Computer simulation of bath dyeing of fibrous material

Abstract

A mathematical model has been formulated for the dyeing process of a fibrous substrate in aqueous dyeing bath of finite ratio. The model has been constructed for the isothermal process kinetically controlled by the diffusion of dyestuff into the mass of fibre polymer for the case of nonlinear partition function of the dyestuff between the phases of fibre and bath. The numerical simulation by the Schmidt method of finite differences has been used to find the functions of concentration fields of dyestuff in cylindrical space of fibre and the transfer function of kinetic integral amount of dyestuff to fibre. The model has been formulated on the basis of dimensionless criteria of the theory of similarity. On the basis of the model suggested, the dimensionless criterial parameters have been found for the dyeing system which crucially affect the rate of dyestuff transfer from bath to fibre, the development of concentration field of dyestuff in fibre, and the degree of utilization of dyestuff in dyeing process. The results found can be applied in selecting and developing the dyestuffs for optimized and high-speed processes for the dyestuffs of disperse and reactive technological classes.