Theory of nonlinear transport processes in a dilute gaseous mixture

Abstract

The modified moment method is applied for studying nonlinear transport processes in a dilute gaseous mixture described by the Boltzmann equation. The method supplies a variational functional which may be regarded as a nonlinear generalization of the Rayleigh–Onsager variational functional for linear irreversible processes. A variational principle is formulated with the variational functional, which yields a set of nonlinear equations for fluxes as the condition for the functional to be an extremum. By solving the set iteratively, we obtain nonlinear constitutive relations and transport coefficients which reduce to their linear counterpart as thermodynamic gradients decrease in magnitude. The Knudsen gas limits of the transport coefficients obtained are also briefly discussed, which show a slightly different behavior from that predicted by the collisionless Boltzmann equation.