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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.
Item Metadata
Title |
Kinetic theory derivation of the hydro-dynamic equations for a fluid with internal states
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Creator | |
Publisher |
University of British Columbia
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Date Issued |
1969
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Description |
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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Genre | |
Type | |
Language |
eng
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Date Available |
2012-03-28
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Provider |
Vancouver : University of British Columbia Library
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Rights |
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.
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DOI |
10.14288/1.0062421
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URI | |
Degree | |
Program | |
Affiliation | |
Degree Grantor |
University of British Columbia
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Campus | |
Scholarly Level |
Graduate
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Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use.