Pumping mechanism of helical grooved molecular drag pumps

Abstract

The flow on a rotor of a molecular drag pump varies from viscous to slip to free molecule flow according to the decrease in pressure. As the first step, flow through a groove that is facing a wall which is moving along the groove is analyzed. The Navier–Stokes equations are simplified in the viscous and slip flow regimes and can be solved numerically with relative ease. In the free molecule flow regime, drag is caused by the momentum carried to a wall piece by gas molecules colliding with the wall piece, and the drag must be equated to the force exerted by the pressure on the two cross sections sandwiching the wall piece. A weighted linear combination of the two equations for slip and free molecule flows can illustrate the flow through the three flow regimes. The flow in ridges which leads to a leak is treated in a similar way to the flow in grooves. Then, the flows in grooves and ridges are hitherto treated separately and connected by the continuity condition of the mass flow rate normal for the groove-ridge interface. The pressure gradient which is discontinuous at the groove-ridge interface is smoothed by Boon and Tal’s “narrow groove theory” [E. F. Boon and S. E. Tal, Chemie-Ingenieur Technik 31, 202 (1959)]. The theory proposed here satisfactorily predicts the measured pumping performance throughout the three flow regimes including the transition regime from free molecule to slip flows.