On pendent drops in a capillary tube

Capillary drops on a rough surface

We study liquid drops lying on a rough planar surface. The drops are minimizers of an energy functional that includes a random adhesion energy. We prove the existence of minimizers and the regularity of the free boundary. When the length scale of the randomly varying surface is small, we show that minimizers are close to spherical caps which are minimizers of an averaged energy functional. In p...

Vertex Theorems for Capillary Drops on Supportplanesrobert

A Study on Capillary Tube Flow

Paramecium swimming in capillary tube

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Vertex Theorems for Capillary Drops on Support Planes

We consider a capillary drop that contacts several planar bounding walls so as to produce singularities (vertices) in the boundary of its free surface. It is shown under various conditions that when the number of vertices is less than or equal to three, then the free surface must be a portion of a sphere. These results extend the classical theorem of H. Hopf on constant mean curvature immersion...