Couette flow for a gas with a discrete velocity distribution

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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.