A multi-phase Stefan problem describing the swelling and the dissolution of glassy polymer

In the swelling and the dissolution of certain glassy polymers, three distinctive regimes are present. They are (1) the liquid solution wherein the disassociated polymer molecules are carried away by diffusion, (2) the gel layer of rubbery polymer containing large solvent concentration, and (3) the glassy phase of the polymer where there is very little solvent penetration. The gel/liquid interface that separates the diffusion of the disassociated polymer in the liquid solution from that of the solvent in the polymer is characterized by a constant disassociation concentration. The position of this gel/liquid interface is described explicitly either by a relationship between diffusion processes, or by the rate of disassociation at the interface in addition to the diffusion processes, depending on whether the disassociation rate exceeds the diffusion capability in removing the disassociated polymer molecules at the interface.