BGK equation solution of coagulation for large knudsen number aerosols with a singular attractive contact potential

Abstract

Aerosol coagulation rate expressions in the presence of singular attractive contact potentials such as the van der Waals potential and the electrical image potential are obtained by integrating the characteristics of the BGK equation. The rate expression consists of two parts: (A) the free-molecule regime (Kn → ∝) enhancement, and (B) the first-order correction for a finite but large Knudsen number. For situations involving either the van der Waals or image potential, we present closed form best-fit equations for data calculated from the theory. The experimental data of ionic charging of Pui et al. (9) and data on ultrafine particle coagulation rate of Okuyama et al. (10, 11) are compared with the predictions from the present theory and the empirical Fuchs matching method. We have considered the situations of a combined van der Waals, coulombic, and image potential. The conditions where either coulombic, image, or van der Waals forces predominate are determined.