The osmocapillary effect on a rough gel surface

A gel surface is generally biphasic at equilibrium. Asperities can be submerged under solvent due to osmocapillary phase separation and be flattened due to elastocapillary deformation. The surface behavior of a gel is governed by the interaction between osmocapillary phase separation and elastocapillary deformation. We develop a linear osmocapillary model that numerically predicts the phase separation and deformation on a gel surface. We use the model to simulate the deformation of a sinusoidal surface and a computer-generated self-affine rough surface. The simulation shows that the behavior of a gel surface is governed by the osmocapillary length and elastocapillary length relative to the characteristic length of the surface roughness. As the relative magnitude of these length scales change, the surface can behave like a rigid material with little deformation, a liquid with a completely flattened surface, a dry elastomer where deformation is not accompanied by osmocapillary phase separation, or a wet gel where a large portion of the surface is covered by the solvent. Contrary to the existing understandings, we show that a gel surface can be mostly covered by the liquid solvent, although the gel is solid, and the resulting surface energy can be significantly lower than the prediction from existing models neglecting osmocapillary phase separation.