Equilibrium bridge solution from a sessile drop partially covered by another fluid

Liquid bridges are present in different four-phase systems, like the one studied here, which is formed by a liquid connecting a horizontal solid substrate with a gas phase while surrounded by another immiscible liquid. We obtain the equilibrium solutions by treating each interface as a simple curve with axial symmetry and constant curvature, and satisfying the boundary conditions given by Neumann's and Young's laws. Therefore, the final equilibrium solution is formed by a union of a spherical cap, a catenoid, and portions of onduloids or nodoids. We find that the γ-angle is the control parameter of the problem, as it defines the existence and shape of the final equilibrium solution.