Symmetries of population balance equations for aggregation, breakage and growth processes

The integro-differential population balance equation describing aggregation processes was proposed almost 100 years ago. Aggregation is an important size enlargement process in many industries; the modeling and design of the process can be done using the population balance framework, however it is typically impossible to obtain analytical solutions: in almost every case a numerical solution of the equations must be obtained. In this paper, we present the developed group analysis method for the one-dimensional population balance equation for aggregation in a well-mixed batch system including a crystal growth term. The determining equations are solved, the optimal system, invariant solutions and all the reduced equations are obtained. Furthermore, finding the determining equation by use of the preliminary group classification is also considered.