 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 R2 value was 0.68 for the relationship between individual fiber diffusion coefficients and the calculated values from the model. While this is not a perfect fit the F ratio of 100.5 and P value much less than 0.0001 does support a statistically significant correlation. The influence and significance of dye bath concentration and pH at each dip was re-enforced by evaluating the parameter estimates and effect tests of each. Table 4-11 shows the P value for the dip number, dye bath concentration and pH was much less than 0.0001.

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 ⎢ ⎥ 𝐷 = exp (−27.3480 + 𝑀𝑎𝑡𝑐ℎ(𝐷𝑖𝑝) 4: 0.05783 + 0.77664 ∗ 𝐷𝑦𝑒 𝐵𝑎𝑡ℎ + 0.40316 ∗ 𝑝𝐻) ⎢ ⎥ ⎢ 5: 0.9180 ⎥ ⎢ 6: 1.0880 ⎥ ⎣ 7: 0.9494 ⎦

Equation 4-34: Dye Theory model effective fiber diffusion equation.

The prediction profile was produced and presented in figure 4-37. In the predication profile the calculated value of fiber diffusion is shown as each dye range parameter varies with the 95% confidence intervals shown in dotted blue lines. The general trend was increasing fiber diffusion as

222 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.

Effective Fiber Diffusion Coefficient Prediction Profile for Dye Range Set-up 2.209e-9 [1.89e-9, 2.58e-9] Predicted Fiber Diffusion 1 2 3 4 5 6 7 1 2 3 11 12

(g/l)

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

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 R2 value was 0.72 for the relationship between individual yarn diffusion coefficients and the calculated values from the model. While this was not a perfect fit the F ratio of 106.6 does support a statistically significant correlation. The influence and significance of dye bath concentration, pH, and dwell time at each dip was re-enforced by evaluating the parameter estimates and effect tests of each. Table 4-12 shows the P value for the dip number, dye bath concentration, pH, and dwell time was much less than 0.0001. A strong correlation coefficient, reasonable F ratio for the model, and extremely low P values indicated the model was more likely to cause the variation in yarn diffusion coefficient values than happenstance.

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 Actual Yarn Diffusion Yarn Actual 0.000002 0.000001 0 0 0.000001 0.000003 0.000005 0.000007 0.000009 0.000011 Predicted Yarn Diffusion Coefficient

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

1: 0.0 ⎡2: −0.0516 ⎤ ⎢ ⎥ 3: −0.4549 ⎢ ⎥ 𝐷 = exp (−17.3700 + 𝑀𝑎𝑡𝑐ℎ(𝐷𝑖𝑝) 4: −1.0327 − 0.5033 ∗ 𝐷𝑦𝑒 𝐵𝑎𝑡ℎ + 0.5889 ∗ 𝑝𝐻 − ⎢ ⎥ ⎢5: −1.3927⎥ ⎢6: −1.4830 ⎥ ⎣7: −1.4538⎦ 0.07367 ∗ 𝐷𝑤𝑒𝑙𝑙 𝑡𝑖𝑚𝑒)

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

The prediction profile was created and presented in figure 4-39. As the number of dips increased the yarn diffusion coefficient decreased. This could be due to increasing amounts of residual chemicals (oxidized dye, sodium hydroxide, and/or gluber salt) from the previous dip impeding the path of the dye bath stream. Strangely, as the dye bath concentration increased the yarn diffusion decreased. This is opposite the traditional behavior for concentration dependent diffusion. However, taken in context with residual chemicals impeding the path, this relationship

226 becomes understandable. As the dye bath concentration increases, the amount of residual chemicals from the previous dip increases. Thus the dye stream path was further hindered resulting in a slower diffusion process at greater numbers of dip.

Effective Yarn Diffusion Coefficient Prediction Profile for Dye Range Set-up Conditions 3.172e-6 [2.85e-6, 3.53e-6] Predicted Yarn Diffusion 1 3 5 7 1 2 3 11 12 14 16 18 20 22

(g/l)

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

The effect of pH on yarn diffusion coefficient is also shown in figure 4-39. As the pH was increased the diffusion coefficient also increased. A higher diffusion value means a greater dye bath concentration was penetrating into the structure of the yarn. This resulted in more dye being available for fiber transfer in the yarn interior. This coupled with a higher fiber diffusion coefficient at higher pH values as demonstrated in section 4.3.4.a produced a more penetrated (or less ring dyed) yarn cross section. This supports the concept of ring dyed yarns as a function of pH previously discussed by numerous authors and summarized in chapter 1.

The effect of dwell time on yarn diffusion coefficient must be discussed. As the dwell time was increased, the yarn diffusion coefficient actually decreased. At first glance this seemed counter- intuitive. However, one must realize to increase the dwell time on a fixed dwell length dye range, the speed must be reduced. As the speed was reduced the turbulent forces acting to push the dye

227 bath into the yarn structure were reduced. Whether this was an actual phenomenon or the result of assuming constant dye bath concentration at the outside node surface, it was reasonable for this effect to be present.

4.3.4.c Functional Relationship of Wet Pick-up

In contrast to the fiber and yarn diffusion coefficient analysis, the wet pick-up relationship to individual dye range set-up parameters was not very strong. This was primarily due to the fact that wet pick-up was dye range specific and highly dependent on chemical exchange. The calculated wet pick-up numbers were indirectly measurements of the individual dye range under certain dyeing conditions. Also, it was influenced by the diffusion of dye into the yarn and fiber structure since this was a wet on wet application. Technically speaking the pick-up would be 0% if the yarns were squeezed at the same pressure by the entrance and exit nip running through water only 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 R2 correlation coefficient of 0.26 and F ratio of 43.0 as shown in table 4-13. While this certainly wasn't a great model fit to the data, the significance of dye bath concentration and yarn diffusion coefficients were deemed statistically significant due to P values much less than 0.0001 and 0.0061 for nip pressure as shown in the effect test section of table 4-13. The lack of correlation was certainly due the error or variation surrounding each wet pick-up value.

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 =7.9595𝑒 − 1.5981𝑒 ∗ 𝑁𝑖𝑝 𝑃𝑟𝑒𝑠𝑠𝑢𝑟𝑒 −1.1134𝑒 ∗𝐷𝑦𝑒 𝐵𝑎𝑡ℎ − 3960.69 ∗ 𝐷

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

Figure 4-41 demonstrates the predicted wet pick-up as a function of dye range set-up parameters. As the nip pressure was increased the resulting wet pick-up decreased. This is typical of most textile processes involving squeeze rolls. As the dye bath concentration or yarn diffusion coefficient increased, the wet pick-up decreased. As discussed during the definition of %COWY calculation, wet pick-up was expected to vary as the dye bath concentration varied. One would expect the resulting %COWY to increase if exposed to greater concentration or if the diffusion of chemicals into the yarn structure increased. However, the wet pick-up decreased in order to maintain the correct %COWY value as the dye concentration increased. In any case, the relationship of dye bath concentration and yarn diffusion coefficient was determined to be significant.

230

Wet Pick-up Coefficient Prediction Profile for Dye Range Set-up Conditions 0.031492 ±0.002685 Wet pick-up 1 2 3 0 40 50 60 70 0.000001 0.000002 0.000003 0.000004 0.000005 0.000006 0.000007 0.000008

(g/l) 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.

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.

𝑊𝑎𝑠ℎ 𝑅𝑒𝑑𝑢𝑐𝑡𝑖𝑜𝑛 = −0.1043 +4.3698𝑒 ∗ 𝑠𝑝𝑒𝑒𝑑 − 1.7414𝑒 ∗ 𝐷𝑤𝑒𝑙𝑙 𝑇𝑖𝑚𝑒 + 6.4822𝑒 ∗ 𝑚𝑉 − 6.8279𝑒 ∗𝐷𝑦𝑒 𝐵𝑎𝑡ℎ( )

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

The effect of each parameter on wash reduction is shown in figure 4-43. As the speed increased the wash reduction increased. This seems straight forward as greater speed should facilitate more chemical removal. As the dwell time increased the wash reduction decreased. As with yarn diffusion this seemed counter-intuitive but on fixed length dye ranges an increase in time results from a decrease in speed. As the dye box reduction potential increased the wash reduction also increased. This was possibly due to actual reduction of the oxidized dye thereby increasing the mobility of the dye molecule. In the last column of figure 4-43, as dye bath concentration increased the wash reduction decreased. This probably has more to do with an increase in chemicals to be removed and less with the influence of the concentration on washing. However, dye bath

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

Wash Reduction Coefficient Prediction Profile for Dye Range Set-up Conditions Wash % 0.110581 ±0.006796 1 2 3 27 29 31 33 35 37 14 15 16 17 18 19 20 21 800 900

(g/l)

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.

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 ⎥ 𝑂𝑥𝑖𝑑𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑅𝑎𝑡𝑒 = exp (−10.4654 +𝑀𝑎𝑡𝑐ℎ(𝐷𝑖𝑝) ⎢4: −0.9826 ⎥ + 0.1263 ∗ 𝑠𝑝𝑒𝑒𝑑 + ⎢5: −0.6885⎥ ⎢6: −1.3462 ⎥ ⎣7: −1.3170⎦ 6.8530𝑒 ∗ 𝑜𝑥𝑖𝑑𝑖𝑧𝑎𝑡𝑖𝑜𝑛 𝑡𝑖𝑚𝑒 −1.0179𝑒 ∗𝑚𝑉)

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

The prediction profile which relates the calculated oxidation rate to the input variables is shown in figure 4-45. As the dip number increased the oxidation rate decreased. This was probably related to the increase of residual chemicals on weight of yarn as the number of dips increased. As the speed increased the oxidation rate increased. This was probably due to increase air circulation into and through the yarn structure thereby increasing the amount of available oxygen. Likewise, as the oxidation time increased due to either slower speeds or increased thread-up length, the rate increased. Interestingly as the reduction potential increased, the oxidation rate decreased. This of

236 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.

Oxidation Rate Coefficient Prediction Profile for Dye Range Set-up Conditions 0.086658 [0.07606, 0.09873] Predicted Oxidization Rate 1 3 5 7 27 29 31 33 35 37 60 70 700 800 900

Figure 4-45: Dye theory model oxidation rate functional relationship to dye range set-up conditions.

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

The final program enters in the appropriate dye range set-up conditions: yarn count, dip number, speed, dyeing dwell time, pH, dye bath concentration, nip pressure, and oxidation dwell time. Then the corresponding values for indigo dyeing coefficients: fiber diffusion, yarn diffusion, wet pick-up, wash reduction, and oxidation rate were calculated. The following logic was used to calculate the %IOWY, %COWY, and Integ shade value. The actual computer program is referenced in appendix section A-4-3b.

Enter dye range 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

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 R2 = 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 R2 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 R2 of 0.94. Furthermore the model results were deemed statistically significant following the overall model F ratio of 1077. However, like %COWY, the predicted %IOWY over estimated the actual %IOWY by 1.2% since the slope is 1.012.

%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

%IOWY Actual

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 R2 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 R2 of 0.97 with an F ratio of 1823 as shown in table 5-7. These values indicate an extremely strong correlation to the actual values and perform as well as the empirical model. Unfortunately, the slope of the fit is 1.097 with an intercept of -5.8. These are the result of the dye theory model over predicting the Integ shade at low values and slightly under predicting at high values. However, the general trend is for comparable Integ prediction performance to the empirical model.

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 R2 of 0.63 which isn’t extremely strong but deemed statistically significant by the F ratio of 109 and P-value < 0.0001. The reason for poor correlation is due to the great variation as evident by the wider range of the confidence intervals in figure 5-7. The mean penetration level is 0.38 units. The slope of the data fit is 0.97 which is very close to a 1 to 1 ratio as visibly evident. However, the intercept is -0.05 penetration units which is 1/8 of the mean value. This causes the empirical model to over predict the level of penetration in the yarns. In other words the empirical model predicts the yarns are less ring dyed or more penetrated than what actually occurred.

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 R2 correlation coefficient of 0.67 and F ratio of 129. However, the slope wasn't close 1 to 1. A slope of 0.81 coupled with an intercept of 0.04 indicates the dye theory model also over estimates the level of penetration.

