The flow of rarefied gases

Abstract

It has been shown experimentally by Knudsen and others that gases flowing a t decreasing total pressures through small capillaries pass from a region of Poiseuille flow to a so-called slip flow region which contains a flow minimum. Frequently the practice has been followed of approximating this behavior with a linear relationship which, although it gives a fairly good approximation to the actual curve, is incomplete in theory. Some discussion of the use of this equation in the design of vacuum piping and its applicability to flow through porous solids is also given.

Modeling molecular transport in slit pores

“…18 In transport where viscous effects dominate, it has been observed that the transport coefficient generally increases with density, after a small decrease at transition-regime densities. 1,5,6 This increasing trend has also been observed in methane transport in silica mesopores, 16,17 and the results depicted in Fig. 4 are consistent with these findings, in the wider pores.…”

“…In order to permit momentum exchange between the solid and the fluid parallel to the walls, diffuse boundary conditions were applied. 35 Data were obtained by averaging results from runs of length 2ϫ10 6 time steps, each beginning from distinct initial conditions. For each run, averages were collected only after the system had been allowed to relax to equilibrium or the steady state ͑over approximately 40 000 time steps͒.…”

“…3 However, there is a range-the so-called transition region, 3 corresponding approximately to 0.1ϽKnϽ1-where none of the aforementioned models can be applied. 3,4 Other models have been subsequently developed to bridge the transition region, include kinetic theory models that explicitly addressed both wall collisions and intermolecular collisions, 5,6 and solutions to the Boltzmann equation. 7,8 These models were developed for systems where the molecular radius was typically much smaller than the container dimension, and thus where hard-wall ͑and often hardsphere͒ approximations are appropriate.…”

Neon isotope separation by gaseous diffusion transport in the transition flow regime with regular geometries

“…He assumed that the total gas transport in a long capillary is given at all pressures by the addition of (1) G) • EXPERIMENTAL DATA [19].…”

“…The above equation (18), in the same form as equation (10), is (19) If the Lund and Berman equations are considered as differential equations and (AP1/L) + (dP1/dx) and (A~/L) + (dP/dx), then there are only two significant differences between equations (10) and (19). The coefficient of .the second term is smaller for the GCM than for PBM and is the primary source of the differences in the calculated separation efficiencies for the same long capillary.…”