Heat and momentum transport in a multicomponent mixture far from equilibrium

Abstract

Explicit expressions for the heat and momentum fluxes are given for a low-density multicomponent mixture in a steady state with temperature and velocity gradients. The results are obtained from a formally exact solution of the Gross-Krook model [Phys. Rev. {\bf 102}, 593 (1956)] of the Boltzmann equation for a multicomponent mixture. The transport coefficients (shear viscosity, viscometric functions, thermal conductivity and a cross coefficient measuring the heat flux orthogonal to the thermal gradient) are nonlinear functions of the velocity and temperature gradients and the parameters of the mixture (particle masses, concentrations, and force constants). The description applies for conditions arbitrarily far from equilibrium and is not restricted to any range of mass ratios, molar fractions and/or size ratios. The results show that, in general, the presence of the shear flow produces an inhibition in the transport of momentum and energy with respect to that of the Navier-Stokes regime. In the particular case of particles mechanically equivalent and in the tracer limit, previous results are recovered.