Stability of Constrained Capillary Surfaces

A capillary surface is an interface between two fluids whose shape is determined primarily by surface tension. Sessile drops, liquid bridges, rivulets, and liquid drops on fibers are all examples of capillary shapes influenced by contact with a solid. Capillary shapes can reconfigure spontaneously or exhibit natural oscillations, reflecting static or dynamic instabilities, respectively. Both instabilities are related, and a review of static stability precedes the dynamic case. The focus of the dynamic case here is the hydrodynamic stability of capillary surfaces subject to constraints of (a) volume conservation, (b) contact-line boundary conditions, and (c) the geometry of the supporting surface.