250

Dye Theory Model Compared to Canadian Dye Range Actual Penetration Level 0.6

0.5

0.4

0.3 Penetration Level Actual Penetration

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 actually closer to the observational curve. This indicates the dye theory model better predicts the penetration level than the empirical model.

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.

By constructing similar build profile curves for the other Canadian dye range set-ups a similar relationship developed. Figure 5-10 was constructed from 32 m/min, 1.66 g/l, and 11.8 pH dye set-up and figure 5-11 from 32 m/min, 2.09 g/l, and 12.1 pH. In figure 5-10 both models slightly under predict the %IOWY and the resulting Integ shade. However, the dye theory models build profile better matches the observational measured profile even though both models predict more penetionrat than measured. In figure 5-11, the empirical model slightly under estimates the %IOWY and Integ values while the dye theory model slightly over estimates the %IOWY but underestimates the Integ. In this dye range set-up, both models over estimate penetration level by basically the same degree.

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.

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

The superior performance of empirical model prediction of penetration level compared to dye theory model results from the model's ability to calculate the penetration level independent of the %IOWY and Integ shade values. The dye theory model penetration level is indirectly converted from the predicted %IOWY and Integ values. This ability gives the empirical model a false sense of conformity. The analysis of empirical model penetration level prediction is repeated but this time the penetration level is calculated from the predicted %IOWY and Integ values. Figure 5-12 and table 5-10 compares the empirical model predicted indirect penetration level to the actual penetration level calculated from the measured %IOWY and Integ. Now the correlation coefficient is R2 of 0.59 with an F ratio of 92.7. This is actually a slightly inferior fit to the data than the dye theory model. More importantly, with a slope of 0.70 and intercept of 0.066 the shape of the fit was worse than the dye theory model. Recall dye theory had a slope of 0.80 and intercept of 0.04.

Empirical Model Indirect Penetration Level Comparison on Canadian Dye Range 0.6

0.5

0.4

Penetration Level Actual 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.

256

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 researched decided to find the porosity value that would match the target %IOWY. This would allow the predicted Integ values to be calculated and the final porosity value would be analyzed. Given this assumption the dye theory model predicted %IOWY will match the production yarn actual value.

The results of the empirical model predicted %IOWY are presented in figure 5-13 and table 5-13. The model predicts the %IOWY extremely well as the correlation coefficient of 0.97 and F ratio of 180 indicates. This is visually evident in the graph of predicted versus actual with all points falling extremely close to the center line and well within the 95% confidence intervals demarcated by the dotted lines. Furthermore, the slope of 0.98 and intercept of -0.10% confirms the empirical model performed exceptional well at predicting the %IOWY on actual production scale dyed yarns.

%IOWY Actual

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

259

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.

%IOWY Actual

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.

261

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.

262

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 R2 was 0.90 and F ratio was 47.4. While this isn't the strongest correlation it was deemed to be statistically significant due to P values of 0.0023.

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.

266

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.

𝑀𝑜𝑛𝑜𝑝ℎ𝑒𝑛𝑜𝑙𝑎𝑡𝑒𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛 = .. 𝐶𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡𝐴 = 0.016492 ∗ 𝑀𝑜𝑛𝑜𝑝ℎ𝑒𝑛𝑜𝑙𝑎𝑡𝑒𝐹𝑟𝑎𝑐𝑖𝑜𝑛 +0.003465 𝐶𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡𝐵 = −0.244296 ∗ 𝑀𝑜𝑛𝑜𝑝ℎ𝑒𝑛𝑜𝑙𝑎𝑡𝑒𝐹𝑟𝑎𝑐𝑡𝑖𝑜𝑛 +0.816158 %𝐼𝑂𝑊𝑌 = 𝐶𝑜𝑚𝑝𝑜𝑛𝑒𝑛𝑡𝐴 ∗ 𝐷𝑦𝑒𝐶𝑜𝑛𝑐𝑒𝑛𝑡𝑟𝑎𝑡𝑖𝑜𝑛 Equation 6-1: Equations to calculate %IOWY as a function of dye bath concentration and pH under equilibrium sorption conditions.

267

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.

% Penetration Level = M %

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

An extensive observational study was conducted on production scale indigo chain rope dye ranges. During this study various dye range set-up parameters were recorded: yarn count, dip, speed, dwell length, dwell time, oxidation time, nip pressure, dye bath indigo concentration, dye bath pH, dye bath reduction potential, and dye bath total alkalinity. After processing each yarn skein the %COWY, %IOWY, and Integ shade values were measured. The results from the observational study provided the basis for general trend analysis, empirical dye modeling, and theoretical dye modeling.

The general trends confirm many previously published conclusions but also indentified several new relationships never before discussed. Measurement and analysis has never been conducted on the %COWY after each dip of indigo. At first glance this value may seem trivial since the property never shows up at the doff end of the indigo dye range. However, the residual chemicals washed off during the wash section have monetary value. A better understanding of the dye range set-up parameters that cause %COWY to increased while not improving either the %IOWY

268 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.

270

Table 6-1: Empirical model performance review

Response Correlation Coef, R2 Slope Intercept %COWY 0.91 1.014 -0.000 %IOWY 0.94 1.012 -0.001 Integ 0.97 1.084 -1.344 Penetration Level 0.59 0.680 0.066

The empirical model was compared to actual production yarns from full scale indigo chain rope dye equipment. Surprising the %IOWY was predicted with exceptional level of accuracy. Unfortunately, that level of performance was not carried over to the Integ shade prediction. The empirical model correlated well with measured values but over predicted the actual value. At the higher Integ levels the differences between actual and empirical model prediction approached 30%. As a result, the penetration level wasn't predicted well either. A second indigo dye model was also created based on general dye and diffusion theory. In the dye theory model, dye coefficients such as fiber diffusion, yarn diffusion, wet pick-up, wash reduction, and oxidation rate were calculated based on the dye range set-up conditions. Then, using these dye coefficients the dye theory model calculated the resulting %COWY, %IOWY, Integ, and indirectly penetration level.

Just like the empirical model, the dye theory model was compared to a third independent indigo dye range. The resulting comparison demonstrated poorer correlation in predicting %COWY then the empirical model. However, the dye theory model performed as well as the empirical model at predicting the %IOWY and Integ. Further, the dye model actually outperformed the empirical model at predicting penetration level. The correlation coefficients, slopes, and intercepts from the dye theory model predicted compared to actual values are listed in table 6-2.

Table 6-2: Dye theory model performance review

Response Correlation Coef, R2 Slope Intercept %COWY 0.74 0.764 0.007 %IOWY 0.95 0.943 -0.001 Integ 0.97 1.097 -5.764 Penetration Level 0.67 0.806 0.041

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 R2 of 0.99 with a slope of 0.945 and intercept of 0.643.

The outperformance of the dye theory model compared to the empirical model was due to the ability to compensate for yarn porosity changes between the observational data collection state, non-tension, and production state, high tension. Furthermore, potential porosity dependence on dye range speed was introduced. While six data points were certainly not enough evidence to present a compelling argument, the strong correlation does warrant further investigation.

Recommendations

1. Expansion of the equilibrium sorption experiments would add more insight in the behavior and dependence of indigo dye uptake at various dye bath indigo concentrations and pH levels. Additional data points at lower pH levels are required to confirm the mathematical relationships presented. Specifically, higher dye bath indigo concentrations at much lower pH levels are required. While the current study coupled with Etters' previously published results offers a compelling argument, more data points are required to provide statistically strong support.

2. Additional observational studies need to be conducted from other full scale production chain rope indigo dye ranges. By adding more data points to the dye theory model, confidence intervals would be increased and observed general trends clarified. Specifically, a wider range of dye bath pH levels must be explored which incorporates pH buffering systems. The inability to reproduce published %IOWY and pH relationship must be further explored. Additionally, the speed and dwell time effect on response variables needs a greater variety in the range of values. These can only be achieved by varying the thread-up dwell length.

3. Refinement of the dye theory model nodal mesh would provide more insight in physico- chemical effects during the indigo dye process. Making changes in the finite difference nodal mesh which models the fiber and yarn structural characteristics would provide better prediction of dye

272 bath movement within the yarn structure and thereby better prediction of %IOWY, Integ shade, and indigo distribution or penetration level. Furthermore, it may be possible to decouple the yarn and fiber diffusion coefficients back into four elements instead of two. This would allow description of dye affinity or adsorption for the fiber surface and diffusion into the fiber interior. As well as understanding the difference between dye movement through the dye bath medium and boundary layer surrounding the individual fibers.

4. Incorporate additional production scale dyed yarn data points to expand dye theory model prediction and explore the effects of porosity value relating zero and production state tension. The current dye theory model preformed well at predicting the production yarn %IOWY and Integ shade. Additional data points are required to confirm the relationship. The relationship between dye range speed and actual yarn porosity presented is extremely enticing. However more data points are required from many different indigo chain rope dye ranges to confirm the relationship presented.

5. Combine current presented information and recommendations to create a commercial quality indigo dye prediction program. An accurate indigo dye prediction program would greatly assist the manufacturing quality control engineer. By coupling the prediction software with end item shade analysis and production history, the production engineer would know how current production conditions will affect the end item. This would allow for intelligent dye range adjustments to be made to control %IOWY and indigo distribution. Additionally, the indigo dye prediction software would assist dye range equipment manufactures. By understanding the dye range mechanical affects on %IOWY, Integ, and penetration level; certain fixed dye range mechanical properties could be tailored to a customer's requirements. Finally, the indigo dye prediction software would greatly assist an indigo dye house when developing new production shades. The ability to predict %IOWY, Integ, and indigo distribution without the need for trials would reduce development time and costs.

273

REFERENCES

1. Buffalo Color Corporation, Technical Information Bulletin, Indigo Paste: Common Sense Practices in Indigo Dyeing, 1997.

2. J. Crank, Mathematics of Diffusion, Oxford University Press, 1957.

3. P.B. Weisz, Sorption-Diffusion in Porous Solids and the Dyeing Process, 1966.

4. R. McGregor, Diffusion and Sorption in Fibers and Films, Academic Press, London, 1974.

5. Y.A. Cengel and M.A. Boles, Thermodynamics: An Engineering Approach, 1989, McGraw-Hill.

6. P.M. Gerhart, R.J. Gross, and J.I. Hochstein, Fundamentals of Fluid Mechanics, 2nd Edition, Addison-Wesley Publishing, 1992.

7. A. Bejan, Heat Transfer, John Wiley and Sons, 1993.

8. P. Atkins, Physical Chemistry, 5th Edition, 1994, Oxford University Press.

9. R. McDonald, Colour Physics for Industry, 2nd Edition, Society of Dyers and Colourists, 1997.

10. J.N. Etters, “Diffusion Equations Made Easy”, source, June 1980 Vol 12, No 6 p. 37-42.

11. J.N. Etters, “The Diffusional Boundary Layer: Some Implications for the Dyeing Technologist”, Journal of Society of Dyers & Colorist, April 1981, Vol 97 p. 170-179.

12. J.N. Etters, “An Automatic Computation of Diffusion Equation Solutions”, Textile Research Journal, 1983, 53, p. 598-605.

13. J.A. Greer and G.R. Turner, “Indigo Denims: The Practical Side”, Textile Chemist and Colorist, Vol 15, No 6, June 1983, p.11-18.

14. J.N. Etters, “Efficient Use of Sodium Hydrosulfite in Commerical Vat Dyeing Processes”, American Dyestuff Reporter, March 1989, p18-26.

274

15. J.N. Etters, “Effect of Dyebath pH on Color Yield in Indigo Dyeing of Cotton Denim Yarn”, Southeastern Section of AATCC, 1989 ITPC Paper, Textile Chemist and Colorist, 21 (12) p25-31.

16. I.L. Haas, “Indigo Dyeing: Process and Machine Concepts”, International Textile Bulletin, Feb. 1990, p45-48.

17. J.N. Etters, “New Opportunities in Indigo Dyeing”, American Dyestuff Reporter, Sept. 1990, p19,101.

18. J.N Etters, “Estimating and Using Surface Reflactance in Kubelka-Munk Computations”, American Dyestuff Reporter, April 1991, p 15- 21.

