Coagulation of aerosol particles in the free-molecule regime: regime has been studied theoretically by converting the nr governing partial integrodifferential equation into a set oftwo ordinary differential equations. The approach asNffi (Y7rln2) sumes that the s u e distribution of an aerosol attains or can at least be represented by a time-dependent lognorwhere n is the particle size distribution functi0n, Nm is mal distribution function during the coagulation process. the total number of particles, r is the particle radius, andThe calculations haye been performed and the results rgm is the geometric Itlean particle radius. In the found to be in good agreement with results for previous parameters used by the self-preserving sue distribution theories. In addition, the following asymptotic size distrithe proposed distribution is written bution function is found as an alternative solution for the self-preserving particle size distribution function forBrownian coagulation of an aerosol in the free-molecule ( Y r l n 2 )