Analytic Solution for Diffusional Filtration across Granular Beds in Low Knudsen Number Regime

Abstract The collection efficiency of aerosols in the low Knudsen number region was studied using a system of multiple spheres. Kuwabara's free vorticity model was expanded to include the effects of gas slip at the collector surface, with the collection efficiency due to diffusion obtained analytically and compared with existing experimental results. The results showed that the diffusional collection efficiency increases as the Knudsen number increases due to gas slippage at the collector surface. The obtained analytical solution converged to the existing collection efficiency of a solid sphere system with a Knudsen number of zero, and that of a bubble with an infinite Knudsen number. The comparison of the experimental results with analytic solution in this study shows that the trends agree well. Therefore, this study is a subsequent expansion of the collection efficiency in the finite Knudsen number region, and can be used for a broad range of collector sizes, pressures and temperatures.