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

In the estimation of the aerosol single fiber efficiency using fibrous filters, there is a size range, where the particles penetrate most effectively through the fibrous collectors, and corresponding minimum single fiber efficiency. For small particles in which the diffusion mechanism is dominant, the Cunningham slip correction factor (C_c) affects the single fiber efficiency and the most penetrating particle size (MPPS). Therefore, for accurate estimation, C_c is essential to be considered. However, many previous studies have neglected this factor because of its complexity and the associated difficulty in deriving the appropriate parameterization particularly for the MPPS. In this study, the expression for the MPPS, and the corresponding expression for the minimum single fiber efficiency are analytically derived, and the effects of C_c are determined. In order to accommodate the slip factor for all particle-size ranges, C_c is simplified and modified. Overall, the obtained analytical expression for the MPPS is in a good agreement with the exact solution.