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We study the equilibrium solutions of a sessile drop on top of a horizontalsubstrate when it is partially covered by another inmiscible liquid, so thatpart of the drop is in contact with a third fluid (typically, air). The shapesof the interfaces are obtained by numerical integration of the differentialequations resulting from the application of the Neumann's and Young's laws atthe three fluids junction (triple point) and the two fluids--solid contact line(at the substrate), as well as no--flow boundary conditions at the wall of thecontainer under axial symmetry. The formulation shows that the solutions areparametrized by four dimensionless variables, which stand for: i) the volume ofthe external liquid in the container, ii) two ratios of interfacial tensions,and iii) the contact angle of the liquid drop at the substrate. In thisparameters space, we find solutions that consist of three interfaces: one whichconnects the substrate with the triple point, and two that connect this pointwith the symmetry axis and the wall. We find that the shape of the firstinterface strongly depend on the height of the external liquid, while thecontact angle and the two ratios of surface tensions do not introducequalitative changes. In particular, the solution can show one or more necks, oreven no neck at all, depending on the value of the effective height of theexternal fluid. An energetic analysis allows to predict the breakups of thenecks, which could give place to separated systems formed by a sessile drop anda floating lens, plus eventual spherical droplets in between (depending on thenumber of breakups).

Equilibrium solutions of a sessile drop partially covered by another liquid