Log-Normally Preserving Size Distribution for Brownian Coagulation in the Free-Molecule Regime

Abstract

Coagulation of aerosol particles in the free-molecule regime has been studied theoretically by converting the governing partial integrodifferential equation into a set of two ordinary differential equations. The approach assumes that the size distribution of an aerosol attains or can at least be represented by a time-dependent log-normal distribution function during the coagulation process. The calculations have been performed and the results found to be in good agreement with results for previous theories. In addition, the following asymptotic size distribution function is found as an alternative solution for the self-preserving particle size distribution function for Brownian coagulation of an aerosol in the free-molecule regime:

, where n is the particle size distribution function, N _∞ is the total number of particles, r is the particle radius, and r_g∞ is the geometric mean particle radius. In terms of the parameters used by the self-preserving size distribution theory, the proposed distribution is written

.