Rarefaction throttling effect: Influence of the bend in micro-channel gaseous flow

Micro-bends are frequently encountered in micro-electro-mechanical systems as a basic unit of complex geometry. It is essential for a deep understanding of the rarefied gas flow through bent channels. In this paper, a two-dimensional pressure-driven gas flow in a micro-channel with two bends is investigated by solving the Bhatnagar-Gross-Krook kinetic equation via the discrete velocity method in the slip and transition flow regimes. The results show that the mass flow rate (MFR) through the bent channel is slightly higher than that in the straight channel in the slip flow regime but drops significantly as the Knudsen number increases further. It is demonstrated that the increase in MFR is not due to the rarefaction effect but due to the increase in cross section of the bent corners. As the rarefaction effect becomes more prominent, the low-velocity zones at the corners expand and the gas flow is "squeezed" into the inner corner. The narrowed flow section is similar to the throttling effect caused by the valve, and both the changes in MFRs and the pressure distribution also confirm this effect. The classical Knudsen minimum changes due to this "rarefaction throttling effect." The Knudsen number at which the minimum MFR occurs gradually increases with the bend angle and finally disappears in the transition flow regime. In addition, the onset of rarefaction throttling effect shifts to a smaller Knudsen number with a lower tangential momentum accommodation coefficient.