19. P.A. Annis, J.N.Etters, and G.L. Baughman “Dyeing with Indigo: New Data Correlating Colour Yeild with Ionic Form of Applied Dye”, Canadian Textile Journal, May 1991, p20-23.

20. J.N Etters and M. Hou, “Equilibrium Sorption Isoterms of Indigo on Cotton Denim Yarn: Effect of pH”, Textile Research Journal, Dec. 1991 Vol 61(12), p. 773-776.

21. J.N. Etters, “Predicting Shade Depth and Wash-Down Characteristics of Indigo-Dyed Denim: A Mathematical Analysis”, American Dyestuff Reporter, Feb. 1992, p42-46.

22. J.N. Etters, “Quality Control of Cotton Denim in Indigo Dyeing”, American Dyestuff Reporter, March 1992, p17-24.

23. J.N. Etters, “Sorting Dyed Denim Fabric to Possess Similar Wash-Down Characteristics”, American Dyestuff Reporter, Aug. 1992, p26-37.

24. J.N Etters, “Reducing Environmental Contamination by Indigo in Continuous Dyeing of Cotton Denim Yarn”, American Dyestuff Reporter, Feb. 1993, P30-33,50.

25. J.N. Etters, “Indigo dyeing of cotton denim yarn: correlating theory with practice”, Journal of Society of Dyers & Colorist, July/Aug. 1993, Vol 109 p.251-255.

26. J.N. Etters, “Quick-Wash Denim: New Opportunity for Denim Garment Manufacturers”, American Dyestuff Reporter, May 1994, p15-16.

27. J.N. Etters, “Reproducibility in Indigo Dyeing”, American Dyestuff Reporter, June 1994, p26-29.

275

28. J.N. Etters, “Kinetics of Dye Sorption: Effect of Dyebath Flow on Dyeing Uniformity”, American Dyestuff Reporter, Jan. 1995.

29. C.L. Chong, L.W. Poon, and W.C. Poon, “Improving Indigo dyeing Colour Yield”, Textile Asia, Jan. 1995, p55- 57.

30. J.N Etters., “Advances in Indigo Dyeing: Implications for the Dyer, apparel Manufacture and Enironment”, American Dyestuff Reporter, Feb. 1995 p17-22.

31. J.N. Etters, “Diffusion-Controlled Sorption of Dye by Cylindrical Fibers: Matching Empirical and Theoretical Models”, AATCC 1995 International Conference & Exhibition Book of Papers, Oct 8-11.

32. P.J. Hauser and B.D. Basinger, “Creative Textile Finishing: Two Commercial Examples”, AATCC 1995 International Conference & Exhibition Book of Papers, Oct 8-11.

33. J.N. Etters, “Recent Progrss in Indigo Dyeing of Cotton Denim Yarn”, Indian Journal of Fibre & Textile Research, Vol 21 March 1996, p-30-34.

34. P.J. Hauser, A. Bairathi, “New System for Improved Denim Dyeing”, American Dyestuff Reporter, Aug. 1996, p55-57,69.

35. M.S. Parmar, S.S. Satsangi, and J. Prakash, “Indigo Dyed Warp Yarn – An Essential Requirement for Manufacturing Denim”, Colourage, Sept. 1996, p45-50.

36. R. Paul, S.R. Naik, and R. Rajagopal, “The Indigo Phenomenon: Evolution from Natural to Synthetic”, Denim Series – Part III, Textile Dyer & Printer, Nov.6, 1996, p12-16.

37. R. Paul, S.R. Naik and R. Kumar, “The Indigo Machine – The Cradle of Blue Revolution”, Denim Series – Part V, Textile Dyer & Printer, Dec.4, 1996, p15-21.

38. R. Paul, S.R. Naik and U. Sharma, “Indigo Dyeing: Chemistry Process and Trouble Shooting”, Denim Series – Part VI, Textile Dyer & Printer, Dec.18, 1996, p18-23.

39. R. Paul and S.R. Naik, “The Continuous Indigo Dyeing of Cotton Denim Warp Yarn”, Denim Series – Part VII, Textile Dyer & Printer, Jan.1, 1997, p11-14.

40. R. Paul and S.R. Naik, “Historical Aspects of Indigo Dyeing”, Denim Series – Part VIII, Textile Dyer & Printer, Feb.12, 1997, p13-16.

276

41. R. Paul and S.R. Naik, “Full Spectrum Denim – A Recent Development”, Denim Series – Part X, Textile Dyer & Printer, Mar. 12, 1997, p16-17.

42. R. Paul and S.R. Naik, “The Technology of Ring Dyeing – An Economically Viable, Environment Friendly Development”, Denim Series – Part XI, Textile Dyer & Printer, April 9, 1997, p16-22.

43. T. Bechtold, E. Burtscher, G. Kuhnel, and O. Bobleter, “Electrochemical Reduction Processes in Indigo Dyeing”, Journal of Society of Dyers and Colorist, Vol 113, April 1997, p135-144.

44. T.Bechtold, E. Burtscher, A. Turcanu, and O. Bobleter, “Dyeing Behavior of Indigo Reduced by Indirect Electrolysis”, Textile Research Journal, Vol 69, Sept. 1997, p635-642.

45. J.N. Etters, “pH-Controlled Indigo Dyeing: Buffered Dyebaths vs Caustic Dosing”, American Dyestuff Reporter, Sept. 1998, p15-17.

46. J.H. Xin, “Colour Variation in the Dyeing of Denim Yarn with Indigo”, Journal of Society of Dyers & Colorist, Sept. 2000, Vol 116, P. 260-265.

47. P.J. Hauser and J.T. Merritt, “Improved Determination of Indigo on Fibers or Fabrics”, Textile Chemist and Colorist & American Dyestuff Reporter, Vol 32, No 12, Dec. 2000, p33-35.

48. X. Zhou, “Studies on Indigo Dyeing and Diffusion by the Film Roll Method”, Color Technology, 117, 2001, p. 68-75.

49. E.G. McFarland, W.W. Carr, and S. Michilsen, “Determining Diffusion and Convective Mass Transfer Coefficients in Dyeing a thin Flat Film”, Textile Research Journal, Vol 72, Sept. 2002, p756-763.

50.C. Choi, J. Nah, “Seperation of Dye Substance form Polygoum Tinctoris and It’s Dyeing Characterization”, Theories and Applications of Chemical Engineering, Vol9, N02, 2003, p624-627.

51. P. Westbroek, “Improving Quality and Reproducibility of the Indigo Dye Process by Measuring and Controlling Indigo and Sodium Dithionite Concentrations”, Textile Research Journal, Dec. 2003 Vol 73(2), p. 1079-1084.

52. H.T Deo and R. Paul, “Standing Bath Technique for Indigo Denim Dyeing”, International Textile Bulletin, Feb. 2004, p66-68.

277

53. U. Sahin, “Real Time Monitoring of Indigo Concentrations in the Dye bath with a Laser Diode Spectrometer”, Textile Research Journal, Mar. 2004 Vol 74(3), p 193-197.

54. E.P.A. Kumbasar, “Automatic Indigo Measurement System as Part of a Dosing System for Indigo Dyeing”, Fibers & Textiles, July/Sept. 2006 Vol 14 No 3 p. 86-90.

55. N. Meksi, “Cotton dyeing by Indigo with the Borohydride Process: Effect of Some Experimental Conditions on Indigo Reduction and Dyeing Quality”, Chemical Engineering Journal, 2007, Vol 131, p. 187-193.

56. P. Hudson, A. Clapp, D. Kness, Joseph's Introductory Textile Science, Sixth Ed., Harcourt Brace Jovanovich Publishers, 1993.

57. Y. Mogahzy, "Understanding the Fiber-to-Yarn Conversion System PART II: Yarn Characteristics", Auburn.edu, 1993.

58. A. Nabovati, "Through-thickness Permeability Prediction of three-dimensional Multifilament Woven Fabrics", Composites, Part A41, 2010, p453-463.

59. M. Ozisik, Heat Transfer: A Basic Approach, McGraw-Hill, 1985.

60. J.R. Welty, C.E. Wicks, R.E Wilson, Fundamentals of Momentum, Heat, and Mass Transfer, 3rd Ed, John Wiley & Sons, 1984.

61. J.T. Merritt, K.R. Beck, C.B. Smith, P. Hauser, W.J. Jasper, "Determination of Indigo in Dyebaths by Flow Injection Analysis and Redox Titrations", AATCC Review, 53-57, 2001.

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

= (−%𝑇 ∗ 0.0373) + 3.628

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

280

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.

𝑔/𝑙 𝐴𝑙𝑘𝑎𝑙𝑖𝑛𝑖𝑡𝑦 = 0.2 ∗ 𝑣𝑜𝑙𝑢𝑚𝑒 𝑜𝑓𝑎𝑐𝑖𝑑𝑢𝑠𝑒𝑑

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

281

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

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 22.78 15.15 11.40 9.33 420 28.23 19.75 15.23 12.70 440 27.56 18.64 14.14 11.63 460 25.10 16.23 12.06 9.78 480 23.09 14.31 10.38 8.25 500 21.16 12.69 9.07 7.08 520 18.82 10.87 7.49 5.71 540 15.90 8.77 5.95 4.48 560 14.25 7.64 5.07 3.80 580 12.60 6.48 4.26 3.20 600 10.82 5.40 3.56 2.69 620 9.44 4.60 3.07 2.35 640 7.96 3.83 2.62 2.05 660 7.03 3.51 2.49 1.95 680 9.24 4.58 3.15 2.46 700 18.45 10.63 7.54 5.78

284

Table A-4-1: Continued

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 36.576 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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 36.576 14.1 59.1 0.764 11.91 762 2.5 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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 36.576 14.1 59.1 0.764 11.91 762 2.5 8.63 36.03 60.00 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 6.7962 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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 36.576 14.1 59.1 0.764 11.91 762 2.5 8.63 36.03 60.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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 36.576 14.1 59.1 0.764 11.91 762 2.5 8.63 36.03 60.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1162 31.0896 16.7 69.5 1.066 11.76 743 3.42 8.63 36.03 70.00 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 6.9125 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1162 31.0896 16.7 69.5 1.066 11.76 743 3.42 8.63 36.03 70.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 5 Dip 7 400 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

