Dye uptake of textile substrates can be described as time-dependent by a new mathematical model, in which the sorption process is divided into fast and slow subprocesses. The fast subprocess describes the adsorption of the dye onto the fiber surface, and the slow one details the diffusion of the dye into the fiber. In addition, dye desorption is simultaneously considered along with adsorption. Relating this concept to the dyeing process, it is possible to divide the process into two parts—dye adsorption and diffusion. The model is verified by dyeing cotton with direct dyes, but the results are also transferable to other fibers and dye classes. Using this model, optimum dyeing parameters and dye combinations can be determined from the sorption curves, which are easily obtained by UV-VIS spectrophotometry.

Time-dependent dye uptake of textile substrates can be described by a new mathematical model that divides the dyeing process into two parts, dye adsorption and dye diffusion. Using this model, the influence of temperature (20-80°C) and NaCl concentration (2.5-10.0 g/L) on the dye uptake of a trichrome dye combination of C.