Capillary ratio dependence of thermal-solutal capillary convection in a shallow annular pool with radial temperature and concentration gradients

Abstract

In order to understand the effect of capillary ratio on the thermal-solutal capillary convection in an annular pool subjected to simultaneous radial thermal and solutal gradients, a series of three-dimensional direct numerical simulation have been conducted. The working fluid was the toluene/n-hexane mixture fluid with the Prandtl number of 5.54 and the Schmidt number of 142.8. The capillary ratio Rσ varied from −5 to 0. Results show that fluid flow occurs at very small thermocapillary Reynolds number except for case of Rσ = −1. There are three types of two-dimensional steady flow depending on the capillary ratio, i.e., counter-clockwise unicellular flow, clockwise unicellular flow and flow pattern with two separate cells. When the Reynolds number exceeds the first critical thermocapillary Reynolds number, three-dimensional steady flow appears, while the three-dimensional or two-dimensional oscillatory flow takes place above the second critical point. The fluctuations of temperature and concentration on the free surface indicate that three-dimensional oscillatory thermal-solutal capillary flow appears as either the coexistence of “hydro-thermal wave” (HTW) and “hydro-solutal wave” (HSW), or the “vibrating straight spokes”. Both the first and second critical thermocapillary Reynolds numbers firstly decrease, and then increase slowly when the capillary ratio varies from 0 to −1. Moreover, it is found that the critical frequency and critical wave number for the flow pattern transitions are greatly dependent on the capillary ratio.