The Population Balance Equation (PBE) which is used for describing the dynamic behavior of the aerosol system where the condensation, the agglomeration, and the nucleation and removal of particles occur in a complicated pattern, can be written in two different forms depending on whether the particle size distribution is represented in a discrete or continuous manner. Orthogonal collocation on finite elements method(OCFEM) and sectional method(SM) are used to solve the nonlinear PBE. Numerical computations were carried out for the cases with analytical solutions available to verify the soundness of numerical schemes.
Both OCFEM and SM show very good agreement with analytical solution and the present numerical scheme can be assumed to be able to simulate any particulate system of interest. Numerical simulations have been applied to two aerosol systems of NaCl and $H_2SO_4-H_2O$ for which experimental data are reported. Husar's data on the crystallized NaCl aerosols are in a qualitatively good correlation with the numerical predictions, obtained on the basis of agglomeration only. McMurry's data on the $H_2SO_4-H_2O$ system have been also shown to correlate well with the predictions, which has been obtained by considering the combined effects of nucleation, agglomeration and condensation, even if there exists some deviation for the range of smaller particle sizes.
