Buoyancy and capillary effects on floating liquid lenses

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 nonwetting 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 solutions correspond to drops whose center of mass is above or below the level of the external liquid surface. By means of energetic considerations, we determine the family that has the smallest energy, and therefore is the most probable to be found in nature.