Nearly Free-Molecular Channel Flow at Finite Pressure Ratio

Abstract

The problem of nearly free-molecular flow of a gas from one reservoir to another through a two-dimensional channel is studied. The width of the channel is much smaller than the length which is of the order of the mean free path of the gas. The ratio of the equilibrium pressures in the reservoirs is finite, whereas the equilibrium temperatures are the same. The fundamental solution of the linear Boltzmann equation is used for the evaluation of total mass flow rate. The result is presented in the form of an asymptotic series, of which the first-order terms are of the order of α ln α and α, where α is the inverse Knudsen number. Computations shows that the first-order terms, which represent intermolecular collisions in the counter flows, have a net negative value. The total mass flow rapidly decreases as the length of the channel increases.