Solving the inverse Knudsen problem: Gas diffusion in random fibrous media

About a century ago, Knudsen derived the groundbreaking theory of gas diffusion through straight pipes and holes, which since then found widespread application in innumerable fields science inspired development vacuum related coating technologies, from academic research to numerous industrial sectors. Knudsen's can be straightforwardly applied filter membranes with arrays extended holes for example, however, inverse geometry arrangement, arises when solid nanowires or fibers are arranged into porous interwoven material (like carpets brushes) derivation an analytical framework was still missing. In this paper, we have identified specific geometric thermodynamic parameters that determine kinetics randomly oriented cylinders provide set expressions allowing comprehensively describe transport such structures. We confirmed solutions by Monte Carlo simulations. specify our findings atomic layer deposition process, trimethyaluminium molecules carbon nanotube array, but highlight applicability other comprising membranes, composite materials, fuel cells more.