Electrical current density in a sheared dilute gas

Electrical current density of charged particles across a rarefied gas of neutral particles under shear flow is analyzed in the limit of small electric fields. The concentration of the charged species is assumed to be much smaller than that of the neutral species so that the interactions of charged–neutral and neutral–neutral type are the dominant ones. The study is made from the exact Boltzmann equation for Maxwell molecules as well as from a kinetic model for general repulsive interactions. By performing a perturbation expansion around a nonequilibrium state, the current density is explicitly evaluated in the first order of the external field. We get a generalized Ohmʹs law, where an electrical conductivity tensor can be identified. The nonzero elements of this tensor are nonlinear functions of the shear rate, the mass ratio, the force constant ratio, and the interaction parameter.