Table A-4-1: Continued

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 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) T3675 34.75 14.7 62.2 1.932 11.5 836 4.82 8.63 36.03 70.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 2 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) T3675 34.75 14.7 62.2 1.932 11.5 836 4.82 8.63 36.03 70.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) T3675 34.75 14.7 62.2 1.932 11.5 836 4.82 8.63 36.03 70.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 4257 31.09 16.7 69.5 2.084 11.62 847 4.71 8.63 36.03 70.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1169 31.09 16.7 69.5 2.34 11.6 888 6.27 8.63 36.03 70.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1134 31.09 16.7 69.5 2.314 11.89 805 5.17 8.63 36.03 70.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1134 31.09 16.7 69.5 2.314 11.89 805 5.17 8.63 36.03 70.00 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 6.8377 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1134 31.09 16.7 69.5 2.314 11.89 805 5.17 8.63 36.03 70.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1134 31.09 16.7 69.5 2.314 11.89 805 5.17 8.63 39.40 70.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) t3688 32.92 15.8 65.7 2.417 11.82 867 4.93 8.63 39.40 70.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1156 36.58 14.1 59.1 2.572 11.72 797 5.55 8.63 39.40 70.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1156 36.58 14.1 59.1 2.572 11.72 797 5.55 8.63 39.40 70.00 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 6.9734 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1156 36.58 14.1 59.1 2.572 11.72 797 5.55 8.63 39.40 70.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1156 36.58 14.1 59.1 2.572 11.72 797 5.55 8.63 39.40 70.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1156 36.58 14.1 59.1 2.572 11.72 797 5.55 8.63 39.40 70.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1156 36.58 14.1 59.1 2.572 11.72 797 5.55 8.63 39.40 70.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1157 32.92 15.9 65.7 2.497 12.41 847 3.67 8.63 39.40 70.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1157 32.92 15.9 65.7 2.497 12.41 847 3.67 8.63 39.40 70.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1157 32.92 15.9 65.7 2.497 12.41 847 3.67 8.63 39.40 70.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) X3254 27.43 18.9 78.8 2.614 12.29 778 2.85 8.63 39.40 70.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1156 36.58 14.1 59.1 2.716 11.94 836 6.06 8.63 39.40 70.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1156 36.58 14.1 59.1 2.716 11.94 836 6.06 8.63 39.40 70.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1156 36.58 14.1 59.1 2.716 11.94 836 6.06 8.63 39.40 70.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1134 31.09 16.7 69.5 2.994 11.98 789 6.6 8.63 39.40 70.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1134 31.09 16.7 69.5 2.994 11.98 789 6.6 8.63 39.40 70.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1134 31.09 16.7 69.5 3.133 12.54 801 6.16 8.63 39.40 70.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1134 31.09 16.7 69.5 3.133 12.54 801 6.16 8.63 39.40 70.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) t3735 34.75 19.6 63.9 0.761 11.08 722 2.13 11.37 40.50 40.00 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 6.3 1 only 1 8.2806 7.9396 8.0993 7.9339 2.01% 0.137% 0.443% 8.2 0.31 6.3 1--2 2 8.1831 7.8587 8.00842 7.8595 1.91% 0.305% 0.765% 18.4 0.40 6.3 1--3 3 8.3069 7.9597 8.2823 7.9829 4.05% 0.577% 1.141% 32.7 0.51 6.3 1--4 4 8.236 7.9002 8.2137 7.934 3.97% 0.666% 1.539% 41.1 0.43 6.3 1--5 5 8.2356 7.8895 8.2191 7.936 4.18% 0.902% 2.312% 51.8 0.39 6.3 1--5,4 6 8.3191 7.9783 8.3805 8.0502 5.04% 1.167% 3.321% 61.9 0.35 1--5,4- 6.3 5 7 8.1713 7.8316 8.2105 7.9057 4.84% 1.358% 3.884% 66.5 0.35 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1110 32.92 20.7 67.5 0.733 12.23 813 2.79 11.37 40.50 40.00 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 6.9391 6.6999 6.8035 6.6768 1.55% 0.134% 0.370% 6.9 0.36 7.1 1--2 2 6.9948 6.782 6.8888 6.7635 1.57% 0.220% 0.627% 12.9 0.35 7.1 1--2,1 3 6.854 6.62 6.746 6.6079 1.90% 0.365% 0.763% 18.3 0.48 1--2,1- 7.1 2 4 6.9343 6.7022 6.8375 6.6915 2.02% 0.446% 0.875% 23.5 0.51

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1110 32.92 20.7 67.5 0.733 12.23 813 2.79 11.37 40.50 40.00 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 8 1 only 1 6.1777 5.9717 6.0737 5.9531 1.71% 0.131% 0.284% 5.5 0.46 8 1--2 2 6.0447 5.8247 5.939 5.8135 1.96% 0.245% 0.572% 11.3 0.43 8 1--2,1 3 6.1363 5.9296 6.0544 5.9254 2.10% 0.369% 0.726% 16.6 0.51 1--2,1- 8 2 4 6.1302 5.9119 6.0437 5.9109 2.23% 0.455% 0.864% 23.0 0.53

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1110 32.92 20.7 67.5 0.733 12.23 813 2.79 11.37 40.50 40.00 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 12 1 only 1 3.9485 3.8069 3.8929 3.802 2.26% 0.171% 0.375% 7.0 0.46 12 1--2 2 3.9064 3.7635 3.8499 3.7621 2.30% 0.305% 0.630% 13.0 0.48 12 1--2,1 3 3.9594 3.8156 3.9091 3.819 2.45% 0.417% 0.756% 17.9 0.55 1--2,1- 12 2 4 4.0246 3.8837 3.9877 3.8952 2.68% 0.583% 0.930% 25.8 0.63 1--2,1- 12 2,1 5 3.9455 3.805 3.9101 3.8191 2.76% 0.670% 1.041% 29.8 0.64 1-2,1- 12 2,1-2 6 3.8618 3.7262 3.8285 3.747 2.75% 0.821% 1.271% 35.9 0.65 1-2,1- 12 2,1-2,1 7 3.8127 3.6766 3.7908 3.6985 3.11% 0.964% 1.530% 40.9 0.63 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) t3706 34.75 19.6 63.9 0.94 11.48 861 2.22 11.37 40.50 40.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) t3706 34.75 19.6 63.9 0.94 11.48 861 2.22 11.37 40.50 40.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1142 34.75 19.6 63.9 0.946 11.49 742 3.4 11.37 40.50 40.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1142 34.75 19.6 63.9 0.946 11.49 742 3.4 11.37 40.50 40.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1126 34.75 19.6 63.9 1.051 11.38 792 3.32 11.37 40.50 40.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1126 34.75 19.6 63.9 1.051 11.38 792 3.32 11.37 40.50 40.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1126 34.75 19.6 63.9 1.117 11.55 771 2.79 11.37 40.50 40.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1126 34.75 19.6 63.9 1.117 11.55 771 2.79 11.37 40.50 40.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) t3738 34.75 19.6 63.9 1.409 11.36 874 2.35 11.37 40.50 40.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1099 32.92 20.7 67.5 1.827 11.71 867 3.11 11.37 40.50 40.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1099 32.92 20.7 67.5 1.738 11.71 873 3.07 11.37 40.50 40.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1099 32.92 20.7 67.5 1.827 11.71 867 3.11 11.37 40.50 40.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1099 32.92 20.7 67.5 1.615 11.61 863 3.12 11.37 40.50 40.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) x3319 27.43 25 81 1.848 12.19 801 2.55 11.37 40.50 40.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) q1910 34.75 19.4 63.9 1.831 11.54 875 4.56 11.37 40.50 40.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) q1910 34.75 19.4 63.9 1.831 11.54 875 4.56 11.37 40.50 40.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) q1910 34.75 19.4 63.9 1.831 11.54 875 4.56 11.37 40.50 40.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) q1910 34.75 19.4 63.9 1.831 11.54 875 4.56 11.37 40.50 40.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) x3313 32.92 20.7 67.5 1.762 12.31 795 3.12 11.37 40.50 40.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) x3313 32.92 20.7 67.5 1.762 12.31 795 3.12 11.37 40.50 40.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) x3313 32.92 20.7 67.5 1.762 12.31 795 3.12 11.37 40.50 40.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) x3313 32.92 20.7 67.5 1.762 12.31 795 3.12 11.37 40.50 40.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 4223 32.92 20.7 67.5 2.07 12.49 907 3.75 11.37 40.50 40.00 Yarn Skein Response Variables Yarn Greige Boil Off Dyed Washed 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 6 7.025 6.916 7.252 6.9043 4.86% 1.551% 2.859% 57.6 0.54 1- 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 4223 32.92 20.7 67.5 2.07 12.49 907 3.75 11.37 40.50 40.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 1 Dip 2 Dip 3 Dip 3 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) x3313 32.92 20.7 67.5 1.93 12.33 800 3.26 11.37 40.50 40.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) t3663 34.75 19.6 63.9 2.053 11.84 865 4.29 11.37 40.50 40.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1472 34.75 19.6 63.9 2.259 11.85 858 4.17 11.37 40.50 40.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1472 34.75 19.6 63.9 2.158 11.88 846 4.4 11.37 40.50 40.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) x3626 31.09 21.7 71.5 2.283 11.8 783 4.48 11.37 40.50 40.00 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 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 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) x3626 31.09 21.7 71.5 2.134 11.76 789 4.58 11.37 40.50 40.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1139 28.35 24.1 78.4 2.261 11.69 810 5.09 11.37 40.50 40.00 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 6.3 1 only 1 8.2729 7.9479 8.207 7.9275 3.26% 0.290% 0.709% 15.9 0.41 6.3 1--2 2 8.3119 7.9733 8.3618 7.9816 4.87% 0.609% 1.181% 33.7 0.52 6.3 1--3 3 8.3462 8.0196 8.4306 8.05 5.12% 1.042% 2.285% 51.5 0.46 6.3 1--3,2 4 8.3676 8.0251 8.4956 8.0903 5.86% 1.258% 2.984% 58.8 0.42 6.3 1-3,2-3 5 8.2123 7.8902 8.3684 7.9789 6.06% 1.624% 4.320% 69.7 0.38 1-3,2- 6.3 3,2 6 8.2672 7.9373 8.4549 8.057 6.52% 1.986% 5.539% 77.4 0.36 1-3,2- 6.3 3,2-3 7 8.2995 7.9644 8.5276 8.1316 7.07% 2.410% 7.229% 85.5 0.33 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) x3669 31.09 21.7 71.5 2.277 11.92 880 5.14 11.37 40.50 40.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1139 28.35 24.1 78.4 2.307 11.77 822 5.62 11.37 40.50 40.00 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 7.2476 7.0441 7.3261 7.0477 4.00% 0.351% 0.767% 18.5 0.46 7.1 1--2 2 7.2488 7.0476 7.4163 7.0762 5.23% 0.708% 1.338% 37.3 0.53 7.1 1--3 3 7.218 7.0199 7.4125 7.0754 5.59% 1.042% 2.061% 48.8 0.51 7.1 1-3,1 4 7.0859 6.8954 7.2841 6.9645 5.64% 1.249% 3.124% 60.1 0.40 7.1 1-3,1-2 5 7.263 7.0584 7.5089 7.1656 6.38% 1.588% 4.651% 72.0 0.34 7.1 1-3,1-3 6 6.9719 6.7815 7.243 6.9018 6.81% 1.839% 5.282% 75.9 0.35 1-3,1- 7.1 3,3 7 7.2627 7.0641 7.5541 7.204 6.94% 2.036% 6.052% 80.1 0.34 % Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1134 26.52 25.7 83.8 3.228 11.4 873 6.15 11.37 40.50 40.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-4-1: Continued

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) 1134 29.26 23.5 75.9 3.497 11.62 897 5.13 11.37 40.50 40.00 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7

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 <= num_yarns; cty++) { for (ctx = 1; ctx<=num_dips; ctx++) { new_stdev[ctx] = 0.5; old_stdev[ctx] = 0.5; Df_total[ctx] = 0.0; Dy_total[ctx] = 0.0; WP_total[ctx] = 0.0; AO[ctx] = 0.02; Df_AO[ctx] = 4.6e-10; Dy_AO[ctx] = 1.18e-6; WP_AO[ctx] = 0.05; } } for (cty=0; cty<=num_yarns; cty++) { for (ctx = 0; ctx <= num_dips; ctx++) wash_dip[cty][ctx] = 0.01; } while (AO_change < 0.99 || AO_change > 1.01) { //while loop to cycle thru until stdev reaches limit yarn_count = 1; // Open each yarn count while (yarn_count <= num_yarns) { printf ("Processing yarn # %i\n", yarn_count); wash = wash_dip[yarn_count][1]; slope = 1.0; while (slope < -0.005 || slope > 0.005 { IOWYsurface_ratio = IOWYtotal_ratio = COWYtotal_ratio = 0.99; for (ctx=0; ctx <= (num_dips+1); ctx++) { Df_constantAO[ctx]=0.0; Dy_constantAO[ctx]=0.0; WP_constantAO[ctx]=0.0; dip_error[ctx]=0.0; pickup_error[ctx]=0.0; } for (ctx=0; ctx<=rows; ctx++) { IOWYpre[ctx] = 0.0; COWYpre[ctx] = 0.0; IOWY[ctx] = 0.0; IOWYoxd[ctx] = 0.0; COWY[ctx] = 0.0; } for (x=0; x<=19; x++) input[0][x]=0.0;

for (current_dip = 1; current_dip <= num_dips; current_dip++) { printf ("Processing dip # %i\n", current_dip); if (yarn_count == 1) oFile = fopen ("yarninput1.txt", "rb" ); if (yarn_count == 2) oFile = fopen ("yarninput2.txt", "rb" );

