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Free-Flight Theory of Gas Mixtures

1967; AIP Publishing; Volume: 10; Issue: 7 Linguagem: Inglês

10.1063/1.1762296

2163-4998

L. Monchick, Edward A. Mason,

Advanced Thermodynamics and Statistical Mechanics

A free-flight theory is developed for transport processes in gases and gas mixtures. In the limit of infinitely many free flights, an integral equation is found similar to that given by the Chapman-Enskog second approximation, but the two theories are not equivalent because they obey somewhat different auxiliary conditions. This is interpreted to mean that the free-flight method describes a relaxation process and the Chapman-Enskog method a quasi-steady state. For Maxwellian molecules the free-flight theory is summed to all orders; this allows an estimate of the rate of convergence and demonstrates the close resemblance to the old persistence-of-velocity arguments. With no ad hoc assumptions, the free-flight theory yields a nonzero thermal diffusion effect in first order, which depends for its existence on the variation of the collision frequency with molecular speed. This furnishes the first rigorous elementary explanation of thermal diffusion.