Highly rarefied gas flow through a right-angled micro-corner

We study the two-dimensional steady flow of a highly rarefied gas through a right-angled corner element. Driven by an external pressure gradient, the free-molecular regime is analyzed for both diffuse and specular reflecting surfaces, and the solutions are validated through comparisons with direct simulation Monte Carlo calculations at finite Knudsen numbers. Imposing the pressure gradient through differences in the densities and temperatures of the gas reservoirs connected to the channel inlet and outlet, the results for the density- and temperature-drop-driven flows are analyzed and contrasted. The characteristic differences between the diffuse- and specular-wall-system flows, indicating sharper flow gradients and higher flow velocities in the latter, are rationalized. Closed-form expressions for the mass flow rate through the corner are derived, indicating a decrease of more than 40% in its mass transfer permeability due to the bend, compared with a straight channel configuration.