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

Abstract

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.