Contents/conteúdo

Mathematics Department Técnico Técnico

Colloquium  RSS

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 S 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 H of such an interface is constant; in a gravity field, H varies linearly with height. If S 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:

  1. discontinuous disappearance at critical data,
  2. non-uniqueness and symmetry breaking
  3. discontinuous behavior of liquid bridges,
  4. existence and nonexistence of C-singular solutions,
  5. discontinuous reversal of comparison relations at low gravity.

Results of drop tower and space experiments based on some of these predictions will be shown.

link

Colloquium_logo

The Mathematics Colloquium is a series of monthly talks organized by the Department of Mathematics of IST, aiming to be a forum for the presentation of mathematical ideas or ideas about Mathematics. The Colloquium welcomes the participation of faculty, researchers and undergraduate or graduate students, of IST or other institutions, and is seen as an opportunity of bringing together and fostering the building up of ideas in an informal atmosphere.

Organizers: Conceição Amado, Lina Oliveira e Maria João Borges.