Change of particle size distribution during Brownian coagulation

Abstract Change in particle size distribution due to Brownian coagulation in the continuum regime has been studied analytically. A simple analytic solution for the size distribution of an initially lognormal distribution is obtained based on the assumption that the size distribution during the coagulation process attains or can, at least, be represented by a time-dependent lognormal function. The results are found to be in a form that corrects Smoluchowski's solution for both polydispersity and size-dependent kernel. It is further shown that regardless of whether the initial distribution is narrow or broad, the spread of the distribution is characterized by approaching a fixed value of the geometric standard deviation. This result has been compared with the self-preserving distribution obtained by similarity theory.