373

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<1; z++) { for (x = 0; x <=19; x++) fscanf (oFile, "%f", &input[0][x]); } } fclose (oFile); printf ("%i\t%e\t%e\n", yarn_count, input[0][2], input[0][3]); Df = Df_AO[current_dip]; Dy = Dy_AO[current_dip]; wetpickup = WP_AO[current_dip]; dwelltime = input[0][5]; oxd_time = input[0][6]; num_time_steps = dwelltime/DT; dt = DT; radius = (-0.1655+(1.951/sqrt(input[0][2])))/20.0; //cm dr = radius/(rows); //cm DOy = 0.219; //oxygen diffusion coefficient cm2/sec Ur = 0.0; UOr = -1.0 * input[0][19] * input[0][14]*100/60; //air velocity cm/sec A = input[0][15]; IOWYsurface_ratio=0.0; IOWYtotal_ratio=0.0; COWYtotal_ratio=0.0; gmIplit = input[0][7]; //g/l gmNaOHplit = input[0][8]; // g/l pH = input[0][9]; //dye bath pH Integ = input[0][11]; //shade IOWYtarget = input[0][10]; IOWYsurface_target = 0.0; // %IOWY at the surface from Integ conversion COWYtarget = input[0][12]; // Conversion of Integ to target %IOWY at the surface of the yarn IOWYsurface_target = 0.0; IOWYsurface_target = -0.02646465 + (9.53859e-4*Integ) + (1.35931e-5*pow ((Integ-55.2088),2)) + (3.909e-8*pow((Integ-55.2088),3)); IOWYsurface_target = IOWYsurface_target + (2.42444e-9*pow((Integ-55.2088),4)) + (6.4303e-11*pow((Integ-55.2088),5)); for (ctx = 0; ctx<=rows; ctx++) { gms_ctn_node[ctx] = 1.54*porosity*2.0*PI25DT*ctx*dr*dr; liter_per_node[ctx] = (1-porosity)*2.0*PI25DT*ctx*dr*dr; } gms_ctn_node[0] = 1.54*porosity*PI25DT*0.25*dr*dr; liter_per_node[0] = (1-porosity)*PI25DT*0.25*dr*dr; gms_ctn_node[rows] = 1.54*porosity*PI25DT*(radius*dr-(0.25*dr*dr)); liter_per_node[rows] = (1-porosity)*PI25DT*(radius*dr-(0.25*dr*dr)); while (COWYtotal_ratio < 0.995 || COWYtotal_ratio > 1.005 || IOWYsurface_ratio<0.995 || IOWYsurface_ratio>1.005||IOWYtotal_ratio<0.995 ||IOWYtotal_ratio>1.005) { x=i=j=k=ctx=cty=0; pivot=0; IOWYtotal=0.0; COWYtotal=0.0; IOWYsurface=0.0; // Set-up initial conditions for (ctx = 0; ctx<=rows; ctx++) {

374

X[ctx]=0.0; Cj[ctx]=0.0; Cj1[ctx]=0.0; d[ctx]=0.0; temp[ctx]=0.0; RBL[ctx]=0.0; RBL1[ctx]=0.0; RBLgm[ctx]=0.0; RBL1gm[ctx]=0.0; IOWY[ctx]=0.0; //these will change for multiple dips IOWYoxd[ctx]=0.0; COWY[ctx]=0.0; IOWYstep[ctx]=0.0; dumb[ctx]=0.0; OBL[ctx]=0.0; OBL1[ctx]=0.0; OBLgm[ctx]=0.0; OBL1gm[ctx]=0.0; TBL[ctx] = RBL[ctx] + OBL[ctx]; TBL1[ctx] = RBL1[ctx] + OBL1[ctx]; for(cty = 0; cty<=rows; cty++) { AA[ctx][cty]=0.0; BB[ctx][cty]=0.0; } } Cj[rows]=gmIplit; Cj1[rows]=gmIplit; lamda = (Dy*dt)/(2.0*dr*dr); alpha = (Ur*dt)/(4.0*dr); beta = (Dy*dt)/(4.0*dr); for (ctx = 0; ctx

375

Mt = (((4.0/pow(PI25DT,0.5))*(pow((Df*dwelltime/(0.0009*0.0009)),0.5))) -(Df*dwelltime/(0.0009*0.0009))-((1.0/(3.0*pow(PI25DT,0.5)))*(pow((Df* dwelltime/(0.0009*0.0009)),(3.0/2.0)))))/num_time_steps; for (ctx = 0; ctx < rows; ctx++) { if (Cj[ctx] <= 0.0) IOWYstep[ctx] = 0.0; else IOWYstep[ctx] = Mt*CompA*pow(Cj[ctx],CompB); d[ctx] = -1.0 * gms_ctn_node[ctx] * IOWYstep[ctx] / liter_per_node[ctx]; } d[rows-1] = d[rows-1] + (Cj[rows]*2.0*((beta/(radius))+lamda-alpha)); if (Cj[rows] <= 0.0) IOWYstep[rows] = 0.0; else IOWYstep[rows] = Mt*CompA*pow(Cj[rows],CompB); // Find new dye concentration by Guass-Jordan elimination for (ctx = 0; ctx

376

} } } 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]; } for (ctx = 1; ctx < rows; ctx++) { { IOWY[ctx] = IOWY[ctx] + IOWYstep[ctx]; } } IOWY[rows] = IOWY[rows] + IOWYstep[rows]; for (ctx = 0; ctx <= rows; ctx++) dye_bath_dist[yarn_count][current_dip][ctx] = Cj1[ctx]; } // Close time step loop for process in dye box // Nip process for (ctx = 0; ctx <= rows; ctx++) { RBL1[ctx] = Cj1[ctx]; RBL1gm[ctx] = Cj1[ctx] * liter_per_node[ctx] * wetpickup; OBL1gm[ctx] = (COWYpre[ctx] - IOWYpre[ctx]) * gms_ctn_node[ctx] * wash; if (OBL1gm[ctx] < 0.0) OBL1gm[ctx] = 0.0; } IOWYtotal=0.0; IOWYsurface=0.0; COWYtotal=0.0; oxd_time_steps = oxd_time/DT; dt=DT; Air = 0.2541; // gm per liter of oxygen for (ctx = 0; ctx<=rows; ctx++) { Cj[ctx]=0.0; // g/l of oxygen Cj1[ctx]=0.0; d[ctx]=0.0; X[ctx]=0.0; Xrbl[ctx]=0.0; Xiowy[ctx]=0.0; for(cty = 0; cty<=rows; cty++) { AA[ctx][cty]=0.0; BB[ctx][cty]=0.0; } } Cj1[rows]=Air; lamda = (DOy*dt)/(2.0*dr*dr); alpha = (UOr*dt)/(4.0*dr); beta = (DOy*dt)/(4.0*dr); for (ctx = 0; ctx

377

BB[ctx][ctx]=1.0 + (-2.0*lamda); } for (ctx = 1; ctx <(rows-1); ctx++) { AA[ctx][ctx+1]=(-beta/(ctx*dr))-lamda+(alpha); AA[ctx+1][ctx]=(beta/((ctx+1)*dr))-lamda-(alpha); BB[ctx][ctx+1]=(beta/(ctx*dr))+lamda-(alpha); BB[ctx+1][ctx]=(-beta/((ctx+1)*dr))+lamda+(alpha); } AA[0][1]=-2.0*lamda; AA[1][0]=(beta/dr)-lamda-(alpha); BB[0][1]=2.0*lamda; BB[1][0]=(-beta/dr)+lamda+(alpha); // Start time step for oxidation for (ts = 1; ts <= oxd_time_steps; ts++) { for (ctx = 0; ctx <= rows; ctx++) { Cj[ctx]=Cj1[ctx]; RBL[ctx]=RBL1[ctx]; RBLgm[ctx]=RBL1gm[ctx]; OBLgm[ctx]=OBL1gm[ctx]; temp[ctx]=0.0; } for (ctx = 0; ctx <= rows; ctx++) { if (Cj[ctx] <= 0.0) { Xrbl[ctx] = 0.0; Xiowy[ctx] = 0.0; X[ctx] = Xrbl[ctx] + Xiowy[ctx]; } else { if (RBLgm[ctx] > 0.0) X[ctx]=1/(AO[current_dip]*Cj[ctx]* liter_per_node[ctx]*dt/(RBLgm[ctx]+(IOWY[ctx]*gms_ctn_node[ctx]))); else if (IOWY[ctx] > 0.0) X[ctx]=1/(AO[current_dip]*Cj[ctx]* liter_per_node[ctx]*dt/((IOWY[ctx]*gms_ctn_node[ctx]))); else X[ctx]=0.0; } if (X[ctx] > 1.0) X[ctx]=1.0; d[ctx] = -1.0 * X[ctx] * Cj[ctx] * dt; if (d[ctx] > 0.0) d[ctx] = 0.0; } d[rows-1] = d[rows-1] + (Cj[rows]*2*((beta/radius)+lamda-alpha)); // Find new oxygen concentration by Guass-Jordan elimination for (ctx = 0; ctx

378

for (i = 0; i < rows; i++) { if (AAinvt[i][i] == 0) { pivot = 0; j = i + 1; while ((pivot == 0) && (j <= rows)) { if (AAinvt[j][i] != 0.0) { pivot = j; } j = j + 1; } if (pivot == 0 ) printf("Stop, matrix is singular"); } if(pivot == (j-1)) { for (j = 0; j < (rows+1); j++) { temp1 = AAinvt[i][j]; AAinvt[i][j]=AAinvt[pivot][j]; AAinvt[pivot][j] = temp1; } } for (j = (i+1); j < rows; j++) { Multi = -AAinvt[j][i] / AAinvt[i][i]; for (k = i; k < (rows+1); k++) { AAinvt[j][k] = AAinvt[j][k] + (Multi * AAinvt[i][k]); } } } 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 Mt = (((4.0/pow(PI25DT,0.5))*(pow((Df*oxd_time/(0.0009*0.0009)),0.5))) -(Df*oxd_time/(0.0009*0.0009))-((1.0/(3.0*pow(PI25DT,0.5)))*(pow( (Df*oxd_time/(0.0009*0.0009)),(3.0/2.0)))))/oxd_time_steps; for (ctx = 0; ctx <=rows; ctx++) { if (RBLgm[ctx] > 0.0) { dumb[ctx] = (AO[current_dip]*Cj1[ctx]*liter_per_node[ctx]* dt)/RBLgm[ctx]; if (dumb[ctx] > 1.0) { RBL1gm[ctx] = 0.0; RBL1[ctx] = 0.0; OBL1gm[ctx] = OBLgm[ctx] + RBLgm[ctx]; } else

