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Asymptotic theory of the Boltzmann equation at large Knudsen number
Journal article   Peer reviewed

Asymptotic theory of the Boltzmann equation at large Knudsen number

A. L. Cooper and B. B. Hamel
The Physics of fluids (1958), v 16(1), pp 35-42
Jan 1973
DOI: https://doi.org/10.1063/1.1694170

Abstract

A study of an asymptotic theory of hyperthermal flow past a blunt object for large Knudsen number is presented. The greatest demands on such a theory are present for flow past two‐dimensional bodies. This is because the large lateral extent of the emitted molecules in free molecular flow gives rise to a singularity in the integrated collision frequency of the incoming free stream molecules. This singularity is removed by accounting for the effects of collisions upon the emitted molecules which augments the usual geometric free molecular decay. The method of matched asymptotic expansions is applied to regions near the body and far from the body (one mean free path and greater). For two‐dimensional bodies, the surprising result is obtained that the first correction to free molecular flow [Kn−1 ln(Kn)−1] cannot be obtained without explicitly taking into account the collisional effects on the emitted particles in the far region. For three‐dimensional bodies, although there is no problem in the determination of the leading term (Kn−1), the evaluation of the next order term [Kn−2 ln(Kn)−1 involves precisely the same difficulties as the leading term for two‐dimensional bodies.

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