Thermocapillary Convection in a Binary Mixture with Moderate Prandtl Number in a Shallow Annular Pool

Abstract

This paper presented a series of numerical simulations on thermocapillary convection for mixed toluene/hexane solution with mass fraction of $c_{0}= 26.27$ % in a shallow annular pool. The Prandtl number of the binary solution is 5.54. Results indicate that when the annular pool subjects to a radial temperature gradient, the solute shifts toward the inner wall under the Soret effect, which leads to a concentration gradient with the opposite direction to the temperature gradient. With the increase of surface heat dissipation, thermocapillary convection is enhanced and the flow is more prone to destabilization. Therefore, the critical thermocapillary Reynolds number of the flow destabilization and the corresponding critical oscillation frequency all decrease, but the critical wave number increases. After flow destabilization, the concentration fluctuation similar to the temperature fluctuation on the free surface appears. No matter the free surface is adiabatic or not, the flow always undergoes a transition from two-dimensional steady axisymmetric flow to the hydrothermal waves, and then to chaos with the increase of thermocapillary Reynolds number.