Highly rarefied gas flows in rough channels of finite length

Abstract

Highly rarefied gas flows through a rough channel of finite length with small bumps appended to its surfaces are investigated, by varying the accommodation coefficient $$\alpha$$ in Maxwell’s diffuse-specular boundary condition, the characteristic size and position of the bumps, and the channel length. First, we study the influence of the surface bumps and consider the rarefied gas flow in a unit channel with periodic boundary conditions to remove the end effect. It is found that the surface bumps have a significant impact on the flow permeability. When $$\alpha$$ is very small (i.e., nearly specular reflection of gas molecules at the channel surface), the apparent gas permeability is dramatically reduced, even in the presence of small bumps, to a value that is almost comparable to the one when fully diffuse gas-surface scattering is assumed. This impact can be taken into account through an effective accommodation coefficient, i.e., the permeability of the rough channel is taken equivalently as that of a smooth channel without bumps but having gas-surface scattering under the effective accommodation coefficient. Second, we study the end effect by connecting a smooth channel of length $$L_0$$ to two huge gas reservoirs. It is found that (i) the end correction length is large at small $$\alpha$$ . Consequently, the mass flow rate barely reduces with increasing $$L_0$$ rather than scales down by a factor of $$1/L_0$$ as predicted by the classical Knudsen diffusion theory; and (ii) the end correction is related to the channel’s aspect ratio. Finally, based on the effective accommodation coefficient and end correction, we explain the exotic flow enhancement in graphene angstrom-scale channels observed by Geim’s research group (Keerthi et al, Nature 558:420–424, 2018).