Theory of the Dynamics of Simple Fluids for Large Spatial Gradients and Long Memory

Abstract

A generalization of the classical fluid dynamics which describes noninstantaneous, nonlocal, and nonlinear responses of flows to the thermodynamic forces (gradients) is derived by statistical-mechanical methods. The conservation equations determining the mass, momentum, and energy densities are unchanged in form, but new expressions are given for the pressure tensor and heat current vector. The new expressions are specified functionals of the temperature, flow velocity, and Helmholtz free energy density, are determined by microscopic quantities (e.g., interparticle potential), and consist of a reversible and an irreversible part. The reversible parts are the expected fluxes in a local-equilibrium ensemble that includes nonlocal effects. The reversible contribution to the heat current is nonvanishing for large enough gradients. The expressions for the irreversible parts are the analog of the classical transport relations, and are linear combinations of integrals over space and time of correlation-function kernels convoluted with the thermodynamic forces. The kernels, which are specified functionals of the fluid densities and are a kind of local-equilibrium correlation of subtracted fluxes, are natural generalizations of the autocorrelation expressions for the classical transport coefficients.