On Tanaka-Fillmore's kinetics swelling of gels

Abstract

Tanaka and Fillmore treated the swelling of a gel as a process where a crosslinked polymer network having been initially under uniform stress is expanded by osmotic pressure, sucking up the surrounding fluid medium. We point out that their physical reasoning is unnatural and leads to an unacceptable conclusion; we propose a more sound approach to the same problem. Our treatment assumes that the gel network is extended not by the osmotic pressure of the gel, but rather by the swelling pressure which is generated by the excess fluid penetrating in against the real nature of a polymer network that tends to shrink. The diffusion equation of the fluid, hence, plays a dominant role and gives the distribution of fluid concentration in contrast to Tanaka-Fillmore's scheme. The expression for the distribution of local strain in a spherical gel is deduced from the relation of mechanical balance between two forces, the one is due to the elasticity of the network and the other due to the gradient in the chemical potential of the fluid. The results obtained have forms analytically similar to Tanaka-Fillmore's, but are differ in the physical meanings.