The flow of rarefied gases through long tubes of circular cross‐section

Abstract

A brief review is presented of various models of rarefied gas flow in long tubes. The complex treatments based on the Boltzmann equation provide only numerical solutions for the transition region unless pome arbitrary assumptions are made, while thosc based on the traditional approach of simple kinetic theory have usually involved empiricism to a greater or lesser extent. An analytic expression is derived here based on a physically realistic model, making use of simple kinetic theory and containing no arbitrary assumptions. The model is completely predictive and adequately describes the flow in long tubes over the entire pressure range, from free-molecule to continuuni laminar flow, and also predicts the "Knudsen minimum" in the transition region. The concept of a "geometric mean free path" is introdiiced and appears to be useful in analyzing rarefied gas dynamics in a confined space. A relation is also obtained for the viscositv coefficient in the transition region.

An alternative procedure for modeling of Knudsen flow and surface diffusion

“…The direction in which a molecule is leaving the wall is completely independent of the incident one. [19], and [20] give good reviews of the Knudsen flow. It is also noted that the cosine law can be accepted as a correct basis for the evaluation of rarefied gas flow in both simple and complex vacuum systems as well as related fields [19].…”

Multiscale models of sweep gas and porous support effects on zeolite membranes

“…Flow of a single component fluid through such a support can be described as a combination of Knudsen and viscous flow. Knudsen flow, which occurs in the limit where the mean free path is much larger than the pore diameter, λ ≫ 2 r p , gives a molecular flux N k of46, 47 Here, P is the pressure, s is the direction of the flow through the tube, R is the gas constant, and T is temperature. The Knudsen diffusivity D k for a species with molecular weight MW is …”

“…There is a large body of work that has explored various means to describe the transition between Eqs. 7 and 9 46‐53. We have used a description developed by Datta and Rinker that gives accurate predictions for gas flow over a wide range of pressures and pore widths 46.…”

“…7 and 9 46‐53. We have used a description developed by Datta and Rinker that gives accurate predictions for gas flow over a wide range of pressures and pore widths 46. With this description, the molecular flux is expressed by with Here, ϕ K is the fraction of molecules that does not experience any intramolecular collisions between two successive collisions with the wall and Φ is the ratio of the transition viscosity to the continuum viscosity.…”