Behavior of the dispersed phase in a biphasic liquid-liquid Comportement de la phase dispersé dans un contacteur diphasique liquide-liquide

In this work two major hydrodynamic parameters: the holdup of the dispersed phase and the Sauter diameter are considered. In the first part, this is done for describing the hydrodynamics of interacting liquid–liquid dispersions with using different drop breakup, coalescence and growth models in a droplet population balance model. Based on the variational iteration method, different process cases have been performed and, it is possible to find the exact solution or a closed approximate solution of a problem. For the simultaneous growth and the coalescence terms a comparison between the present method and projection method which include discontinuous Galerkin and collocation techniques are made respectively. The results are encouraging and the new method has proven to be suitable to predict holdup and Sauter diameter profiles. In the second part, we extended the dual quadrature method of generalized moments (DuQMoGeM) to solve the population balance model for the hydrodynamics of liquidliquid extraction columns using a multi-compartment model. The DuQMoGeM results were compared to analytical solutions for batch and continuous well-mixed vessels and extraction columns, showing that it is accurate for predicting the evolution of the low order moments and the drop number distribution along with the column height. We also modeled a K¨ uhni column for which the simulation accurately predicted the steadystate experimental holdup, encouraging the DuQMoGeM usage to solve the population balance equation for heterogeneous systems and different columns

Variational iteration method and projection method solution of the spatially distributed population balance equation

In this work, two major hydrodynamic parameters, the holdup of the dispersed phase and the Sauter diameter, are considered. This is done for describing the hydrodynamics of interacting liquid–liquid dispersions using different particle breakage, coalescence and growth models in a particle population balance model. Based on the semi-analytical solution method of the population balance, namely, the variational iteration method (VIM), different process cases have been performed, and it is possible to find the exact solution or a closed approximate solution of a problem. For the simultaneous growth and coalescence terms comparisons between the present method and projection method which include discontinuous Galerkin and collocation techniques are made, respectively. The VIM technique overcomes the difficulties of discretization of the variables, introduces an efficient algorithm that improves the standard discretization method and is able to handle quite successful these process of population balance equations. The results are encouraging and the new method has proven to be suitable to predict holdup and Sauter diameter profiles