Visualization of dyeing based on diffusion and adsorption theories

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. We calculate the diffusion coefficient 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 the weave patterns on diffusion. In this model, the total mass is conserved. We describe the cloth model using a two-layered cellular model that includes the essential 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.