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The Boltzmann Collision Integrals for a Binary Gas Mixture with a Combination of Maxwellian Distribution Functions

William P. Walters, S. M. Yen

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Abstract

Abstract : If the distribution function, F, is a linear combination of two Maxwellians with distinct temperatures, densities, average velocities, and masses, both the gain and loss terms of the collision integral in the Boltzmann equation can be evaluated analytically. A gas with such a bimodal distribution function is referred to here as a Mott-Smith gas. (Mott-Smith (1951) was the first to use this form of the distribution function to analyze the shock wave structure. (Author)

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Key concepts: Collision, Boltzmann equation, Distribution (mathematics), Distribution function, Maxwell–Boltzmann distribution, Boltzmann constant, Binary number, Function (biology)