Surface instability of a swollen cylinder hydrogel

Cylinder hydrogel is simple in geometry and easy to synthesize, therefore was widely used to investigate the swelling/shrinking instability of hydrogel and many instability patterns were accumulated in the literature. The mechanism of instability pattern formation of this unique configuration, nevertheless, is far from being fully understood. We applied and extended the recently developed nonlinear theory of polymer gels into cylindrical coordinates, and performed linear perturbation analysis of swelling-induced stability of a constrained cylinder hydrogel. We derived the incremental formulations of stresses and the associated equilibrium equations. We obtained the critical conditions for the onset of instability and probed in details the effects of various parameters on the stability diagram of the hydrogel. The physical meaning of the variation of stability diagram was also interpreted.