Electrical conductivity in a dilute gas far from equilibrium

Abstract

Electrical conductivity of a minor constituent of charged particles through a background of neutral particles is studied in the limit of small electrical fields. The neutral gas is in a steady state with both arbitrary velocity and temperature gradients. The results are obtained from the Gross-Krook model [Phys. Rev. 102, 593 (1956)] of the Boltzmann equation for a binary mixture. The transport properties of the charged species are obtained from a perturbation expansion in powers of the electrical field. In the first order, the current density obeys a generalized Ohm's law where an electrical conductivity tensor is identified. The nonzero elements of this tensor are nonlinear functions of the shear rate, the mass ratio, and the force constant ratio. The results show that, in general, the presence of the shear produces an inhibition in the diffusion of charged particles.