Kinetics of Swelling Gels

Abstract

We develop a general theory of the swelling kinetics of polymer gels, with the view that a polymer gel is a two-phase fluid. The model we propose is a free boundary problem and can be used to understand both contraction and swelling, including complete dissolving or dehydration of polymeric gels. We show that the equations of motion satisfy a minimum energy dissipation rate principle similar to the Helmholtz minimum dissipation rate principle which holds for a Stokes flow. We also show, using asymptotic analysis and numerical simulation, how the equilibrium swelled state and the swelling rate constant are related to the free energy and rheological properties of the polymer network.