The equations of a Donnan model for equilibrium sorption of ions by polymers are expressed in dimensionless form and extended to cover the sorption of polysulfonated acid dyes by polyamide fibers. New expressions for key dimensionless groups are developed, and these groups are used to describe and analyze the equilibrium sorption of CI Acid Blue 45 by polyamide fibers. Improved estimates of key sorption parameters are obtained. This extension of the dimensionless group approach makes possible its application to the simulation and control of practical dyeing processes for ionic dyes.

Fiber bundles from the rind of sugar cane are extracted and characterized. Cane rind is separated from the pith using the Tilby process, and the separated rind is submitted to a high temperature water pretreatment followed by extraction with sodium hydroxide. Water pretreatment affects the amount of lignin removed from cane fiber bundles as well as the physical and mechanical properties of the fibers. Higher temperature pretreatment and longer treatment times produced finer, shorter fiber bundles with higher tenacity. The most severe treatments, however, reduced the bundles to ultimate fibers that are too short for textile uses. Extracted fibers were stiffer than other textile fibers but could be formed into nonwoven geotextile mats.

Closed-loop control of the dosing of dyes and chemicals is used to obtain an on-tone build-up of shade in dyeing polyamide fibers with a binary mixture of monosulfonated acid dyes. Computerized dosing pumps control the pH, the dyebath concentrations of the individual dyes, and the total sorption of each dye during the process. This real-time, closed-loop adaptive control yields good reproducibility and uniform shade build-up in a laboratory dyeing machine. It is possible to reuse a dyebath containing residual dyes and chemicals from a previous dyeing.

The equations of a dimensionless Donnan model for equilibrium sorption of ions by polymers are applied to sorption data for acid dyes in binary mixtures on nylon 66 fabric. The two acid dyes are commercial samples of C.I. Acid Blue 25 and C.I. Acid Yellow 49. Excellent fits of the data to the dimensionless model are obtained. The ratio of the distribution coefficients of the two dyes in the mixtures is estimated. Dimensionless sorption parameters have a linear dependence on the initial dye concentrations in the finite dyebaths and a linear dependence on the initial salt concentration. The equilibrium concentration distribution ratios of the two dyes on the fabric are linearly related to the ratios of their initial dyebath concentrations.