Swelling Dynamics of a Disk-Shaped Gel

When a gel absorbs a solvent from the surrounding, a stress field is created in the gel, and this causes complex dynamics of the swelling behavior. Here, we study this effect for a disk-shaped gel by rigorously solving the diffusio-mechanical coupling equation. We show that (a) while the macroscopic thickness and the radius of the gel increase monotonically in time, the gel is compressed near the midplane, and that (b) while the swelling time depends on the shear modulus G of the gel, its dependence is weak, and the time is mainly determined by the friction constant of the gel network and the osmotic bulk modulus of the gel. We also show that these characteristic features are reproduced accurately by a simple variational calculation for the gel deformation. An analytical expression is given for the swelling time.