Theory of one-dimensional swelling dynamics of polymer gels under mechanical constraint

Recently, the swelling kinetics of thin-plate gels with rectangular surfaces under mechanical constraint was experimentally investigated [ A. Suzuki and T. Hara, J. Chem. Phys. 114, 5012 (2001) ]. In this system, the top and bottom surfaces of gels were chemically clamped on the glass plates, and the gels could swell and shrink only along the thickness direction when the osmotic pressure of the solvent is changed. Here, we analyze this process using the linearized stress-diffusion coupling model of gels based on the two fluids model. The result is somewhat unusual in that the time evolution of the thickness is described by a single exponential even though the swelling is governed by the diffusion of solvent. This result and that the characteristic relaxation time depends on the lengths of the rectangular surfaces and not on the thickness of gels agree well with the experiment.