Generalized hydrodynamics of a~van der Waals liquid

Yu. V. Gurikov

Teoretičeskaâ i matematičeskaâ fizika, Tome 28 (1976) no. 2, pp. 250-261

Résumé

A statistical theory of viscoelastic relaxation is constructed for a van der Waals liquid whose intermolecular potential contains long-range attraction as well as a hard core. The dynamical processes in the liquid are divided into three groups: 1) slow hydrodynamic processes; 2) moderately fast stochastic processes with characteristic time $\tau_a$, which characterizes smooth variations of the long-range component of the total force acting on a particle in the liquid; 3) rapid processes with characteristic time $\tau_c$ ($\tau_c\ll\tau_a$), which determines the duration of dynamical coupling. Mori's method of projection operators is used to obtain a system of integrodifferentiaI equations with memory for the set of quasiconserved variables (densities of the particle number, energy, momentum, and long-range component of the stress tensor). In the long-wave limit, the equations of generalized hydrodynamics go over into the ordinary continuityl heat conduction, and Navier–Stokes equations. The coefficients of shear and bulk viscosity break up into two terms, one of which is determined by the damping of shortlived correlations and the other by the duration of the relaxation process of the longrange forces.