Hostname: page-component-cd9895bd7-fscjk Total loading time: 0 Render date: 2024-12-27T14:46:04.790Z Has data issue: false hasContentIssue false
  • English
  • Français

Couette flow for a gas with a discrete velocity distribution

Published online by Cambridge University Press:  11 April 2006

Henri Cabannes
Henri Cabannes
Affiliation:
Université Pierre et Marie Curie, Mécanique Théorique, Tour 66, 4 Place Jussieu 75005, Paris, France
Get access Rights & Permissions [Opens in a new window]

Abstract

We consider a kinetic theory model of a gas, whose molecular velocities are restricted to a set of fourteen given vectors. For this model we study the Couette flow problem, the boundary conditions on the walls being the conditions of pure diffuse reflexion. The kinetic equations can be integrated by quadrature under the assumption that the walls have opposite velocities and equal temperatures. The presence on the walls of tangential velocities leads to the consequence that the velocity slip coefficient does not in general vanish when the Knudsen number goes to zero.

Considering the same problem again after the suppression of tangential velocities, we obtain formulae for the velocity and temperature slip coefficients which generalize results of Broadwell (1964b), and which agree qualitatively with experiments.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 76 , Issue 2 , 28 July 1976 , pp. 273 - 287
Copyright
© 1976 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Broadwell, J. E. 1964a Shock structure in a simple discrete velocity gas. Phys. Fluids, 7, 1243–1247.Google Scholar
Broadwell, J. E. 1964b Study of rarefied shear flow by the discrete velocity method. J. Fluid Mech 19, 401–414.Google Scholar
Cabannes, H. 1975 Etude de la propagation des ondes dans un gaz à quatorze vitesses. J. Méc. 14, 1–40.Google Scholar
Gatignol, R. 1975a Kinetic theory for a discrete velocity gas and application to the shock structure. Phys. Fluids, 18, 153–161.Google Scholar
Gatignol, R. 1975b Théorie cinétique des gaz à répartition discrète de vitesses. In Lecture Notes in Physics, vol. 36, pp. 179–187. Springer.
Hardy, I. & Pomeau, Y. 1972 Thermodynamics and hydrodynamics for a modelled fluid. J. Math. Phys 13, 1042–1051.Google Scholar
Harris, S. 1966 Approach to equilibrium in a moderately dense discrete velocity gas. Phys. Fluids, 9, 1328–1332.Google Scholar