Linear-stability analysis of thermocapillary convection in an annular two-layer system with free surface subjected to a radial temperature gradient

The linear-stability analyses of thermocapillary flow in an annular two-layer system subjected to a radial temperature gradient were conducted. The annular pool with upper free surface and adiabatic bottom is filled with immiscible double layer liquid of 5cSt silicone oil / HT-70. The outer wall of the annular pool is heated and inner wall is cooled. The results indicate that the critical Marangoni number decreases with the increase of aspect ratio and radius ratio. The effect of the ratio of the lower liquid thickness to the total double layer thickness on the convection onset is complicated. The minimum critical Marangoni number is located near the thickness ratio of 0.125. Moreover, there is one Hopf bifurcation from the steady to oscillatory flow when the thickness ratio varies from 0.625 to 0.75. At the same time, two types of flow destabilizing mechanism are identified. Comparing with the results with upper rigid wall, it can be found that the stability of thermocapillary convection in annular two-layer system with the free surface reduces largely.