Transition from Free-Molecule to Continuum Flow in an Annulus

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Abstract
Results of precise measurements of the pressure dependence of the flow of gases through annuli of various radius ratio are presented. The data cover a range of Knudsen numbers for about 0.01 to 450. The depth of the Knudsen minimum is found to vary markedly with radius ratio and increases as the radius ratio increases. (Radius ratio is defined as the ratio of inside to outside radii). About 50% of the total change in the depth of the Kundsen minimum occurring between flat plates (radius ratio = 1.0) and capillaries (radius ratio = 0) is effected by a 13% change in radius ratio from 1.0 to 0.8711. Previously observed deviations from classical kinetic theory are verified; and, in particular, in the free-molecule and near free-molecule regimes, the flows are found to be lower than those predicted based on diffuse scattering of gas molecules from the annulus wall. The data are generally found to be in good agreement with flows predicted by the BGK and variational techniques presented by Berman and Maegley [Phys. Fluids 15, 772 (1972)].