Exact solutions of population balance equations for breakage and growth processes, using group analysis

Abstract

Population balance equations have been applied to model a wide range of processes including breakage, crystal nucleation, growth, agglomeration, comminution of ores and other solids, but the lack of exact solutions necessitates the use of numerical methods. A class of population balance equations with time independent but size dependent growth rate and breakage rate is investigated analytically. All invariant solutions, explicit exact solutions, reduced equations and optimal system of subalgebras for the corresponding system of equations are presented in this paper.