To describe the process of dyeing textile materials, in the general case, it is not enough to consider the kinetics of dye adsorption by a single fiber.This assumption is valid in the case of low intensity low temperature processes, when the diffusion coefficient of the dye to the fiber is several orders of magnitude smaller than the diffusion coefficient in the space between the fibers.In this case, the mass transfer process is determined by the transfer in the fiber.As the temperature rises or with other methods of intensifying the process, there is a sharp increase in the diffusion coefficient in the fiber, while the diffusion coefficient in the liquid phase outside the fiber changes to an incomparably lesser extent, i.e. the difference in the values of the diffusion coefficients in the fiber and outside the fiber decreases sharply.
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Furtat et al. (2024) studied this question.
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