Statistical Mechanical Theory of Transport Processes in Liquids

Abstract

The hydrodynamic equations of the transport processes are developed in a form in which the irreversibility appears explicitly in terms of the instantaneous time derivatives of the stresses in a molecular scale nonequilibrium region of a system otherwise at equilibrium. The time derivatives of the stresses are shown to be proportional to the gradients of the properties being transported and to the squares of the transport coefficients. The corresponding time derivatives in the statistical mechanical treatment can be expressed as ensemble averages of molecular interactions using instantaneous values of the molecular pair density functions directly without recourse to time‐smoothing with considerable gain in simplicity. Expressions for the transport coefficients are obtained by comparison of the hydrodynamic and statistical mechanical equations for the time derivatives of the dissipative stresses. The resulting hydrodynamic frictional and self‐diffusion coefficients turn out to be identical to the expressions for these quantities provisionally suggested by Kirkwood, Buff, and Green. Relatively simple expressions are also obtained for the shear and volume viscosity and thermal conductivity coefficients in terms of integrals over space derivatives of the potential energy and the molecular pair density. It is further shown that, if an inter‐molecular potential of the Lennard‐Jones and Devonshire from is assumed, the integrals may be eliminated between these equations and the corresponding statistical mechanical equations for the hydrostatic pressure and the ideal heat of vaporization. This provides simple expressions for the shear vicsosity and the thermal conductivity coefficients directly in terms of the latter equilibrium properties. The numerical values obtained for the above two transport coefficients from evaluation of the integrals in the statistical mechanical equations and from the simple expressions in terms of equilibrium properties, are each in comparatively good agreement with experiment.