Approximation of most penetrating particle size for fibrous filters considering Cunningham slip correction factor

Abstract

In the estimation of the aerosol collection efficiency using fibrous filters, there exist a size range where particles in fibrous collectors penetrate most effectively, and a corresponding minimum collection efficiency. For small particles, for which the diffusion mechanism is dominant, the Cunningham slip correction factor affects the collection efficiency and the most penetrating particle size. Therefore, for the accurate estimation, the Cunningham slip correction factor should be considered. However, many previous studies have ignored the Cunningham slip correction factor because of its complexity and the associated difficulty in deriving appropriate parameterization, especially for the most penetrating particle size. In this study, the analytic expression for the most penetrating particle size and the corresponding expression for the minimum collection efficiency were analytically derived; furthermore, the effects of the Cunningham slip correction factor were determined. To accommodate the slip factor for all particle size ranges, the Cunningham slip correction factor was simplified and modified. The obtained analytic expression for the most penetrating particle size showed a good agreement with the exact solution.