Effects of Temperature and Salt on Dye Mixtures in the Batch Dyeing Process

Abstract

For real-time control, it is usually desirable to formulate a mathematical model of the process to be controlled. Such a model assists in the selection of control parameters and enhances the understanding of the underlying processes. A mathematical model for two-dye mixtures is developed comprising a diffusion based model to account for dye penetration into the fiber and a nonlinear distribution function at the fiber surface based on the Langmuir isotherm. Since the behavior of dyes in mixtures often deviates from their behavior when used alone, the dyeing process cannot be modeled by a simple combination of single dye models. Numerical simulations of the behavior of direct cotton dye mixtures under varying conditions of temperature and salt concentration are also presented, and compared with experiments.