Extended stress-diffusion coupling model for swelling dynamics of polymer gels

We extend the stress-diffusion model presented by Yamaue and Doi (Yamaue, T.; Doi, M. Phys. Rev. E2004, 69, 41402) by eliminating the solvent velocity but treating the polymer volume fraction as a field variable during swelling. We show two equivalent descriptions of conservation of polymer molecules and incorporate this law via an algebraic relation, simplifying the enforcement of boundary conditions and numerical implementation of the extended model. The extended stress-diffusion model was implemented by finite element method. The examples presented in this paper demonstrate the effectiveness and the versatility of the numerical method, indicating the potential and the capability of simulating more complicated dynamic problems.