title: Variational bounds for the relaxation times of swelling gels.
abstract: 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.
authors.affiliation: Department of Applied Physics, The University of Tokyo, and CREST JST, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-8656, Japan.
authors.forename: Masao
authors.initials: M
authors.lastname: Doi
authors.forename: Tatsuya
authors.initials: T
authors.lastname: Yamaue