An Approximate Analytical Solution for the Knudsen Number-Dependent Self-Preserving Size Distributions of Coagulating Fine Particles in the Transition Regime

Abstract

An approximate analytical solution for the size distribution width of fine particles coagulating in the transition regime is derived. It is assumed that the particle size distribution can be represented by a time-dependent log-normal function, which passes through a series of quasi-self-preserving states. The solution extends a previous solution presented for the near-continuum regime to cover the whole transition regime by adopting Dahneke’s collision kernel based on the flux-matching theory. Good agreement was obtained when the new solution was compared to numerical calculations. The effective degree of homogeneity of collision kernel is defined and used for a comprehensive analysis of the Knudsen number-dependent behavior of the quasi-self-preserving size distributions. Although the new solution is valid for the whole particle size range from the free-molecule regime (Knudsen number larger than ~50) through the transition regime (Knudsen number between ~1 and ~50) to the continuum regime (Knudsen number smaller than ~1), it is practically applicable in the transition regime because the self-preserving behavior in the continuum regime or in the free-molecule regime had previously been investigated and understood well.