The log-normal size distribution theory of brownian aerosol coagulation for the entire particle size range: part II—analytical solution using Dahneke’s coagulation kernel

In this study an analytical solution of the Brownian coagulation equation utilizing the method given in Park et al. [(1999) J. Aerosol Sci. 30, 3–16] but using a more detailed coagulation coefficient instead of the simple approach—the harmonic mean—Park et al. [(1999) J. Aerosol Sci. 30, 3–16] is derived. Comparisons are made with the analytical solution given in Park et al. [(1999) J. Aerosol Sci. 30, 3–16], with a method of moments model, with a log-normal reference model as well as with a sectional model (J. Colloid Interface Sci. 139, 63–86). In order to make a fair comparison between the models, all of them should use the same coagulation coefficients except Park et al. [(1999) J. Aerosol Sci. 30, 3–16] which is already fixed to the harmonic mean method. The most frequently used coagulation coefficients to describe the process of Brownian coagulation in the entire size regime (Fuchs, Dahneke, harmonic mean) were compared and a universal enhancement function to the near-continuum coagulation kernel is given. Furthermore, Fuchs’ coagulation kernel is reviewed and modified for the use with different sized particles. It was shown that Dahneke’s coagulation kernel is very close to those of Fuchs and Wright with a relative error of less than 1%. Based on this finding, Dahneke’s coagulation kernel is used in the models developed as well as during the comparison. In order to develop fast and easy-to-use coagulation models we used the moment method assuming a log-normal size distribution function [J. Colloid Interface Sci. 188, 486–492]. In the first step the integrals over the particle size distribution are solved analytically and DGEAR (KcoN0t=1.