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] <= 0.0) RBL1gm[ctx] = 0.0; if (RBL1[ctx] <= 0.0) RBL1[ctx] = 0.0; IOWY[ctx] = IOWY[ctx] + ((CompA*pow(RBL1[ctx],CompB))*Mt); RBL1gm[ctx] = RBL1gm[ctx] - ((CompA*pow(RBL1[ctx],CompB)) * Mt * gms_ctn_node[ctx]); RBL1[ctx] = RBL1[ctx] - (((CompA*pow(RBL1[ctx],CompB)) * Mt * gms_ctn_node[ctx])/(liter_per_node[ctx] * wetpickup)); if (RBL1gm[ctx] <= 0.0) RBL1gm[ctx] = 0.0; if (RBL1[ctx] <= 0.0) RBL1[ctx] = 0.0; } } else if (IOWY[ctx] > 0.0) { dumb[ctx]=((AO[current_dip]*Cj1[ctx]*liter_per_node[ctx]*dt) /(IOWY[ctx]*gms_ctn_node[ctx])); if (dumb[ctx] > 1.0) { IOWYoxd[ctx] = IOWYoxd[ctx] + IOWY[ctx]; IOWY[ctx] = 0.0; } else { IOWYoxd[ctx] = IOWYoxd[ctx] + (dumb[ctx]*IOWY[ctx]); IOWY[ctx] = IOWY[ctx] - (dumb[ctx]*IOWY[ctx]); if (IOWY[ctx] <= 0.0) IOWY[ctx]=0.0; } } } for (ctx = 0; ctx <= rows; ctx++) air_dist[yarn_count][current_dip][ctx] =Cj1[ctx]; } // end oxidation time step loop for (ctx = 0; ctx <= rows; ctx++) { IOWYoxd[ctx] = IOWYoxd[ctx] + IOWYpre[ctx]; COWY[ctx]=IOWYoxd[ctx]*totalgramsperindigo+IOWY[ctx]*totalgramsperindigo; COWY[ctx] =COWY[ctx]+(OBL1gm[ctx]*totalgramsperindigo/gms_ctn_node[ctx]); COWY[ctx] =COWY[ctx]+(RBL1gm[ctx]*totalgramsperindigo/gms_ctn_node[ctx]); IOWYtotal = IOWYtotal+(IOWYoxd[ctx]*gms_ctn_node[ctx])+(IOWY[ctx] *gms_ctn_node[ctx]); COWYtotal = COWYtotal + (COWY[ctx]*gms_ctn_node[ctx]); } IOWYtotal = IOWYtotal / (1.54*porosity*PI25DT * radius * radius); COWYtotal = COWYtotal / (1.54*porosity*PI25DT * radius * radius); IOWYsurface = IOWYoxd[rows] + IOWY[rows]; IOWYsurface_ratio = IOWYsurface_target/IOWYsurface; IOWYtotal_ratio = IOWYtarget/IOWYtotal; COWYtotal_ratio = COWYtarget/COWYtotal; IOWY_save[yarn_count][current_dip] = IOWYtotal; COWY_save[yarn_count][current_dip] = COWYtotal; Integ_save[yarn_count][current_dip] = 0.0; Integ_save[yarn_count][current_dip] = 45.60937 + (592.19421*IOWYsurface) - (9928.5539*pow((IOWYsurface-0.045773),2)) + (1.83538e+5*pow((IOWYsurface-0.045773),3)); Integ_save[yarn_count][current_dip] = Integ_save[yarn_count][current_dip] - (1.522451e+6*pow((IOWYsurface-0.045773),4)) + (4.27080e+6*pow((IOWYsurface-0.045773),5));

380

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<=rows; ctx++) { IOWYpre[ctx] = IOWYoxd[ctx]; COWYpre[ctx] = COWY[ctx]; } for (ctx=0; ctx<=rows; ctx++) IOWY_dist[yarn_count][current_dip][ctx] =IOWYoxd[ctx]; for (ctx = 0; ctx <= rows; ctx++) COWY_dist[yarn_count][current_dip][ctx] = COWY[ctx]; IOWYsurface_ratio = IOWYtotal_ratio = COWYtotal_ratio = 0.99; Df_constantAO[current_dip] = Df; Dy_constantAO[current_dip] = Dy; WP_constantAO[current_dip] = wetpickup; wash_constantAO[current_dip] = wash; Df_AO[current_dip] = Df; Dy_AO[current_dip] = Dy; WP_AO[current_dip] = wetpickup; } // This ends the yarn count calculations at specific oxidation rate value // Convergence loop for wash efficiency number, which yields constant wet pick-up mean_dip = 0.0; mean_pickup = 0.0; slope = 0.0; demon = 0.0; old_wash = wash; for (ctx = 2; ctx <=(num_dips-1); ctx++) { mean_dip = mean_dip + ctx; mean_pickup = mean_pickup + WP_constantAO[ctx]; } mean_dip = mean_dip/(num_dips-2); mean_pickup = mean_pickup/(num_dips-2); for (ctx = 2; ctx <= (num_dips-1); ctx++) { dip_error[ctx] = ctx - mean_dip; pickup_error[ctx] = WP_constantAO[ctx] - mean_pickup; slope = slope + (dip_error[ctx]*pickup_error[ctx]); } for (ctx = 2; ctx<=(num_dips-1); ctx++) demon = demon + (dip_error[ctx]*dip_error[ctx]); slope = slope/demon; wash = wash * (1.0 + ((slope/0.0001)/100)); if ((old_wash + wash) <= 0.005) { wash = 0.0; slope = 0.0; wash_constantAO[current_dip] = wash; }

381

if (wash <= 0.0) { wash = 0.0; wash_constantAO[current_dip] = wash; } printf("slope, wash %e\t%e\n", slope, wash); } // Close wash convergence loop // Open and save other yarn counts for (ctx = 1; ctx <=num_dips; ctx++) { Df_dip[yarn_count][ctx] = Df_constantAO[ctx]; Dy_dip[yarn_count][ctx] = Dy_constantAO[ctx]; WP_dip[yarn_count][ctx] = WP_constantAO[ctx]; wash_dip[yarn_count][ctx] = wash_constantAO[ctx]; } yarn_count = yarn_count + 1; } // this is the oxidation optimumize section for (ctx = 1; ctx <=num_dips; ctx++) { new_stdev[ctx] = 0.0; normal_ave[ctx] = 0.0; } for (cty = 1; cty <=num_yarns; cty++) { for (ctx = 1; ctx <=num_dips; ctx++) { Df_AO[ctx] = 0.0; Dy_AO[ctx] = 0.0; WP_AO[ctx] = 0.0; } } for (ctx = 1; ctx <=num_dips; ctx++) { for (cty = 1; cty <=num_yarns; cty++) { Df_total[ctx] = Df_total[ctx] + Df_dip[cty][ctx]; Dy_total[ctx] = Dy_total[ctx] + Dy_dip[cty][ctx]; WP_total[ctx] = WP_total[ctx] + WP_dip[cty][ctx]; Df_AO[ctx] = Df_AO[ctx] + Df_dip[cty][ctx]; Dy_AO[ctx] = Dy_AO[ctx] + Dy_dip[cty][ctx]; WP_AO[ctx] = WP_AO[ctx] + WP_dip[cty][ctx]; } } for (ctx = 1; ctx<=num_dips; ctx++) { Df_run_ave[ctx] = Df_total[ctx] / (num_cycles * num_yarns); Dy_run_ave[ctx] = Dy_total[ctx] / (num_cycles * num_yarns); WP_run_ave[ctx] = WP_total[ctx] / (num_cycles * num_yarns); Df_AO[ctx] = Df_AO[ctx] / num_yarns; Dy_AO[ctx] = Dy_AO[ctx] / num_yarns; WP_AO[ctx] = WP_AO[ctx] / num_yarns; } for (cty = 1; cty <=num_yarns; cty++) { for (ctx = 1; ctx <=num_dips; ctx++) { Df_dip[cty][ctx] = Df_dip[cty][ctx]/Df_run_ave[ctx]; Dy_dip[cty][ctx] = Dy_dip[cty][ctx]/Dy_run_ave[ctx]; WP_dip[cty][ctx] = WP_dip[cty][ctx]/WP_run_ave[ctx]; } }

382

for (ctx = 1; ctx <= num_dips; ctx++) { for (cty = 1; cty <=num_yarns; cty++) { normal_ave[ctx] = normal_ave[ctx] + Df_dip[cty][ctx] + Dy_dip[cty][ctx] + WP_dip[cty][ctx]; } } for (ctx = 1; ctx<=num_dips; ctx++) normal_ave[ctx] = normal_ave[ctx] / (3.0 * num_yarns); for (ctx = 1; ctx <= num_dips; ctx++) { for (cty = 1; cty <=num_yarns;cty++) { new_stdev[ctx] = new_stdev[ctx] + pow((Df_dip[cty][ctx] - normal_ave[ctx]), 2.0); new_stdev[ctx] = new_stdev[ctx] + pow((Dy_dip[cty][ctx] - normal_ave[ctx]), 2.0); new_stdev[ctx] = new_stdev[ctx] + pow((WP_dip[cty][ctx] - normal_ave[ctx]), 2.0); } } for (ctx = 1; ctx <= num_dips; ctx++) { new_stdev[ctx] = new_stdev[ctx] / ((3.0 * num_yarns) - 1.0); new_stdev[ctx] = pow(new_stdev[ctx], 0.5); AO_conv[ctx] = old_stdev[ctx] / new_stdev[ctx]; old_stdev[ctx] = new_stdev[ctx]; AO[ctx] = AO[ctx] * AO_conv[ctx]; } AO_change = 0.0; for (ctx = 1; ctx <=num_dips; ctx++) { if (AO_conv[ctx] > AO_change) AO_change = AO_conv[ctx]; } num_cycles = num_cycles + 1.0; printf("This completes an oxidation loop!!!!!!!!\n"); for (ctx=1; ctx <= num_dips; ctx++) printf("%e\t%e\t%e\t%e\n", num_cycles, AO[ctx], AO_conv[ctx], new_stdev[ctx]); } // Close stdev convergence loop to optimize oxidation for (ctx = 1; ctx <= num_dips; ctx++) { for (cty = 1; cty <= num_yarns; cty++) wash_AO[ctx] = wash_AO[ctx] + wash_dip[cty][ctx]; } pFile = fopen ("output_model.out","a"); fprintf(pFile, "number of cycles to converge: %e\n", num_cycles); fprintf(pFile, "Dips\t Df\t Dy\t pickup\t Oxidation\n"); for (x = 1; x <= num_dips; x++) { fprintf(pFile, "%i\t%e\t%e\t%e\t%e\n", x, Df_AO[x], Dy_AO[x], WP_AO[x], AO[x]); } fprintf(pFile, "yarns\t wash\n"); for (x = 1; x <= num_yarns; x++) fprintf(pFile, "%i\t%e\n", x, wash_dip[x][1]); for (cty = 1; cty <= num_yarns; cty++) { fprintf(pFile, "yarn: %i IOWY\t COWY\t Integ\n", cty); for (ctx = 1; ctx <=num_dips; ctx++) { fprintf(pFile, "dip:\t %i\t%e\t%e\t%e\n", ctx, IOWY_save[cty][ctx],

383

COWY_save[cty][ctx], Integ_save[cty][ctx]); } } cty = 1; for (ctz = 1; ctz <=num_dips ; ctz++) fprintf(pFile, "%i\t", ctz); fprintf(pFile, "\n"); for (ctx = 0; ctx <=rows; ctx++) { for (ctz = 1; ctz <=num_dips ; ctz++) fprintf(pFile, "%e\t", dye_bath_dist[cty][ctz][ctx]); fprintf(pFile, "\n"); } cty = num_yarns; for (ctz = 1; ctz <=num_dips ; ctz++) fprintf(pFile, "%i\t", ctz); fprintf(pFile, "\n"); for (ctx = 0; ctx <=rows; ctx++) { for (ctz = 1; ctz <=num_dips ; ctz++) fprintf(pFile, "%e\t", dye_bath_dist[cty][ctz][ctx]); fprintf(pFile, "\n"); } cty = 1; for (ctz = 1; ctz <=num_dips ; ctz++) fprintf(pFile, "%i\t", ctz); fprintf(pFile, "\n"); for (ctx = 0; ctx <=rows; ctx++) { for (ctz = 1; ctz <=num_dips ; ctz++) fprintf(pFile, "%e\t", air_dist[cty][ctz][ctx]); fprintf(pFile, "\n"); } cty = num_yarns; for (ctz = 1; ctz <=num_dips ; ctz++) fprintf(pFile, "%i\t", ctz); fprintf(pFile, "\n"); for (ctx = 0; ctx <=rows; ctx++) { for (ctz = 1; ctz <=num_dips ; ctz++) fprintf(pFile, "%e\t", air_dist[cty][ctz][ctx]); fprintf(pFile, "\n"); } cty = 1; for (ctz = 1; ctz <=num_dips ; ctz++) fprintf(pFile, "%i\t", ctz); fprintf(pFile, "\n"); for (ctx = 0; ctx <=rows; ctx++) { for (ctz = 1; ctz <=num_dips ; ctz++) fprintf(pFile, "%e\t", IOWY_dist[cty][ctz][ctx]); fprintf(pFile, "\n"); } cty = num_yarns; for (ctz = 1; ctz <=num_dips ; ctz++) fprintf(pFile, "%i\t", ctz); fprintf(pFile, "\n"); for (ctx = 0; ctx <=rows; ctx++) { for (ctz = 1; ctz <=num_dips ; ctz++) fprintf(pFile, "%e\t", IOWY_dist[cty][ctz][ctx]); fprintf(pFile, "\n"); } cty = 1; for (ctz = 1; ctz <=num_dips ; ctz++) fprintf(pFile, "%i\t", ctz); fprintf(pFile, "\n"); for (ctx = 0; ctx <=rows; ctx++) {

