On solvent diffusion in a solid with large dilatation

A theoretical framework is developed for solvent diffusion in solids with large dilatation due to solvent induced swelling. The resulting non-linear governing differential equations are not amenable to a closed form solution, and hence, a solution technique based on the finite element method is presented and implemented. Several demonstration problems are solved using an in-house finite element code (NOVA-3D) to highlight the importance of including the effect of finite dilatation in a diffusion model for hygroscopic materials. The effect of finite dilatation on the calculation of diffusivity is discussed, as well as the presence of large shearing stresses induced by the concentration gradient.