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Kinetic theory derivation of the hydro-dynamic equations for a fluid with internal states Thomas, Michael Walter

Abstract

Equations of change for the various hydrodynamic densities are derived for a dilute gas with degenerate internal states. To obtain a consistent set of hydrodynamic equations it is necessary to expand the collision term of the usual Waldmann-Snider Boltzmann equation (W-S equation) in position gradients of the distribution function [formula omitted]. In particular, the extension of the W-S equation to terms "linear" in the position gradients of [formula omitted] yields the correct form for the equation of change for the internal angular momentum density. Specifically, the production term in this equation of change is t he antisymmetric part of the pressure tensor, which is in accord with a hydrodynamic derivation. In addition, equations of change for the mass density, linear momentum density, and total energy density are also obtained. These results are shown to be similar to equations of change derived via a density-operator technique. Unfortunately, this " linear" extension of the W-S equation does not give a closed set of equations of change. However, a consistent set of equations is obtained if a restriction is placed on the form of the extended W-S equation.

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