Rates of transport through a capsule membrane to attain Donnan equilibrium

The swelling of a capsule consisting of salt solution and polyelectrolyte, surrounded by a membrane, is studied. The membrane allows salt and water to pass, but is impermeable to polyelectrolyte molecules. Equilibrium swelling of the capsule is governed by Donnan equilibrium. Transport rates of a salt and water through the membrane are expressed in terms of a Darcy permeability and a salt diffusivity. The governing equations predict that the rate at which equilibrium is attained as the external salt concentration varies is controlled by the timescale for diffusion of salt, rather than by that for Darcy flow. Experiments were performed using capsules with membranes made of covalently linked HSA and alginate. The capsule volume varied with a single relaxation rate when the external salt concentration was changed, as predicted by theory. This constitutes the first step toward a simple method for determining the membrane properties of capsules by measuring rates of change of capsule volume.