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MOMENT DESCRIPTION OF GAS MIXTURES--I.

Author
Kolodner, I. I.
Published
United States : [publisher not identified], 1957.
[Oak Ridge, Tennessee] : [U.S. Atomic Energy Commission], 1957.
Physical Description
microopaque : positive ; 8 x 13 cm

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Summary
A 13n moment description of n'ary gas mixtures can be constructed for the Boltzmann Equation using a procedure due to Grad. The densities, flow velocities, specific energies, stress tensors and heat flow vectors of individual components are considered to be fundamental quantities in this description. To achieve a determined set of macroscopic equations, the component velocity distribution function is approximated by means of a product of an exponential and a third degree polynomial which reduces to a Maxwellian distribution when stresses and heat flows are neglected, and otherwise yields the same fundamental 13 moments as the exact distribution function. The resultlng moment equation includes various gas-mixture theories as special cases. On neglecting the spatial dependence (i.e., for local study) one obtains the theory of relaxation times. If stresses and heat flows are neglected and the temperatures are set equal, one obtains the Euler equations and their generalizations. Lastly, if stress, heat flows, temperature differences, and component velocity differences are assumed to be of first order, then it follows that (a) the temperature differences are, in case of uncharged fluids, of second order and thus can be neglected; (b) the stresses, heat flows and diffusional velocity can be expressed in terms of the thermodynamic variables, leading to the Chapman-Enskog theory of material constants and to the reduction of the system to Navier-Stokes equations complemented by a diffusion relation. For a plasma, the temperature differences are of first order, and thus one obtains a description involving individual temperatures of ions and electrons. Collisional terms in the moment equations were evaluated exactly in terms of certaln integrals depending on the type of interaction. The latter were evaluated explicitly for the case of inverse power inter action laws (including elastic sphere model). In the case of charged components, the Coulomb interaction with a cut-off at Debye radius was assumed. For plasma, a marked simplification in the collisional terms is achieved by assuming that the ratio of electron mass to ion mass is small and by dropping terms multiplied by this ratio. (auth)
Report Numbers
NYO-7980
Other Subject(s)
Collection
U.S. Atomic Energy Commission depository collection.
Note
DOE contract number: AT(30-1)-1480
NSA number: NSA-12-008548
OSTI Identifier 4331920
Research organization: New York Univ., New York. Atomic Energy Commission Computing and Applied Mathematics Cennter.
View MARC record | catkey: 41889872