A moment method of the log-normal size distribution with the critical size limit in the free-molecular regime

The present work proposes new formulations of the moment in the free-molecular size regime involving (1) boundary equations at the critical size for evaporation, condensation, and nucleation, and (2) b coefficient functions for coagulation that are improved by two parameters (standard deviation and nondimensional critical size). Using these formulations based on the error function, the critical particle size is readily introduced into the log-normal moment method for applications in general aerosol dynamics. In the situation that the particle size distribution is located near the critical size, the proposed moment method (which considers the critical size limit) improves predictions of total particle number and particle volume concentrations as compared with previously well-used log-normal moment methods for sizes ranging from 0 to ∞. However, as the size distribution approaches to the continuum size regime, the influence of the critical size becomes smaller. Thus, the new formulations are expected to improve microphysical parameterization in the free-molecular regime in aerosol-transport models.