Part V: Dynamic evolution of the multivariate particle size distribution undergoing combined particle growth and aggregation

The present paper presents a study on the application of the Galerkin finite element method (FEM) for the solution of the dynamic multivariate population balance equation (PBE) in batch particulate systems undergoing aggregation as well as combined aggregation and growth. The performance of the Galerkin FEM in terms of accuracy and stability was assessed by a direct comparison of the calculated particle size distributions and/or their corresponding moments to available analytical solutions as well as by comparison to univariate numerical solutions. Numerical simulations were carried out for a variety of particle aggregation and growth mechanisms including constant, Brownian, and modified Brownian aggregation as well as constant and linear growth rate functions and for a wide range of values for the aggregation and growth rate coefficients. The simulation results revealed that the proposed Galerkin FEM produces very accurate numerical solutions but at significant computational cost.