Numerical Simulation of the Marangoni Effect with Interphase Mass Transfer Between Two Planar Liquid Layers*

The Marangoni effect induced by mass transfer at the interface between two immiscible liquids displays important influence on laboratory and industrial operation of solvent extraction. A systematic numerical study of the two-dimensional Marangoni effect in a two liquid layer system was conducted. The linear relationship of the interfacial tension versus the solute concentration was incorporated into a mathematical model accounting for liquid flow and mass transfer in both phases. The typical cases analyzed by Sternling & Scriven (AIChE J., 1959) using the linear instability theory were simulated by the finite difference method and good agreement between the theory and the numerical simulation was observed. The simulation suggests that the Marangoni convection needs certain time to develop sufficiently in strength and scale to enhance the interphase mass transfer, the Marangoni effect is dynamic and transient, and remains at some stabilized level as long as the mass transfer driving force is kept constant. When certain level of shear is imposed at the interface as in most cases of practical significance, the Marangoni effect is suppressed slightly but progressively as the shear is increased gradually. The present two-dimensional simulation of the Marangoni effect provides some insight into the underlying mechanism and also the basis for further theoretical study of the three-dimensional Marangoni effect in the real world and in chemical engineering applications.