Knudsen Diffusivity of a Hard Sphere in a Rough Slit Pore

An analytic theory for the Knudsen self-diffusivity $D_s$ of hard spheres in an atomically rough slit-shaped pore is presented which quantitatively matches simulation results. The theory assumes that, due to chaotic molecular trajectories caused by surface morphology, collisions of gas molecules with the wall are partly diffuse and partly specular, the relative magnitude of each depending upon the magnitude of the tangential momentum accommodation coefficient $f$. The theory thus represents a universal Knudsen fluctuation-dissipation correlation between longitudinal momentum loss and diffusivity that can simplify efforts to estimate $D_s$. It is also found that $D_s$ computed using Maxwell’s theory of slip, in which collisions with the walls are assumed to be purely diffuse or specular, overpredicts the simulated $D_s$ by a large margin.