Buoyancy and capillary effects in the equilibrium solutions of liquid lens

We study the equilibrium shape of a liquid drop resting on top of a liquid surface, i.e., a floating lens. We consider the surface tension forces in non--wetting situations (negative spreading factor), as well as the effects of gravity. We obtain analytical expressions for the drop shape when gravity can be neglected. Perhaps surprisingly, when including gravity in the analysis, we find two different families of equilibrium solutions for the same set of physical parameters. These equilibrium solutions differ in the curvature sign of the external liquid surface. By means of energetic considerations, we determine the family of solutions that has the smallest energy, and therefore, the most likely to be found in nature. We compare the shape of those solutions with preliminary experiments.