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ABSTRACT
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. |