Theoretical investigation on submicron particle penetration through circular tubes inside a porous medium

Abstract

The analytical infinite series solution of submicron particle transport in a circular tube bounded by a porous wall, such as a pinhole, is determined under the slip velocity boundary condition, and the solution is verified by using the experimental data in the previous studies for the specific cases. The results show that particle penetration rate increases with the increase of the porous parameter, the axial pressure drop, and the pinhole radius, whereas it decreases with increasing the pinhole length. The penetration rate of nano-particles are more sensitive to the variation of these parameters. However, the differences between the penetrations of particles ranging from 0.3 μm to 1 μm are not evident because the diffusion becomes weak gradually in this size range. In addition, a further comparison is performed between the analytical solution and the existing studies, and approximate expressions are presented for accurate calculation of particle penetration rate through pinholes appearing in porous materials including filter devices and masks.