An Improved Analytical Solution of Population Balance Equation Involving Aggregation and Breakage via Fibonacci and Lucas Approximation Method

Abstract

This study presents a novel analytical solution for the Population Balance Equation (PBE) involving particulate aggregation and breakage by making use of the appropriate solution(s) of the associated complementary equation of a nonlinear PBE via Fibonacci and Lucas Approximation Method (FLAM). In a previously related study, travelling wave solutions of the complementary equation of the PBE using Auxiliary Equation Method (AEM) with sixth order nonlinearity was taken to be analogous to the description of the dynamic behavior of the particulate processes. However, in this study, the class of auxiliary equations is extended to Fibonacci and Lucas type equations with given transformations to solve the PBE. As a proof-of-concept for the novel approach, the general case when the number of particles varies with respect to time is chosen. Three cases i.e. balanced aggregation and breakage and when either aggregation or breakage can dominate are selected and solved for their corresponding analytical solution and compared with the available analytical approaches. The solution obtained using FLAM is found to be closer to the exact solution and requiring lesser parameters compared to the AEM and thereby being a more robust and reliable framework.