05/04/2001, 17:00 — 18:00 — Amphitheatre Pa1, Mathematics Building
Robert Finn, Stanford University
Five Remarkable Properties of Capillary Surfaces
A capillary surface is an interface separating two fluids that are in equilibrium adjacent to each other and do not mix. In the absence of external force fields, the mean curvature of such an interface is constant; in a gravity field, varies linearly with height. If extends to a rigid support surface, then it meets that surface in a “contact angle” that is determined physically by the materials. The behavior of capillary surfaces can under some conditions be counterintuitive. In the present talk, five examples will be discussed, all of which were predicted mathematically from the formal equations, and all of which contain features that were unexpected. The examples are:
- discontinuous disappearance at critical data,
- non-uniqueness and symmetry breaking
- discontinuous behavior of liquid bridges,
- existence and nonexistence of C-singular solutions,
- discontinuous reversal of comparison relations at low gravity.
Results of drop tower and space experiments based on some of these predictions will be shown.
