Extending Knudsen theory for gas flow to angstrom-scale channels

Gas transport through angstrom-scale channels plays a pivotal role in both fundamental science and technological applications. However, classical Knudsen theory fails to capture the entrance-induced flux reduction. Molecular simulations and experiments have revealed an anomalous dome-shaped enhancement in smooth angstrom-scale channels, while in rough channels, the gas flux falls below the lower limit predicted by Knudsen theory. These deviations stem from pronounced entrance steric hindrance at molecular scales comparable to the channel dimensions, acting in conjunction with specular reflections within the channel. We extend Knudsen theory by introducing a probabilistic framework that quantifies entrance steric effects. Furthermore, we uncover a strong dependence of the tangential momentum accommodation coefficient, f, on the channel height, particularly at angstrom scale—challenging the prevailing assumption that f is constant for a given wall material and gas. Our model accurately captures the non-monotonic gas flux enhancement and provides a unified description for both smooth and rough channels.