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 m_α, m_β total number density n, viscosity μ, and diffusion coefficient D_αβ, it is shown that the classical Chapman‐Enskog theory of mixtures holds when C = 2μ/[(m_α + m_β)nD_αβ] (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.