Modeling of the diffusion during polyester dyeing - A survey

A common goal of all dyers is to achieve the correct shade as early as the first dyeing. However, the disperse dyeing process is very complex, being characterized by the diffusion-controlled sorption of dyes that depends on several physicochemical parameters such as dye concentration and temperature of dyebath solution. The literature reveals no equation that expresses the influence of experimental and measurable parameters on the diffusion coefficient value. Thus, a mathematical model describing the evolution of this diffusion coefficient for disperses dyes as a function of time, initial dye concentration, temperature and the nature of the dyebath (finite, infinite) is proposed. This model applies to the dyeing of conventional polyester fibers and microfibers with disperse dyes. The critical discussion is developed dealing with the possibility of the model industrial application and its effectiveness.