Analysis of Particulate Systems with Numerical Inverse Laplace Transform

The technique of numerical inversion of the Laplace transform is applied to solve the population balance equation (PBE). The model considers the dispersed phase systems in which nucleation and heterogeneous condensation are present. The studied phenomena model corresponds to a nonlinear integro-partial-differential equation. Test cases are solved considering two different collision mechanisms, the first-order removal mechanism and the effect of simultaneous coagulation and growth. Numerical results are compared with the analytical solution and with the literature. Based on these results, the technique applied in this work demonstrates to be a tool to solve problems in particulate systems, particularly for aerosol modeling where coagulation is the most important inter-particle mechanism affecting the size distribution.