Derivation of momentum and mass transport equations for mixtures using perturbation and projection techniques

Abstract

The kinetic theory of a dilute gas based on the Chapman-Enskog solution of the Boltzmann equation has been the basis of a kinetic description of nonequilibrium transport phenomena in dilute gases. On the basis of this theory, one can derive field equations for nonequilibrium mass, momentum, and heat transport at the macroscopic level, and obtain the temperature dependence of the transport coefficients such as viscosity and heat conductivity. However, the theory is limited. At very low pressures its prediction that for dilute gases transport coefficients are density independent are contradicted by experiments. For moderate to high density gases, the Boltzmann equation is invalid and can not serve as a basis for a description of nonequilibrium behavior.