Swell-induced surface instability of confined hydrogel layers on substrates

In response to external stimuli, polymeric hydrogels can change volume and shape dramatically. Experimental studies have observed a variety of instability patterns of hydrogels, due to swelling or shrinking, many of which have not been well understood. The present paper considers swell-induced surface instability of a hydrogel layer on a rigid substrate. Based on a recently developed theoretical framework for neutral polymeric gels, a linear perturbation analysis is performed to predict the critical condition for the onset of the surface instability. Using a nonlinear finite element method, numerical simulations are presented to show the swelling process, with the evolution of initial surface perturbations followed by the formation of crease-like surface patterns. In contrast to previously suggested critical conditions for surface creasing, the present study suggests a material-specific condition that predicts a range of critical swelling ratios from about 2.5 to 3.4 and quantitatively relates the critical condition to material properties of the hydrogel system. A stability diagram is constructed with two distinct regions for stable and unstable hydrogels depending on two dimensionless material parameters.