Statistical-Mechanical Theory of Transport in Fluids

A statistical-mechanical theory of transport processes in fluids of $g$ components is presented on the assumption that the macroscopic state of the system can be described by one velocity, one temperature, and $g$ mass-density fields. The formulation is based on the explicit recognition of the fact that there are two relaxation processes in fluids: one is the macroscopic process of attaining spatial uniformity and is represented by the hydrodynamical equations, whereas the other is the microscopic process of attaining internal thermal equilibrium in small mass elements of macroscopic size and determines the transport coefficients. For instance, in dilute gases the microscopic process is the relaxation process in momentum space. The coupling of the two processes is investigated to obtain the dissipative terms in the transport equations with the aid of the correlation function method outlined in a previous paper. The hydrodynamic equations, the equation of entropy balance, and the linear relations between the thermodynamic fluxes and affinities are thus derived with explicit expressions for the coefficients of viscosity, thermal conductivity, and diffusion, which are valid for liquids as well as for gases. The classical limits of these expressions, $\hslash \to 0$, are somewhat different from those obtained by Green for classical mechanical systems.