Kinetic theory of dense fluids. II. The generalized Chapman-Enskog solution

Abstract

In the second paper of this series we solve the kinetic equation proposed in the previous paper by a method following the spirit of Chapman and Enskog (generalized Chapman-Enskog method). The zeroth-order solution to the kinetic equation leads to the Euler equations in hydrodynamics for real fluids, and the first-order solution to the Navier-Stokes equations for real fluids. General formulas for transport coefficients such as viscosity and heat-conductivity coefficients are obtained for dense fluids, which are given in terms of time-correlation functions of fluxes conjugate to the thermodynamic forces. The results have the same formal structures as the time-correlation functions in linear response theory except for the collision operator appearing in place of the Liouville operator in the evolution operator for the system.