Accurate modeling of Knudsen diffusion in nanopores using a physical-based boundary model

Abstract

Gas transport in nanopores plays an important role in modern industry, such as shale gas exploitation, sea water desalination, fuel battery, etc. Owing to the small pore size, gas transport in nanopores is dominated by Knudsen diffusion, where the gas molecular motion is fully determined by the gas-surface interaction at the boundary. Classic theories of Knudsen diffusion, such as the “Smoluchowski model” and “extended Smoluchowski model”, were developed based on empirical gas-surface interaction models. These empirical boundary models may not be accurate to capture the key mechanism of Knudsen diffusion, particularly when the surface roughness is small, such as the case of carbon nanotubes. In this work, the influence of the empirical boundary models on Knudsen diffusion is studied in detail. Theoretical analysis indicates that the Knudsen diffusivity in one-dimensional pores critically depends on the correlation between gas molecular scattering angles on the pore surface. Benchmarked by molecular dynamics simulations, empirical boundary models show notable errors in the prediction of the scattering angle correlation, despite the fact that the accurate tangential momentum accommodation coefficient is used. In contrast, the physical-based boundary model, developed recently by our group, can accurately and efficiently reproduce the molecular dynamics simulation results. Its performance is further demonstrated in the modeling of the Knudsen diffusivity in a one-dimensional cylindrical pore, which predicts more accurate results than the Smoluchowski model and extended Smoluchowski model.