Heat and momentum transport in a multicomponent mixture far from equilibrium

TL;DR

This paper derives explicit, nonlinear expressions for heat and momentum fluxes in a multicomponent gas mixture far from equilibrium, using the Gross-Krook model, revealing how shear flow influences transport properties.

Contribution

It provides the first exact analytical solutions for transport coefficients in multicomponent mixtures under far-from-equilibrium conditions.

Findings

Transport coefficients are nonlinear functions of gradients and mixture parameters.

Shear flow inhibits momentum and energy transport compared to Navier-Stokes predictions.

Results recover known solutions in the case of identical particles and tracer limit.

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.