Numerical Simulation of Oscillatory Axisymmetric Marangoni Convection in Small Liquid Bridge

The present numerical simulation explores a thermal-convection mechanism for oscillatory Marangoni convection in a small liquid bridge for a fluid of Prandtl number 3.34. In this work we developed a stability diagram for the critical Marangoni number separating the steady from the time-dependent flow states as a function of the aspect ratio between 1.0 and 3.0 for adiabatic melt surface. These results obtained numerically are compared with the critical Marangoni numbers for axisymmetric oscillatory convection predicted via the energy method by Shen et. al.. We also discussed the effect of heat transfer through the melt surface on the critical Marangoni number