Transport Equations for a Gas Mixture

The Boltzmann equation is applied to a gas mixture in which each constituent is separately in equilibrium without necessarily being close to equilibrium with the rest of the gas. Exact conservation equations for the number density, momentum, and energy of each constituent in the mixture are derived for inverse power interparticle force laws. In the limit when the differences among the individual flow velocities, us — ut, are all small compared to a ``sound speed'' a0 = (2k)½[(Ts/ms) + (Tt/mt)]½, it is found that the conservation equations reduce, for all force laws, to a form similar (but not identical) to the continuum equations commonly used in plasma physics. For larger relative flow velocities, the equations retain this simple form only for Maxwell molecules. For other inverse power laws all the collisional transfer terms increase relative to the Maxwell molecule results with increasing a0 or |ut — us| for shorter-range forces (hard spheres, for example) and decrease with increasing a0 or |ut — us| for longer-range forces (Coulomb, for example). Finally, in the limit when a0 is small compared to |ut — us| it is shown that, with one exception, all collisional transfer terms become temperature independent.