The modelling of a textile dyeing process utilizing the method of volume averaging

In this work the modelling of a process of textile dyeing of a single cotton thread is presented. This thread moves at a constant velocity within a homogeneous dye solution under steady state conditions. The method of volume averaging is applied to obtain the mass transfer equations related to the diffusion and adsorption process inside the cotton thread on a small scale. The one-equation model is developed for the fiber and dye solution system, assuming the principle of local mass equilibrium to be valid. On a large scale, the governing equations for the cotton thread, including the expression for effective diffusivity tensor, are obtained. Solution of these equations permits the dye concentration profile for inside the cotton thread and in the dyeing batch to be obtained and the best conditions for the dyeing process to be chosen.