Numerical simulation of thermal-solutal Marangoni convection in a shallow rectangular cavity with mutually perpendicular temperature and concentration gradients

Abstract

A series of three-dimensional numerical simulations have been carried out to examine the characteristics of thermal-solutal Marangoni convection in a rectangular cavity that is subjected to mutually perpendicular temperature and concentration gradients. In the simulations, the thermal Marangoni number MaT is selected as 0, 1, 3, and 7 × 104, but the solutal Marangoni number MaC is varied in order to be able to investigate the complex flow patterns and flow transitions. Results show that the flow is steady at relatively small MaC. Then, at this MaC value, we observe three types of steady flows as MaT increases, namely, a longitudinal surface flow, an oblique stripe flow, and a lateral surface flow. When MaC exceeds a critical value, the stability of the Marangoni flow is destroyed, and a three-dimensional oscillatory flow appears. For the oscillatory flow, the wave patterns of temperature and concentration fluctuations are highly dependent on the coupling of the thermal and solutal Marangoni effect. Two different propagation directions of wave patterns coexist on the free surface when the contributions of thermal and solutal flows are in the same order (i.e., MaC is approximately equal to MaT). In addition, a sudden drop in the wave frequency and a backward transition phenomenon from chaotic to oscillatory are also observed. For all the cases of the thermal Marangoni numbers, thermal-solutal Marangoni convection becomes chaotic at higher MaC values. The present study would provide more physical insights into industrial processes such as painting and drying.