Applications of He’s methods to the steady-state population balance equation in continuous flow systems

Abstract

The population balance equation has numerous applications in physical and engineering sciences, where one of the phases is discrete in nature. Such applications include crystallization, bubble column reactors, bioreactors, microbial cell populations, aerosols, powders, polymers and more. This contribution presents a comprehensive investigation of the semi- analytical solutions of the population balance equation (PBE) for continuous flow particulate processes. The general PBE was analytically solved using homotopy perturbation method (HPM) and variational iteration method (VIM) for particulate processes where breakage, growth, aggregation, and simultaneous breakage and aggregation take place. These semi-analytical methods overcome the crucial difficulties of numerical discretization and stability that often characterize previous solutions of the PBEs. It was found that the series solutions converged exactly to available analytical steady-state solutions of the PBE using these two methods.