Coupling VOF interfacial mass transfer model with RSM approach in LLE systems: Developing the new correlations for mass transfer, aspect ratio and terminal velocity

Abstract

The performance of liquid-liquid extraction (LLE) systems is determined by terminal velocity and extraction fraction. Several parameters and their interactive effects influence the performance. In the present study, the response surface methodology(RSM) approach has been used to investigate the parameters' effects and their complicated interactions in hydrodynamics and mass transfer. Hydrodynamic and mass transfer simulations of a single droplet system have been carried out using the VOF method and close agreements have been attained in comparison with experimental data. Subsequently, the RSM and central composite design methods were employed in terminal velocity, aspect ratio, and extraction fraction modeling. The drop diameter, density ratio, and viscosity ratio have been chosen as the effective hydrodynamic parameters in the terminal velocity and aspect ratio. The mentioned hydrodynamic parameters, partition coefficient, and diffusivity ratio have been chosen as the mass transfer variables. The suggested quadratic models of terminal velocity(R2 = 0.99) gives accurate predictions in high Re numbers, while the previous correlations could not. The new general quadratic model of aspect ratio having included the viscosity ratio as an effective parameter, can be used in the wide range of material properties with high accuracy (R2 = 0.95), while the previous correlations have not included the viscosity ratio. The new quadratic model of mass transfer with high accuracy (R2 = 0.99), includes partition coefficient and its interactive effects with diffusivity ratio and hydrodynamic parameters which have not been considered yet. More additionally, the developed model could be applied in every LLE system regardless of the mass transfer resistance existence in the drop/continuous phase or both. Finally, the ANOVA showed that the partition coefficient and viscosity ratio are the most effective parameters in mass transfer, hence the reduction in the partition coefficient along with the reduction in viscosity ratio would help to reach the better mass transfer performance. At the final stage, the optimized conditions have been presented.