Microscopic equations of motion for a two-component fluid

Abstract

Recently Fröhlich gave a microscopic derivation of the equations of hydrodynamics for a monoatomic fluid. His results are used here to derive the exact and generally valid macroscopic equations of motion for a fluid which is a mixture of two different types of atoms. It is found that the mixture is described by two sets of coupled equations. One set of equations is a slightly modified form of the usual equations of hydrodynamics for the mass flow of the mixture. The second set are new equations; they describe an internal mode of motion where one component of the fluid performs a relative motion with respect to the other component. The symmetry properties of the two-particle correlation densities lead to the presence in the description of a frictional process proportional to the velocity fields, which is absent in a monoatomic fluid where internal friction involves only second spatial derivatives of the velocity field. This new term leads, e.g., to Ohm's law.