384

for (ctz = 1; ctz <=num_dips ; ctz++) fprintf(pFile, "%e\t", COWY_dist[cty][ctz][ctx]); fprintf(pFile, "\n"); } cty = num_yarns; for (ctz = 1; ctz <=num_dips ; ctz++) fprintf(pFile, "%i\t", ctz); fprintf(pFile, "\n"); for (ctx = 0; ctx <=rows; ctx++) { for (ctz = 1; ctz <=num_dips ; ctz++) fprintf(pFile, "%e\t", COWY_dist[cty][ctz][ctx]); fprintf(pFile, "\n"); } fclose (pFile); return 0; }

385

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; FILE * o3File; FILE * o4File; double AA[61][61], BB[61][61], RBLgm[61], RBL1gm[61], Cj[61], Cj1[61], d[61], TBL[61], TBL1[61], RBL[61], RBL1[61], OBL[61], OBL1[61]; double AAinvt[61][62], X[61], Xrbl[61], Xiowy[61], temp[61], IOWY[61], COWY[61], IOWYoxd[61], temp1, Multi, fraction_dye_affinity, fraction_oxy_affinity; double OBLgm[61], OBL1gm[61], dumb[61], IOWYstep[61], gms_ctn_node[61], liter_per_node[61], Df_constantAO[10], Dy_constantAO[10], WP_constantAO[10], wash_constantAO[10]; double IOWYpre[61], COWYpre[61], dip_error[10], pickup_error[10], Df_dip[5][10], Dy_dip[5][10], WP_dip[5][10], wash_dip[5][10]; double dye_bath_dist[5][10][61], air_dist[5][10][61], IOWY_dist[5][10][61], COWY_dist[5][10][61], Integ_save[5][10], IOWY_save[5][10], COWY_save[5][10]; float input[1][22], num_time_steps, oxd_time_steps; double Mt, Dy, DOy, Df, dt, DT, dr, radius, Monophenate_Ion, CompA, CompB, A, AO[10], AO_old, AO_conv[10], AO_change, wash, old_wash, wetpickup, gmIplit, gmNaOHplit, pH, Air, normal_ave[10], WP_normal_ave; double lamda, alpha, beta, Ur, UOr, K, porosity, Kph, L, percent_to_grams, grams_to_percent, Integ, num_cycles; double IOWYtarget, IOWYsurface_target, COWYtarget, IOWYsurface, IOWYoutside_old, IOWYtotal, COWYtotal, IOWYsurface_ratio, IOWYtotal_ratio, COWYtotal_ratio; double dwelltime, oxd_time, totalgramsperindigo, new_stdev[10], old_stdev[10], Df_temp, Dy_temp, WP_temp, Df_total[10], Dy_total[10], WP_total[10]; double mean_dip, mean_pickup, slope, demon, Df_run_ave[10], Dy_run_ave[10], WP_run_ave[10], Df_AO[10], Dy_AO[10], WP_AO[10], wash_AO[10]; double speed, mV, nip_pressure, Total_IOWY_pre, Total_COWY_pre; long rows, cols; int x, num_nodes, ts, yarn_count, num_yarns; int z, ctx, cty, ctz, current_dip, num_dips; int i, j, pivot, k; double PI25DT = 3.141592653589793238462643;

// Iniatialization num_dips=5; // this is now number of dips in data num_cycles=1; cols=1; num_yarns = 1; // number of yarn counts processed DT=0.01; // Define a actual time step to be used in dyeing and oxidization num_nodes=21; rows=num_nodes-1; porosity=0.65; Ur = 0.0; K = 1.0; percent_to_grams = (0.0154 * porosity)/(1.0 - porosity); grams_to_percent = 1.0/percent_to_grams; totalgramsperindigo = 2.3884; AO_old = 0.0; wash = 0.1; mean_dip = 0.0; mean_pickup = 0.0; slope = 1.0;

386

yarn_count = 1; for (cty = 1; cty <= num_yarns; cty++) { for (ctx = 1; ctx<=num_dips; ctx++) { new_stdev[ctx] = 0.5; old_stdev[ctx] = 0.5; Df_total[ctx] = 0.0; Dy_total[ctx] = 0.0; WP_total[ctx] = 0.0; AO[ctx] = 0.02; } } for (cty=0; cty<=num_yarns; cty++) { for (ctx = 0; ctx <= num_dips; ctx++) wash_dip[cty][ctx] = 0.01; } yarn_count = 1; printf ("Processing yarn # %i\n", yarn_count); slope = 1.0; Total_IOWY_pre = 0.0; Total_COWY_pre = 0.0; for (ctx=0; ctx <= (num_dips+1); ctx++) { Df_constantAO[ctx]=0.0; Dy_constantAO[ctx]=0.0; WP_constantAO[ctx]=0.0; dip_error[ctx]=0.0; pickup_error[ctx]=0.0; } for (ctx=0; ctx<=rows; ctx++) { IOWYpre[ctx] = 0.0; COWYpre[ctx] = 0.0; IOWY[ctx] = 0.0; IOWYoxd[ctx] = 0.0; COWY[ctx] = 0.0; } for (x=0; x<=19; x++) input[0][x]=0.0; for (current_dip = 1; current_dip <= num_dips; current_dip++) { printf ("Processing dip # %i\n", current_dip); if (yarn_count == 1) oFile = fopen ("yarninput1.txt", "rb" ); if (yarn_count == 2) oFile = fopen ("yarninput2.txt", "rb" ); 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<1; z++) { for (x = 0; x <=21; x++) fscanf (oFile, "%f", &input[0][x]); } } fclose (oFile); printf ("%i\t%e\t%e\n", yarn_count, input[0][2], input[0][3]); dwelltime = input[0][5]; oxd_time = input[0][6]; num_time_steps = dwelltime/DT; dt = DT; radius = (-0.1655+(1.951/sqrt(input[0][2])))/20.0; //cm dr = radius/(rows); //cm

387

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)); } else if (current_dip == 3) { Df = exp(-27.3480169 + 0.2868312 + (0.7766363*gmIplit) + (0.4031649*pH)); Dy = exp(-17.3699775 - 0.454878 - (0.503326*gmIplit) + (0.588888*pH) - (0.0736707*dwelltime)); AO[current_dip] = exp(-10.4653532 -0.6931914 + (0.1263413*speed) + (0.0685300*oxd_time) - (0.0010179*mV)); } else if (current_dip == 4) { Df = exp(-27.3480169 + 0.5783337 + (0.7766363*gmIplit) + (0.4031649*pH)); Dy = exp(-17.3699775 - 1.032697 - (0.503326*gmIplit) + (0.588888*pH) - (0.0736707*dwelltime)); AO[current_dip] = exp(-10.4653532 -0.9826215 + (0.1263413*speed) + (0.0685300*oxd_time) - (0.0010179*mV)); } else if (current_dip == 5) { Df = exp(-27.3480169 + 0.9180302 + (0.7766363*gmIplit) + (0.4031649*pH)); Dy = exp(-17.3699775 - 1.392668 - (0.503326*gmIplit) + (0.588888*pH) - (0.0736707*dwelltime)); AO[current_dip] = exp(-10.4653532 -0.6885056 + (0.1263413*speed) + (0.0685300*oxd_time) - (0.0010179*mV)); } else if (current_dip == 6) { Df = exp(-27.3480169 + 1.0879995 + (0.7766363*gmIplit) + (0.4031649*pH)); Dy = exp(-17.3699775 - 1.4830235 - (0.503326*gmIplit) + (0.588888*pH) - (0.0736707*dwelltime)); AO[current_dip] = exp(-10.4653532 -1.3461714 + (0.1263413*speed) + (0.0685300*oxd_time) - (0.0010179*mV)); } else if (current_dip == 7) { Df = exp(-27.3480169 + 0.9494075 + (0.7766363*gmIplit) + (0.4031649*pH)); Dy = exp(-17.3699775 - 1.4538142 - (0.503326*gmIplit) + (0.588888*pH) - (0.0736707*dwelltime)); AO[current_dip] = exp(-10.4653532 -1.3170116 + (0.1263413*speed) + (0.0685300*oxd_time) - (0.0010179*mV)); } 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<=rows; ctx++) { gms_ctn_node[ctx] = 1.54*porosity*2.0*PI25DT*ctx*dr*dr; liter_per_node[ctx] = (1-porosity)*2.0*PI25DT*ctx*dr*dr; } gms_ctn_node[0] = 1.54*porosity*PI25DT*0.25*dr*dr; liter_per_node[0] = (1-porosity)*PI25DT*0.25*dr*dr; gms_ctn_node[rows] = 1.54*porosity*PI25DT*(radius*dr-(0.25*dr*dr)); liter_per_node[rows] = (1-porosity)*PI25DT*(radius*dr-(0.25*dr*dr)); x=i=j=k=ctx=cty=0; pivot=0; IOWYtotal=0.0; COWYtotal=0.0; IOWYsurface=0.0; // Set-up initial conditions for (ctx = 0; ctx<=rows; ctx++) { X[ctx]=0.0; Cj[ctx]=0.0; Cj1[ctx]=0.0; d[ctx]=0.0; temp[ctx]=0.0; RBL[ctx]=0.0; RBL1[ctx]=0.0; RBLgm[ctx]=0.0; RBL1gm[ctx]=0.0; IOWY[ctx]=0.0; //these will change for multiple dips IOWYoxd[ctx]=0.0; //here COWY[ctx]=0.0; // here IOWYstep[ctx]=0.0; dumb[ctx]=0.0; OBL[ctx]=0.0; OBL1[ctx]=0.0; OBLgm[ctx]=0.0; OBL1gm[ctx]=0.0; TBL[ctx] = RBL[ctx] + OBL[ctx]; TBL1[ctx] = RBL1[ctx] + OBL1[ctx]; for(cty = 0; cty<=rows; cty++) { AA[ctx][cty]=0.0; BB[ctx][cty]=0.0; } } Cj[rows]=gmIplit; Cj1[rows]=gmIplit; lamda = (Dy*dt)/(2.0*dr*dr); alpha = (Ur*dt)/(4.0*dr); beta = (Dy*dt)/(4.0*dr); for (ctx = 0; ctx

389

AA[0][1]=-2.0*lamda; AA[1][0]=(beta/dr)-lamda-(alpha); BB[0][1]=2.0*lamda; BB[1][0]=(-beta/dr)+lamda+(alpha); Monophenate_Ion = 1.0/(1.0 + (pow(10,(9.5-pH))) + (pow(10,(pH-12.7)))); CompA = (0.016492 * Monophenate_Ion) + 0.003465; CompB = (-0.244296 * Monophenate_Ion) + 0.816158; for (ts = 1; ts <= num_time_steps; ts++) { for (ctx = 0; ctx <= rows; ctx++) { Cj[ctx]=Cj1[ctx]; RBL[ctx]=RBL1[ctx]; OBL[ctx]=OBL1[ctx]; TBL[ctx]=TBL1[ctx]; RBLgm[ctx]=RBL1gm[ctx]; OBLgm[ctx]=OBL1gm[ctx]; temp[ctx]=0.0; } Mt = (((4.0/pow(PI25DT,0.5))*(pow((Df*dwelltime/(0.0009*0.0009)),0.5)))-(Df*dwelltime/(0.0009*0.0009))- ((1.0/(3.0*pow(PI25DT,0.5)))*(pow((Df*dwelltime/(0.0009*0.0009)),(3.0/2.0)))))/num_time_steps; for (ctx = 0; ctx < rows; ctx++) { if (Cj[ctx] <= 0.0) IOWYstep[ctx] = 0.0; else IOWYstep[ctx] = Mt*CompA*pow(Cj[ctx],CompB); d[ctx] = -1.0 * gms_ctn_node[ctx] * IOWYstep[ctx] / liter_per_node[ctx]; } d[rows-1] = d[rows-1] + (Cj[rows]*2.0*((beta/(radius))+lamda-alpha)); if (Cj[rows] <= 0.0) IOWYstep[rows] = 0.0; else IOWYstep[rows] = Mt*CompA*pow(Cj[rows],CompB); // Find new dye concentration by Guass-Jordan elimination for (ctx = 0; ctx

