A Numerical Simulation Study of the Effect of Deformed Free Surface on the Thermo-Solutal Marangoni Convection in a Shallow Cavity

Abstract

This research utilized three-dimensional numerical simulations to analyze the effect of volume ratio on fluid dynamics of a range of Prandtl (Pr) number and Schmidt (Sc) number fluids under steady and unsteady Marangoni conditions. Key outcomes highlight that while the volume ratio has a negligible effect on temperature distribution in low Pr number fluids under steady conditions, it becomes important under unsteady Marangoni convection. Conversely, in high Pr number fluids, the volume ratio significantly influences temperature and flow velocity distributions across all conditions, underscoring its critical role in achieving uniform fluid dynamics. Additionally, the volume ratio predominantly affects concentration distribution rather than temperature distribution under steady conditions in fluids of high Sc and low Pr numbers. Concentration and flow velocity distributions are uniform in the flat free surface under steady conditions for high Sc number and all Pr numbers fluids. Low Pr and high Sc number fluids exhibit irregular and quasi-periodic patterns in concentration and flow velocity distributions, and oscillatory flow patterns dominate in high Sc and high Pr number fluids under unsteady conditions.

Keywords

• Marangoni convection
• Volume ratio
• Flow patterns
• Schmidt and Prandlt numbers
• Shallow cavity system