Derivation of aerosol collision rates for singular attractive contact potentials

Abstract

A rigorous derivation is given of the collision rate for spherical aerosol particles in the free‐molecular regime interacting via an attractive potential which diverges at particle contact. The Lifshitz–van der Waals and electrical image potentials are two examples of such particle interactions that play important roles in aerosol dynamics. The method employed in the derivation of this extended free‐molecular collision rate is then used to derive an expression for transition regime collision rates by means of Fuchs’ method. This is the first time that the influence of a particle interaction potential upon the collision rate has been incorporated into the Fuchs formula. Results of computations employing the extended free‐molecular formula derived here are compared with published data and the computations used in their interpretation. By utilizing the same interaction potentials as in those interpretative computations, the corrected free‐molecular formula is shown to improve the data fits.