Numerical simulation of the kinetics of aerosol formation in the free molecular collision regime

At present there are two different theoretical approaches to describe nucleation and growth of aerosols. The first is based on a classical description of the kinetics of new phase formation and focuses on the determination of an expression for the free energy of formation of critical clusters. When this value and the size of a critical embryo are known, conventional methods are used to write down the expression for the rate of new particle formation. The formation of the size distribution of the aerosol particles is further determined by the rate of condensation growth as well as by the rate of the appearance of the new critical embryos. The alternative approach involves the solution of a set of kinetic equations (Smolouchovsky equations) the number of which equals the number of monomers in the largest particle. In this report we suggest a numerical method for solving the Smolouchovsky equation and analyze the kinetics of the size spectrum of aerosol particles which are formed in the process of gas-dispersed phase transition in the high saturation regime.