The shape and stability of wall-bound and wall-edge-bound drops and bubbles

The behavior of wall-bound drops and bubbles is fundamental to many natural and industrial processes. Key characteristics of such capillary systems include interface shape and stability for a variety of gravity levels and orientations. Significant solutions are in hand for axisymmetric pendent drops for a variety of uniform boundary conditions along the contact line with gravity acting normal to a planar wall. The special case of a wall-bound drop or bubble that is also pinned at an edge (i.e. a ‘wall-edge-bound’ drop) is considered here where numerical solutions are obtained for interface shape and stability as functions of drop volume, contact angle, fluid properties, and uniform gravity vector. For a semi-infinite zero-thickness planar wall (plate), a critical contact angle is identified below which wall-edge-bound drops are always stable. The critical contact angle is computed as a function of the gravity vector. The numerical procedure, which makes no account for contact angle hysteresis, predicts that such wall-edge-bound drops are unconditionally unstable for any gravity field with a component that is tangent to the wall while inwardly normal to the edge. Select experiments are conducted that support the conclusions drawn from the numerical results.