Vacuum radial flow from the viscous through the free molecule regime

Abstract

The radial flow of a gas in which transition from viscous to slip to free molecule flow occurs is studied theoretically and experimentally. For the geometric model, radial flow is considered to take place between two uniform circular disks separated by a distance h. First the flow equations are separately derived for the viscous, slip and free molecule regimes ; Maxwell's theory is applied for slip flow and Knudsen's equation employed for free molecule flow. Next, the equations are superposed to obtain an overall equation for the three regimes. Weber's technique, successful for flow in circular tubes, combines the viscous equation with altered expressions for slip and free molecule flow ; this technique is employed here with modifications to account for the radial geometry. In the resulting equation, flow is expressed as throughput in terms of pressure difference, disk geometry and Knudsen Number. This equation features a smooth transition from viscous to free molecule flow and can be used to predict the flow rate for a given set of conditions in any of the three regimes. In addition it applies to situations where several regimes may exist simultaneously along the flow path due to pressure changes in the radial direction.