Nonlinear transport in a dilute binary mixture of mechanically different particles

Abstract

The hierarchy of moments of the Boltzmann equation for a binary mixture of mechanically different Maxwell molecules is exactly solved. The solution corresponds to a nonequilibrium homogeneous steady state generated by an external force that accelerates particles of each species (or “color”) along opposite directions. As a consequence, macroscopic fluxes are induced in spite of the absence of concentration gradients. Explicit expressions for the fluxes of mass and momentum as functions of the field strength, the mass ratio, the molar fractions, and the interaction constant ratio are obtained. In particular, the color conductivity coefficient reduces to the mutual diffusion coefficient in the zero-field limit. Some physically interesting limiting cases are discussed. The maximum-entropy method is used to construct an approximate velocity distribution function from the exact knowledge of the mass and momentum fluxes. This distribution is exact up to second order in the color field and also in the limit of large color field.