Dr. Loren Sumner talked about

 "The Development of Stability Analyses for a Thermocapillary Driven Flow".
W 11/16/99, 4:45pm, WSC 109

Motivated as a model of the float-zone crystal-growth process, the half zone has become an interesting case for the application of the two extremes of stability theories, energy and linear theory. The half zone consists of a liquid bridge held by surface tension between the ends of two, vertically oriented, solid cylinders. The cylinders are heated separately to maintain a temperature gradient along the free surface inducing thermocapillary forces that cause bulk fluid motion. With a large enough temperature difference, the resulting flow becomes unstable and begins to oscillate prompting a stability analysis to determine critical parameters. The three dimensionality and the presence of a free surface at the radial boundary complicate the stability analyses such that simplifying assumptions are necessary to facilitate manageable mathematics. Consequently, the first attempts considering flow stability proved to be over simplified, and a development has since been evolving to include additional physics of the flow. A synopsis of both energy and linear theory will be presented along with an explanation of a series of half-zone analyses. The latest theoretical stability results of both linear and energy theories are compared to a set stability boundaries determined experimentally. These results are from various research groups.