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Key Words free-surface flow, surface-tension-driven instability, hydrodynamic instability, pattern formation, thermal convection, thermocapillarity, Benard-Marangoni convection, liquid bridge, hydrothermal waves, oscillatory convection
* Abstract This review summarizes recent experimental studies of instabilities in free-surface flows driven by thermocapillarity. Two broad classes are considered, depending upon whether the imposed temperature gradient is perpendicular (Marangoni-- convection instability) or parallel (thermocapillary-convection instability) to the free surface. Both steady and time-dependent instabilites are reviewed in experiments employing both large- and small-aspect-ratio geometries of various symmetries.
1. INTRODUCTION
3. THERMOCAPILLARY CONVECTION INSTABILITY
3.1 Preliminaries
Thermocapillary convection refers to motions driven by the application of a temperature gradient along the interface. Flow will be driven for any such surface-- temperature gradient, no matter how small, and thus the existence of a critical, or threshold, temperature gradient is not required. These basic states become unstable for large enough applied temperature gradients and lead to alternate states consisting of either steady, cellular (most often, a form of roll cell) structures or oscillatory states.
Most of the research done over the last few decades on such instabilities has been motivated by the transition to oscillatory flow because of its importance in technological applications such as crystal growth. The appearance of oscillatory thermocapillary convection, coupled with solidification processes has been shown (see, e.g. the paper by Gatos 1982) to lead to a degradation of the resulting crystal. A review by Schwabe (1981) describes some of the earlier work on this problem.
For the purpose of classifying the types of experiments that have been performed, it is useful to think in terms of three categories, shown schematically in Figure 10. The direction of the body-force vector g is indicated for all three cases for those experiments conducted on Earth. The geometry of Figure 10a is a model of a float-zone or, for the case in which the temperature gradient is of a single sign along the free-surface, the half-zone. The latter case has been studied extensively as a model of the full float-zone. The actual crystal-growth application obviously possesses melting and solidifying interfaces at the top and bottom, but they will not be discussed here. The planar layer of Figure lOb is a model system motivated by the hydrodynamic-stability analysis of Smith & Davis (1983)...