A transport model for swelling of polyelectrolyte gels in simple and complex geometries

A model for the swelling of polyelectrolyte gels in salt solutions is developed and solved numerically. The model accounts for the effect of network stress, osmotic pressure, and electrical potential on the species diffusive flux. The osmotic pressure and the network stress are derived from the Helmholtz free energy of the system that is the sum of mixing, elastic, and electrostatic components. One- and two-dimensional swelling in unconstrained and constrained geometries are simulated for a salt–solvent–polymer system. The transient and equilibrium fields of electrical potential, concentrations, deformation, and stress are obtained. Transient overshoots and non-uniformities in the residual profiles are predicted.