Simulation of Marangoni convection effects on the hydrodynamics of liquid–liquid extraction drops

Concentration induced Marangoni convection (MC) effect has many applications in the chemical engineering processes. In this study, the MC effects have been investigated in the toluene/acetone/water (T/A/W) liquid–liquid extraction system, focusing on the mass transfer and hydrodynamics. For the first time, the VOF-CSS model has been used, and the mass transfer equation has been coupled with the hydrodynamic equations of the VOF model, using the surface tension force model of the CSS. A single mass transfer equation has been solved for the two phases, modifying the unsteady, convective, and diffusive terms based on the equilibrium distribution coefficient. The MC effect has been implemented in the CSS surface tension model with a concentration-dependent surface tension coefficient. Simulations have been carried out in 1, 1.5, and 2?mm drops in the wide range of concentration (0.9–30?g/L). Good agreements have been achieved for the concentration and reduced velocity values compared with the existing experimental data. Simulation results showed that the reduced velocity values remain almost constant for every drop diameter, in the initial concentration range from 3.7 to 30?g/L. The reacceleration time for the three drop sizes with the different initial concentrations has been obtained from the simulation results and compared. The MC effects on the axial velocity profiles and drag coefficients were also reported providing comprehensive information about the MC effects on the hydrodynamics.