Investigating the Validity of the Knudsen Diffusivity Prescription for Mesoporous and Macroporous Materials

The primary objective of this article is to investigate the validity of the Knudsen prescription for pore diffusivity. Published experimental data on transient permeation of He–Ar, He–N₂, He–CO₂, He–C₃H₈, and CO₂–C₃H₈ mixtures across mesoporous and macroporous membranes are analyzed using the Maxwell-Stefan (M-S) formulation, combining molecule–wall and molecule–molecule interactions. For He–Ar and He–N₂ mixtures, both components are poorly adsorbed within the pores, and the experimental permeation data can be modeled adequately taking M-S diffusivity for molecule–wall interactions, Đ_i = D_i,Kn, the corresponding Knudsen diffusivity. For He–CO₂ and He–C₃H₈ mixture permeation, the equality Đ_i = D_i,Kn holds only for He. For either CO₂ or C₃H₈, Đ_i is lower than D_i,Kn by a factor ranging from 0.55 to 0.98, depending on the species and operating temperature. The stronger the adsorption strength, the lower the ratio Đ_i/D_i,Kn. The observed lowering in the M-S diffusivity below the Knudsen value, D_i,Kn, is in line with the published Molecular Dynamics (MD) data for cylindrical mesopores. The Knudsen prescription is based on the requirement that a molecule experiences diffuse reflection on collision with the pore wall, i.e., the angle of reflection bears no relation to the angle of incidence. Adsorption at the pore wall introduces a bias that makes a molecule hop to a neighboring site on the surface rather than return to the bulk; this bias increases with increasing adsorption strength and has the effect of reducing the pore diffusivity.