VOF simulation of single rising drops in three liquid-liquid extraction systems using CSF and CSS interfacial force models

Abstract

In liquid-liquid extraction contractors, mass transfer and stage efficiency are closely related to drop hydrodynamics. In the present study, hydrodynamic simulation of three standard liquid-liquid extraction systems recommended by the EFCE (European Federation of Chemical Engineering) has been investigated. Toluene/water, n-butyl acetate/water, and n-butanol/water with different drop diameters were considered in the simulations, representing systems with high, medium, and low interfacial tension respectively. In the current research, for the first time simulations have been carried out using the VOF-PLIC (Volume of Fluid - Piecewise Linear Interface Calculation) model, implementing two surface tension force models of CSS (Continuum Surface Stress) and CSF (Continuum Surface Force) as a source term in the momentum equation. Simulations have been carried out in an axisymmetric geometry with a moving droplet in the static zone. The stages of droplet acceleration, deformation, and stability in terms of shape and velocity have been captured through simulations. Simulation results show that the average relative error reduces by using the CSS model and the most enhanced effect is observed in the toluene/water system, followed by the n-butyl acetate/water and n-butanol/water systems, respectively. This is due to higher parasitic current effects in the highest surface tension system (toluene/water). The onset of oscillations in the toluene/water system was correctly predicted by the CSS model, while the CSF model could not. Droplet shapes, aspect ratio, terminal and transient velocity and streamlines were also reported in the two surface tension models and compared.