Equations for Gas Mixtures

Abstract

Starting with the exact Boltzmann equations for gas mixtures with arbitrary intermolecular potentials, a macroscopic theory of mixtures is obtained. For a binary gas with masses mα, mβ total number density n, viscosity μ, and diffusion coefficient Dαβ, it is shown that the classical Chapman-Enskog theory of mixtures holds when C = 2μ/[(mα + mβ)nDαβ] (which is related to the Schmidt number) is near unity. This criterion delimits the region of validity of the Chapman-Enskog equations. For situations outside the Chapman-Enskog range a new system of equations, referred to as the two-temperature theory, is shown to be valid. The latter includes a new diffusion effect which involves temperature differences. The temperature difference in the Chapman-Enskog regime which becomes higher order is also explicitly obtained. For problems widely removed from equilibrium a two-fluid theory is advanced. The last has the Chapman-Enskog and two-temperature theories as limiting forms in near equilibrium situations. A heat flow problem illustrating the new equations is discussed.