Statistical theory of viscoelastic properties of fluids

Mori's method of projection operators is used to derive equations for the mass density, momentum density, and momentum-current density. By means of Bogolyubov's condition of correlation weakening, averaged equations (in the linear approximation in the amplitude deviations from equilibrium) of causal-retarded nature are obtained. Unlike the previously known equations, space and time dispersiou are taken into account in these equations completely. Symmetry relations are established for the transport coefficients. It is shown that if space and time dispersion are ignored, the equations go over into the usual Maxwell theologic equations for the stress-tensor deviator and the relaxation pressure. Rigorous microscopic expressions are obtained for the times of shear relaxation and pressure relaxation; these differ from the ones found previously by nonrigorous application of the Chapman–Enskog procedure for the elimination of the time derivatives. Rigorous microscopic expressions are also obtained for the shear and bulk moduli of viscous fluids.