Capillary Flow in Cotton Fabric Based on Fiber Orientation Probability Density Function

In natural fiber fabrics such as cotton fabric, bleeding and dye transfer in household washing have always been a concern. Due to the complex fabric structure and the closed washing process, a dynamic model for predicting the concentration of bleed dyes and soils in the fabric is lacking. This study uses the fiber orientation probability density function based on the fiber radius and the fiber volume fraction to build a capillary flow model of the fabric’s dye concentration. The numerical results were calculated by taking the hydrolyzed reactive black 5 solutions in the cotton fabric. The calculation matches the experimental results well. Numerical results show that the fabric’s washing time should be appropriately reduced to inhibit the dye transfer. Also, reducing the surface tension will result in a lower soil concentration. Increasing the fabric washing system’s viscosity is another way to slow down the hydrolyzed dyes into the fabric. More discussions about different soils with complex boundary conditions and fabric structures will be conducted in the future.