Thin Films Seminar
Friday, January 25, 2002, 3:15pm, 216 Physics
Karl Glasner (Duke University)
Dissipative Fluid System and Gradient Flows

Abstract:

Many physical systems possess dynamics which are dirven only by their desire to decrease their total free energy. Mathematically, this asserts that the dynamics are a gradient flow, given by the "steepest descent" of an energy functional. This notion, however, depends on the geometry assigned to the underlying function space. The task is therefore to find a metric appropriate for the given dynamics. For the problem of surface tension driven Hele-Shaw flow, the correct metric turns out to have a remarkable connectin to an optimal transport problem. This connection points the way to a diffuse interface description of Hele-Shaw flow. A numerical method for gradient systems will be presented and some computational examples of this model will be given. As a second example, a model of a thin fluid film subject to van der Waals forces will be discussed. Experiments and numerical simulation both demonstrate that an initially uniform film is subject to a long wavelengh instability which leads to an array of droplets connected by a very thin fluid layer. a coarsening process ensues. which can be understood by gradient flow techniques.

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