Effect of Marangoni forces on interfacial heat and mass transfer driven by surface cooling

A fully resolved numerical study was performed to investigate interfacial heat and mass transfer enhanced by the fully developed Rayleigh–Bénard–Marangoni instability in a relatively deep domain. The instability was triggered by evaporative cooling modelled by a constant surface heat flux. The latter allowed for temperature-induced variations in surface tension giving rise to Marangoni forces reinforcing the Rayleigh instability. Simulations were performed at a fixed Rayleigh number ( Raₕ ) and a variety of Marangoni numbers ( Maₕ ). In each simulation, scalar transport equations for heat and mass concentration at various Schmidt numbers ( Sc=16-200 ) were solved simultaneously. Due to the fixed (warm) temperature prescribed at the bottom of the computational domain, large buoyant plumes emerged quasi-periodically both at the top and bottom. With increasing Marangoni number a decrease in the average convection cell size at the surface was observed, with a simultaneous improvement in near-surface mixing. The presence of high aspect ratio rectangular convection cell footprints was found to be characteristic for Marangoni-dominated flows. Due to the promotion of interfacial mass transfer by Marangoni forces, the power in the scaling of the mass transfer velocity, K\!L\!∝\! Sc⁻ⁿ , was found to decrease from $n=0.50$ at Maₕ=0 to ≈ 0.438 at Maₕ=13.21× 10⁵ . Finally, the existence of a buoyancy-dominated and a Marangoni-dominated regime was investigated in the context of the interfacial heat and mass transfer scaling as a function of Maₕ+ε Raₕ , where ε is a small number determined empirically.