Hydrodynamic instability in thermocapillary liquid bridges
The stability of thermocapillary flow in a liquid bridge made of silicone oil (high Prandtl number) is investigated using the linear stability theory, whose equations have been solved numerically. The flow and temperature of the gas surrounding the liquid bridge, contained in a generic cylindrical chamber, were taken into consideration. The flow between the liquid and gas was fully coupled across the deformed liquid-gas interface. Several approximations were taken into account, ranging from the Boussinesq approximation to a fully-temperature-dependent set of equations. Moreover, both, hydrostatic and dynamic interface deformations were considered. The linear stability boundary was determined by changing the length of the liquid bridge (aspect ratio), its volume, the gravity level, and the blowing conditions of gas around the liquid bridge. The dependence of the critical threshold on these parameters was explained in terms of the characteristics of the critical mode. Noteworthy is the significance of the heat exchange between the surrounding gas and the liquid bridge on the critical conditions.
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