A simple method for modeling the concentration-dependent water sorption in reinforced polymeric materials

Transport problems have long been studied and appear in numerous physical situations: thermal conduction, flow through porous media, molecular diffusion, etc. In this paper, we are interested in the water sorption of a polymer matrix composite which exhibits a concentration and temperature dependent diffusivity. Since it is time consuming and difficult to measure, it is necessary to estimate the water uptake and the time required to reach saturation with an evolving hydro-thermal environment without using sophisticated tools. This study provides an easy-to-implement and practical tool based on a finite difference scheme to solve this non-linear and coupled problem. We focus on the concentration dependency and propose two ways to improve the local space accuracy and thus capture the induced high-gradient frontier. The present mono-dimensional approach can be easily extended to bi-dimensional cases. Some numerical examples are given to show the effectiveness of the scheme.