Dynamic Moisture Absorption Behavior of Polyester-Cotton Fabric and Mathematical Model

We investigate the dynamic moisture absorption behavior of polyester—cotton fabrics of different warp and weft densities, survey the dry-basis moisture contents of these various fabrics under variant temperature and relative humidity, and acquire a dynamic moisture absorption curve and balanced moisture content of these fabrics. The results show that the fabric moisture absorption velocity is in reverse relation with its warp and weft densities. By applying the Fick’s Law for diffusion in porous media, a mathematical model for the fabric’s dynamic moisture absorption is established, which is represented in the form of a non-linear partial differential equation boundary value problem; in order to simplify the calculation of the solution, a model parameter a is put forward, defined as the “structural factor”, relating to the fabric structure. After the model is solved under six-point format finite difference method, the distribution of the dry-basis moisture content in the diffusion direction at different times can be obtained. Based on the experimental data, the golden section method is utilized to estimate the model parameter a, and the linear relation between the parameter a and the product of warp and weft densities j is obtained by mathematical software “Mathematica”. The simulation value of dry-basis moisture content from the model matches the experimental observations.