  When a gel absorbs solvent from surrounding, stress field is created in the
gel, and this causes complex dynamics of the swelling behavior. Here we study
this effect for 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 increases monotonically in time, the gel is compressed near
the mid-plane, 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.
