Viscosity of a classical gas: The rare-collision versus the frequent-collision regime.

Abstract

The shear viscosity η for a dilute classical gas of hard-sphere particles is calculated by solving the Boltzmann kinetic equation in terms of the weakly absorbed plane waves. For the rare-collision regime, the viscosity η as a function of the equilibrium gas parameters-temperature T, particle number density n, particle mass m, and hard-core particle diameter d-is quite different from that of the frequent-collision regime, e.g., from the well-known result of Chapman and Enskog. An important property of the rare-collision regime is the dependence of η on the external ("nonequilibrium") parameter ω, frequency of the sound plane wave, that is absent in the frequent-collision regime at leading order of the corresponding perturbation expansion. A transition from the frequent to the rare-collision regime takes place when the dimensionless parameter nd^{2}(T/m)^{1/2}ω^{-1} goes to zero. The scaled absorption coefficient for sound waves calculated in the rare and frequent-collision regimes is found to be in qualitative agreement with the experimental data.