Transition gas flow in drag pumps and capillary leaks

Abstract

Modern turbomolecular pumps include a drag stage in the exhaust, operating roughly in the pressure range of 10 mTorr–10 Torr. Flow conditions range from molecular flow at the drag inlet, to viscous flow at the outlet, known as ‘‘transition’’ flow. In general, models of transition flow in drag pumps have not been developed. Moreover, the model of a Gaede pump given in journals and textbooks up to the present, gives values of compression ratio that are orders of magnitude too high. In 1913, Gaede proposed a differential equation for transition flow in a drag pump. He did not solve the general equation, and the model was incomplete. We have developed a new model that takes transition flow in a differential element and integrates it over the length of the pump. This model is modified by a ‘‘pumping leak’’ expression for the gas stripper, which separates the inlet from the outlet. The result is compared with experimental measurements, and good agreement is obtained over the entire pressure range from molecular, through transition, and into viscous flow. Up to a critical pressure in viscous flow, compression ratio is constant as a function of exhaust pressure, within a factor of 2. Within this factor, increasing compression arises from the reduced pressure drop across the inlet aperture as its conductance increases in the transition flow regime. Above the critical pressure, compression drops rapidly as laminar backflow increases. This critical pressure is controlled by the dimensions of the channel. Below the critical pressure, compression is determined by the pumping leak, and is somewhat independent of molecular weight. If the surface velocity is zero, the model reduces to a capillary leak. Predictions of our model agree with Knudsen’s data for capillary leaks in transition flow, in addition to giving a better account of the ‘‘conductance minimum.’’ ‘‘Slip flow’’ is not an obvious factor, and it cannot be distinguished from the right combination of viscous and molecular flow.