Symmetries and exact solutions of the population balance equation with growth and breakage processes, using group analysis

Abstract

Population balance equation which may be employed to handle a wide variety of particle processes has certainly received unprecedented attention, but the absence of explicit exact solutions necessitates the use of numerical approaches. The one‐dimensional population balance equation with time independent but size dependent growth and breakage rate is investigated. The corresponding system of equation is solved analytically by use of the Lie group analysis method. Symmetries, reduced equations, invariant solutions, explicit exact, and unphysical solutions are presented in this paper.