Droplets on Lubricated Surfaces: The slow dynamics of skirt formation

Abstract

A key question in the interaction of droplets with liquid-infused surfaces is what determines the apparent contact angle of droplets. Previous work has used measured values of the skirt geometry (e.g. the radius of curvature of the skirt) to determine this. Here, we consider theoretically the equilibrium of a droplet on a smooth (inverse opal) lubricant-coated surface, and argue that the small effect of gravity within the skirt and the size of the substrate are important for determining the final equilibrium. However, we also show that the evolution towards this ultimate equilibrium is extremely slow (on the order of days for typical experimental parameter values). We therefore suggest that previous experiments on inverse opal or nano-textured surfaces may have observed only slowly-evolving transients, rather than 'true' equilibria, potentially explaining why a wide range of skirt sizes have been reported.