Frequency-Dependent Transport Coefficients in Fluid Mechanics

Abstract

Exact time‐correlation formulas for frequency‐dependent shear viscosity, bulk viscosity, and thermal conductivity are presented. These formulas are evaluated for a fluid composed of molecules with internal degrees of freedom, in the limit of very weak coupling of internal and translational motions. In this limit, the shear viscosity is unaffected by internal modes. The bulk viscosity consists of two parts, one due to translational motions, and the other due to relaxation of the energy contained in internal modes. The thermal conductivity consists of two parts, one due to translational motions, and the other due to diffusion of energy in internal modes (the Eucken correction). The resulting excess sound absorption is in complete agreement with the predictions of the thermodynamic theory of relaxation in fluids.