Knudsen Diffusion in Nanochannels

Measurements on helium and argon gas flow through an array of parallel, linear channels of $12$~nm diameter and $200$~$\rm\mu$m length in a single crystalline silicon membrane reveal a Knudsen diffusion type transport from $10^{\rm 2}$ to $10^{\rm 7}$ in Knudsen number $Kn$. The classic scaling prediction for the transport diffusion coefficient on temperature and mass of diffusing species, $D_{\rm He}\propto \sqrt{T}$ is confirmed over a $T$-range from 40~K to 300~K for He and for the ratio of $D_{\rm He}/D_{\rm Ar} \propto \sqrt{m_{\rm Ar}/m_{\rm He}}$. Deviations of the channels from a cylindrical form, resolved with electron microscopy down to subnanometer scales, quantitatively account for a reduced diffusivity as compared to Knudsen diffusion in ideal tubular channels. The membrane permeation experiments are described over 10 orders of magnitude in $Kn$, encompassing the transition flow regime, by the unified flow model of Beskok and Karniadakis. Simon Gruener and Patrick Huber, Phys. Rev. Lett. 100, 064502 (2008).