Swell-induced surface instability of hydrogel layers with material properties varying in thickness direction

Upon swelling in a solvent, a thin hydrogel layer on a rigid substrate may become unstable, developing various surface patterns. Recent experimental studies have explored the possibilities to generate controllable surface patterns by chemically modifying the molecular structures of the hydrogel near the surface. In this paper, we present a theoretical stability analysis for swelling of hydrogel layers with material properties varying in the thickness direction. As a specialization of the general procedure, hydrogel bilayers with different combinations of the material properties are examined in details. For a soft-on-hard bilayer, the onset of surface instability is determined by the short-wave limit, similar to a homogeneous layer. In contrast, for a hard-on-soft bilayer, a long-wave mode with a finite wavelength emerges as the critical mode at the onset of surface instability, similar to wrinkling of an elastic thin film on a compliant substrate, and the critical swelling ratio is much lower than that for a homogeneous hydrogel layer. A smooth transition of the critical mode is predicted as the volume fraction of the top layer changes, linking surface instability of a homogeneous layer to thin film wrinkling as two limiting cases. The results from the present study suggest that both the critical condition and the instability mode depend sensitively on the variation of the material properties in the thickness direction of the hydrogel layer.