Internal Rarefied Gas Flows with Backscattering

Abstract

A modification of the boundary condition describing the interaction between a gas molecule and a wall is proposed for use in the calculation of internal rarefied gas flows. The effect of the altered boundary condition on a number of flows of interest is calculated. In several cases, for which experimental data are available, comparison is made between predicted and measured transport. It is found that significant improvement in the predicted transport results from the suggested boundary condition modification.

Hydrodynamic force measurements under precisely controlled conditions: Correlation of slip parameters with the mean free path

“…(4), the parameter may take values between 0 and 2, with the upper limit indicating perfect back-reflection. These authors 41,65 (as well as others 25,34 ), found good agreement with experimental data for α > 1, in particular on rough surfaces. However, the values α 2 > 1.4 seen in Table III for Kr, CO 2 , and C 2 H 6 seem rather (and possibly too) high.…”

“…For α > 1 (a rare case), a fraction of the molecules is back-reflected with inversion of the lateral and normal momenta. 41 …”

“…In this respect, Berman and Maegley 41 have suggested to include back-scattering in the velocity distribution function entering the calculation of friction forces, which leads to a modified TMAC. Translated into a form of α that is applicable in Eq.…”

Influence of surface phenomena on free-molecule gas flow in fine channels

“…In this model it is supposed that a fraction of molecules f is scattered according to the cosine law and a fraction 1 − f is scattered in the direction opposite to the velocity of incident molecules. In the backscattering model w ¼ f 2Àf [8]. At first, let us consider the diffuse-specular scattering model.…”

“…It is worth noting that for rough surfaces the backscattering model is used [8]. In this model it is supposed that a fraction of molecules f is scattered according to the cosine law and a fraction 1 − f is scattered in the direction opposite to the velocity of incident molecules.…”