Effect of surface tension on swell-induced surface instability of substrate-confined hydrogel layers†

Swell-induced surface instability has been observed experimentally in rubbers and gels. Here we present a theoretical model that predicts the critical condition along with a characteristic wavelength for swellinduced surface instability in substrate-confined hydrogel layers. The effect of surface tension is found to be critical in suppressing short-wavelength modes of instability, while the substrate confinement suppresses long-wavelength modes. Together, an intermediate wavelength is selected at a critical swelling ratio for the onset of surface instability. Both the critical swelling ratio and the characteristic wavelength depend on the initial thickness of the hydrogel layer as well as other material properties of the hydrogel. It is found that the hydrogel layer becomes increasingly stable as the initial layer thickness decreases. A critical thickness is predicted, below which the hydrogel layer swells homogeneously and remains stable at the equilibrium state.