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

## TL;DR

This paper calculates the shear viscosity of a dilute classical gas in both rare- and frequent-collision regimes, revealing different dependencies on gas parameters and external frequency, and identifies the transition between these regimes.

## Contribution

It provides a new analysis of shear viscosity in the rare-collision regime using the Boltzmann equation, highlighting the dependence on external frequency absent in the frequent-collision regime.

## Key findings

- Viscosity differs significantly between the rare- and frequent-collision regimes.
- In the rare-collision regime, viscosity depends on the external frequency of sound waves.
- A transition criterion between the regimes is identified based on a dimensionless parameter.

## Abstract

The shear viscosity $\eta$ 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 $\eta$ 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 $\eta$ on the external ("non-equilibrium") parameter $\omega$, 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 $nd^2 (T/m)^{1/2} \omega^{-1}$ goes to zero.