Shape of a fluid drop at a fluid-liquid interface. II. Theory for three-phase systems

The equilibrium shape of a liquid or gas drop (Phase 1 of density d₁) at a horizontal interface separating two fluid phases (Phases 2 and 3 of densities d₂ and d₃) can be calculated from the principles of capillarity. In the most general system these calculations are extremely complicated, and solutions have been obtained only for some special cases (very small drops; systems with d₁ = d₃; and very large drops when d₃ < d₁ < d₂).

When d₁ < d₃ there is a critical drop size above which the drop cannot be supported by the interface and ascends to the top of the system. This is illustrated with the model system of an infinitely long cylinder at an interface. The same model system is used to illustrate the experimental observation that a cluster of two or more drops, each of which is below the critical size, may cross the interface.