Numerical simulation of the Marangoni effect on mass transfer to single slowly moving drops in the liquid–liquid system

The Marangoni effect is a frequently observed phenomenon of enhancement of interphase mass transfer in liquid-liquid systems. Such an effect, originating front the hydrodynamic instability induced by surface tension sensitivity to surface concentration of transferred solute, is mathematically formulated and numerically simulated for slowly moving single spherical drops in an axisymmetric boundary-fitted coordinate system by solving coupled fluid flow and solute mass transfer equations. Numerical simulation demonstrates the occurrence of the Marangoni effect under typical conditions in liquid-liquid systems, and is in reasonable agreement with the classic theoretical analysis. Sufficient spatial and temporal resolution in simulation reveals the multi-scale interaction of the drop-scale Marangoni effect with the sub-drop-scale local interfacial convection. The effect of solute transfer direction, Peclet number, surface tension sensitivity to solute concentration, and level of random perturbation on surface concentration are investigated numerically. It is shown that the Marangoni effect occurs in the middle stage of a transient interphase mass transfer process, and the Marangoni convection at the interface does not necessarily results in the Marangoni effect of mass transfer enhancement. Besides, the Marangoni effect occurs only when the surface tension sensitivity to the solute concentration variation is above certain critical level. The present axisymmetric simulation of the Marangoni effect provides necessary basis for further work on three-dimensional numerical analysis. (C) 2004 Elsevier Ltd. All rights reserved.