390

} 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--) { 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]; }

for (ctx = 1; ctx < rows; ctx++) { { IOWY[ctx] = IOWY[ctx] + IOWYstep[ctx]; } } IOWY[rows] = IOWY[rows] + IOWYstep[rows]; for (ctx = 0; ctx <= rows; ctx++) dye_bath_dist[yarn_count][current_dip][ctx] = Cj1[ctx]; } // Close time step loop for process in dye box // Nip process for (ctx = 0; ctx <= rows; ctx++) { RBL1[ctx] = Cj1[ctx]; RBL1gm[ctx] = Cj1[ctx] * liter_per_node[ctx] * wetpickup; OBL1gm[ctx] = (COWYpre[ctx] - IOWYpre[ctx]) * gms_ctn_node[ctx] * wash; if (OBL1gm[ctx] < 0.0) OBL1gm[ctx] = 0.0; } IOWYtotal=0.0; IOWYsurface=0.0; COWYtotal=0.0; oxd_time_steps = oxd_time/DT; dt=DT; Air = 0.2541; // gm per liter of oxygen for (ctx = 0; ctx<=rows; ctx++) { Cj[ctx]=0.0; // gm/lit of oxygen Cj1[ctx]=0.0; d[ctx]=0.0;

391

X[ctx]=0.0; Xrbl[ctx]=0.0; Xiowy[ctx]=0.0; for(cty = 0; cty<=rows; cty++) { AA[ctx][cty]=0.0; BB[ctx][cty]=0.0; } } Cj1[rows]=Air; lamda = (DOy*dt)/(2.0*dr*dr); alpha = (UOr*dt)/(4.0*dr); beta = (DOy*dt)/(4.0*dr); for (ctx = 0; ctx 0.0) X[ctx]=1/(AO[current_dip]*Cj[ctx]*liter_per_node[ctx]*dt/(RBLgm[ctx]+(IOWY[ctx]*gms_ctn_node[ctx]))); else if (IOWY[ctx] > 0.0) X[ctx]=1/(AO[current_dip]*Cj[ctx]*liter_per_node[ctx]*dt/((IOWY[ctx]*gms_ctn_node[ctx]))); else X[ctx]=0.0; } if (X[ctx] > 1.0) X[ctx]=1.0; d[ctx] = -1.0 * X[ctx] * Cj[ctx] * dt; if (d[ctx] > 0.0) d[ctx] = 0.0; } d[rows-1] = d[rows-1] + (Cj[rows]*2*((beta/radius)+lamda-alpha)); // Find new oxygen concentration by Guass-Jordan elimination for (ctx = 0; ctx

392

for (cty = 0; cty = 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 Mt = (((4.0/pow(PI25DT,0.5))*(pow((Df*oxd_time/(0.0009*0.0009)),0.5)))-(Df*oxd_time/(0.0009*0.0009))- ((1.0/(3.0*pow(PI25DT,0.5)))*(pow((Df*oxd_time/(0.0009*0.0009)),(3.0/2.0)))))/oxd_time_steps; for (ctx = 0; ctx <=rows; ctx++)

393

{ 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] <= 0.0) RBL1gm[ctx] = 0.0; if (RBL1[ctx] <= 0.0) RBL1[ctx] = 0.0; IOWY[ctx] = IOWY[ctx] + ((CompA*pow(RBL1[ctx],CompB))*Mt); RBL1gm[ctx] = RBL1gm[ctx] - ((CompA*pow(RBL1[ctx],CompB)) * Mt * gms_ctn_node[ctx]); RBL1[ctx] = RBL1[ctx] - (((CompA*pow(RBL1[ctx],CompB)) * Mt * gms_ctn_node[ctx])/(liter_per_node[ctx] * wetpickup)); if (RBL1gm[ctx] <= 0.0) RBL1gm[ctx] = 0.0; if (RBL1[ctx] <= 0.0) RBL1[ctx] = 0.0; } } else if (IOWY[ctx] > 0.0) { dumb[ctx]=((AO[current_dip]*Cj1[ctx]*liter_per_node[ctx]*dt)/(IOWY[ctx]*gms_ctn_node[ctx])); if (dumb[ctx] > 1.0) { IOWYoxd[ctx] = IOWYoxd[ctx] + IOWY[ctx]; IOWY[ctx] = 0.0; } else { IOWYoxd[ctx] = IOWYoxd[ctx] + (dumb[ctx]*IOWY[ctx]); IOWY[ctx] = IOWY[ctx] - (dumb[ctx]*IOWY[ctx]); if (IOWY[ctx] <= 0.0) IOWY[ctx]=0.0; } } } for (ctx = 0; ctx <= rows; ctx++) air_dist[yarn_count][current_dip][ctx] = Cj1[ctx]; } // end oxidization time step loop for (ctx = 0; ctx<=rows; ctx++) if (RBL1[ctx] >0.0) printf("Node: %i\t RBL Not all oxidized\n", ctx); for (ctx = 0; ctx<=rows; ctx++) if (IOWY[ctx] >0.0) printf("Node: %i\t IOWY Not all oxidized\n", ctx); for (ctx = 0; ctx <= rows; ctx++) { IOWYoxd[ctx] = IOWYoxd[ctx] + IOWYpre[ctx]; COWY[ctx] = IOWYoxd[ctx]*totalgramsperindigo + IOWY[ctx]*totalgramsperindigo; COWY[ctx] = COWY[ctx] + (OBL1gm[ctx]*totalgramsperindigo/gms_ctn_node[ctx]); COWY[ctx] = COWY[ctx] + (RBL1gm[ctx]*totalgramsperindigo/gms_ctn_node[ctx]); IOWYtotal = IOWYtotal + (IOWYoxd[ctx]*gms_ctn_node[ctx])+ (IOWY[ctx]*gms_ctn_node[ctx]); COWYtotal = COWYtotal + (COWY[ctx]*gms_ctn_node[ctx]); } IOWYtotal = IOWYtotal / (1.54*porosity*PI25DT * radius * radius); COWYtotal = COWYtotal / (1.54*porosity*PI25DT * radius * radius); IOWYsurface = IOWYoxd[rows] + IOWY[rows]; IOWYsurface_ratio = IOWYsurface_target/IOWYsurface; // greater then 1 means to increase diffusion coeff Df IOWYtotal_ratio = IOWYtarget/IOWYtotal; // greater then 1 means to increase diffusion coeff Dy COWYtotal_ratio = COWYtarget/COWYtotal; IOWY_save[yarn_count][current_dip] = IOWYtotal; COWY_save[yarn_count][current_dip] = COWYtotal; Integ_save[yarn_count][current_dip] = 0.0;

394

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<=rows; ctx++) { IOWYpre[ctx] = IOWYoxd[ctx]; COWYpre[ctx] = COWY[ctx]; } for (ctx = 0; ctx <= rows; ctx++) IOWY_dist[yarn_count][current_dip][ctx] = IOWYoxd[ctx]; for (ctx = 0; ctx <= rows; ctx++) COWY_dist[yarn_count][current_dip][ctx] = COWY[ctx]; IOWYsurface_ratio = IOWYtotal_ratio = COWYtotal_ratio = 0.99; Df_constantAO[current_dip] = Df; Dy_constantAO[current_dip] = Dy; WP_constantAO[current_dip] = wetpickup; wash_constantAO[current_dip] = wash; Df_AO[current_dip] = Df; Dy_AO[current_dip] = Dy; WP_AO[current_dip] = wetpickup; } // This ends the yarn count calculations at specific oxidization rate value for (ctx = 1; ctx <=num_dips; ctx++) { Df_dip[yarn_count][ctx] = Df_constantAO[ctx]; // reset Df_dip after each AO step Dy_dip[yarn_count][ctx] = Dy_constantAO[ctx]; WP_dip[yarn_count][ctx] = WP_constantAO[ctx]; wash_dip[yarn_count][ctx] = wash_constantAO[ctx]; } for (ctx = 1; ctx <= num_dips; ctx++) { for (cty = 1; cty <= num_yarns; cty++) wash_AO[ctx] = wash_AO[ctx] + wash_dip[cty][ctx]; } pFile = fopen ("output_model.out","a"); fprintf(pFile, "number of cycles to converge: %e\n", num_cycles); fprintf(pFile, "Dips\t Df\t Dy\t pickup\t Oxidization\n"); for (x = 1; x <= num_dips; x++) { fprintf(pFile, "%i\t%e\t%e\t%e\t%e\n", x, Df_AO[x], Dy_AO[x], WP_AO[x], AO[x]); } fprintf(pFile, "yarns\t wash\n"); for (x = 1; x <= num_yarns; x++) fprintf(pFile, "%i\t%e\n", x, wash_dip[x][1]);

for (cty = 1; cty <= num_yarns; cty++) { fprintf(pFile, "yarn: %i IOWY\t COWY\t Integ\n", cty); for (ctx = 1; ctx <=num_dips; ctx++) { fprintf(pFile, "%e\t%e\t%e\n", IOWY_save[cty][ctx], COWY_save[cty][ctx], Integ_save[cty][ctx]); } } fclose (pFile); return 0; }

395

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 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) 443 29.00 20.1 73.6 1.262 12.18 813 2.58 9.70 38.90 95.00 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 6.3 1 only 1 8.2301 7.885 8.1841 7.8671 1.72% 0.166% 0.437% 8.1 0.38 6.3 1--2 2 7.7329 7.3991 7.7581 7.3974 2.75% 0.286% 0.740% 17.2 0.39 6.3 1--3 3 8.3473 8.0082 8.4238 8.0085 3.09% 0.455% 1.034% 29.5 0.44 6.3 1--4 4 7.7045 7.3799 7.7854 7.4011 3.38% 0.510% 1.269% 35.8 0.40 6.3 1--5 5 8.2838 7.9276 8.3811 7.9722 3.61% 0.744% 2.164% 50.1 0.34 6.3 1--6 6 8.3773 8.0322 8.44 8.0778 4.30% 0.885% 2.836% 57.4 0.31

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-5-1: Continued

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) 443 29.00 20.1 73.6 1.262 12.18 813 2.58 9.70 38.90 95.00 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 6.9605 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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

Table A-5-1: Continued

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) 443 29.00 20.10 73.60 1.196 12.06 807 2.51 9.70 38.90 95 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7

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

Table A-5-1: Continued

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) 418 32.00 18.20 66.70 1.658 11.83 814 3.29 9.70 38.90 95 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7

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

Table A-5-1: Continued

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) 402 28.00 20.80 76.30 1.986 12.24 841 3.53 9.70 38.90 95 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7

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

Table A-5-1: Continued

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) 402 28.00 20.80 76.30 1.986 12.24 841 3.53 9.70 38.90 95 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7

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

Table A-5-1: Continued

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) 402 28.00 20.80 76.30 1.986 12.24 841 3.53 9.70 38.90 95 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7

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

Table A-5-1: Continued

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) 471 32.00 18.20 66.70 2.094 12.12 838 3.42 9.70 38.90 95 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7

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

Table A-5-1: Continued

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) 471 32.00 18.20 66.70 2.094 12.12 838 3.42 9.70 38.90 95 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7

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

Table A-5-1: Continued

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) 471 32.00 18.20 66.70 2.094 12.12 838 3.42 9.70 38.90 95 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 6 Dip 6 Dip 7 400 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

Table A-5-1: Continued

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) 401 28.00 20.80 76.30 2.211 12.11 820 3.72 9.70 38.90 95 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 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

% Reflectance Readings

Wave- length (nm) Dip 1 Dip 2 Dip 3 Dip 4 Dip 5 Dip 6 Dip 7 400 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