Liquid Diffusion Model that Accounts for a Variety of Dyeing Parameters

Abstract

This paper describes a method for simulating and visualizing dyeing based on weave patterns and the physical parameters of the threads and the dye. We apply Fick s second law with a variable diffusion coefficient, which is calculated using the porosity, tortuosity, and the dye concentration based on the physical chemistry of dyeing. The tortuosity of the channel was incorporated in order to consider the effect of weave patterns on diffusion. The total mass is conserved in this model. We describe the cloth model using a two-layered cellular model that includes the minimum factors required for representing the weft and warp. Our model also includes a simple dyeing technique that produces dyeing patterns by interrupting the diffusion of the dye in a cloth using a press. The results obtained using our model demonstrate that it is capable of modeling many of the characteristics of dyeing.