Equilibrium Configurations for a Floating Drop

Abstract.

If a drop of fluid of density ρ₁ rests on the surface of a fluid of density ρ₂ below a fluid of density ρ₀, ρ₀ < ρ₁ < ρ₂, the surface of the drop is made up of a sessile drop and an inverted sessile drop which match an external capillary surface. Solutions of this problem are constructed by matching solutions of the axisymmetric capillary surface equation. For general values of the surface tensions at the common boundaries of the three fluids the surfaces need not be graphs and the profiles of these axisymmetric surfaces are parametrized by their tangent angles. The solutions are obtained by finding the value of the tangent angle for which the three surfaces match. In addition the asymptotic form of the solution is found for small drops.