Clauderino Batista - School of Chemical Engineering, Federal University of Pará, UFPA, Campus do Guamá, Rua Augusto Corrêa, ۰۱, Belém, PA, ۶۶۰۷۵-۱۱۰, Brazil‎
Helder Miyagawa - School of Chemical Engineering, Federal University of Pará, UFPA, Campus do Guamá, Rua Augusto Corrêa, ۰۱, Belém, PA, ۶۶۰۷۵-۱۱۰, Brazil‎
Emanuel Macêdo - School of Chemical Engineering, Federal University of Pará, UFPA, Campus do Guamá, Rua Augusto Corrêa, ۰۱, Belém, PA, ۶۶۰۷۵-۱۱۰, Brazil‎
João Quaresma - School of Chemical Engineering, Federal University of Pará, UFPA, Campus do Guamá, Rua Augusto Corrêa, ۰۱, Belém, PA, ۶۶۰۷۵-۱۱۰, Brazil‎
Helcio Orlande - Laboratory of Transmission and Technology of Heat, Mechanical Engineering Department, Federal University of Rio de Janeiro,‎ Rio de Janeiro, RJ, ۲۱۹۴۵-۹۷۰, Brazil‎

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.

Aerosol modeling, numerical inversion of the Laplace transform, Particle size distribution