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

The Marangoni e#ect is a frequently observed phenomenon of enhancement of interphase mass transfer in liquid–liquid systems. Such an e#ect, originating from 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-3tted coordinate system by solving coupled 4uid 4ow and solute mass transfer equations. Numerical simulation demonstrates the occurrence of the Marangoni e#ect under typical conditions in liquid–liquid systems, and is in reasonable agreement with the classic theoretical analysis. Su5cient spatial and temporal resolution in simulation reveals the multi-scale interaction of the drop-scale Marangoni e#ect with the sub-drop-scale local interfacial convection. The e#ect 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 e#ect 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 e#ect of mass transfer enhancement. Besides, the Marangoni e#ect occurs only when the surface tension sensitivity to the solute concentration variation is above certain critical level. The present axisymmetric simulation of the Marangoni e#ect provides necessary basis for further work on three-dimensional numerical analysis. ? 2004 Elsevier Ltd. All rights reserved.