Variational bounds for the relaxation times of swelling gels

Variational bounds are found for the relaxation times of a gel of general shape swelling in a solvent based on the stress-diffusion coupling model. It is shown that in the case of free swelling, the longest relaxation time is inversely proportional to the osmotic modulus K in the limit of K -> 0 and K ->infinity. This indicates that the relaxation time diverges at the point of K=0. The divergence, however, disappears if a part of the gel is mechanically constrained.