EFFECTS OF TEMPERATURE AND SALT ON DYE MIXTURES IN THE BATCH DYEING PROCESS

For real-time control, it is usually desirable to formulate a mathemat ical model of the process to be controlled. Such a model assists in th e selection of control parameters and enhances the understanding of th e underlying processes. A mathematical model for two-dye mixtures is d eveloped comprising a diffusion based model to account for dye penetra tion 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 dyei ng process cannot be modeled by a simple combination of single dye mod els. Numerical simulations of the behavior of direct cotton dye mixtur es under varying conditions of temperature and salt concentration are also presented, and compared with experiments.