3423 Theoretical Analysis of Critical Marangoni Number for Oscillatory Flows

Many experiments to determine the critical Marangoni number at the onset of oscillatory flows for high Prandtl number (Pr) fluids have showed a dependence of a characteristic length such as the diameter of the liquid column. This fact contradicts the similarity principle in fluid physics. The higher Pr fluid formed a thermal boundary layer with a steep temperature gradient in the vicinity of both the hot and cold disks for Marangoni convection experiments, although the middle of the free surface between the hot and cold disks has no temperature gradients. By considering the partial temperature distribution on the free surface, a basic model for the understanding of Marangoni number for higher Pr fluids is proposed by introducing a dimensionless parameter, the effective Marangoni number. Experimental results obtained from microgravity experiments showed that this effective Marangoni number does not have the characteristic length dependence at the onset of oscillatory flows. This parameter is consistent with the similarity principle in Marangoni convection behavior.