Alternative boundary conditions for a drop hanging from a circular tube

Abstract

The stability of pendent liquid drops with axial symmetry is usually discussed for a specific type of boundary condition, ignoring the possibility of transitions between one type and another. The alternative configurations are denoted by θ, r_i and r_e, according to whether the drop contacts the base of the tube or its inner (r_i) or outer edge (r_e). Transitions between these configurations are predicted from the appropriate thermodynamic functions for both volume- and pressure-controlled drops. The main conclusion is that in volume-controlled drops the r configurations are unstable relative to the θ configuration when the actual contact angle is reached, but in pressure-controlled drops the reverse may be true. The behaviour of drops in pressure-controlled conditions depends on the geometry of the system in which the drop is formed. The limiting stable configurations of drops are discussed, taking into account the transitions between different boundary conditions.