Oscillatory thermocapillary convection in liquid bridges with highly deformed free surfaces: Experiments and energy-stability analysis

Abstract

Laboratory experimentation, numerical simulation, and energy-stability theory are used to examine the effect of interface deformation on the onset of oscillatory thermocapillary convection in half zones. Experiments are performed to map the stability boundaries marking the onset of oscillatory flow, modifying the free-surface deformation by adjusting the volume of liquid in the bridge. The stability results presented here along with those of other researchers [Monti et al., Proceedings of the 43rd Cong. Int. Artro. Fed. (1992); Hu et al., J. Cryst. Growth 142, 379 (1994)] show that free-surface curvature can have a pronounced influence on flow stability. Steady, axisymmetric flow simulations are computed using the commercial code FIDAP to model the conditions of the experiments, and reveal that flow structure near the stability boundary is sensitive to several parameters. Energy theory is applied to these simulations to determine sufficient conditions for stability. Comparisons between the theoretical and experimental results show nonconservative energy limits falling above the experimentally determined stability boundaries for bridges of various liquid volumes. While the trend of the experimental data is predicted for zones of large volume ratio (bulging zones), the same cannot be said for those with small volume ratio (necked-down zones). In addition, energy-stability limits for some undeformed-free-surface cases were determined which are above the linear-stability limits determined by other researchers, in clear contradiction of the roles of the respective theories.