Comments on nonlinear viscosity and Grad's moment method

TL;DR

This paper critiques previous steady flow models based on nonlinear viscosity and Grad's moment method, showing their inconsistency with conservation laws and providing an unsteady Boltzmann equation solution for Maxwell molecules.

Contribution

It demonstrates the inconsistency of certain steady flow assumptions with fundamental conservation laws and offers an unsteady solution from the Boltzmann equation for Maxwell molecules.

Findings

Steady unidirectional flow assumptions are inconsistent with conservation laws.

The stationarity assumption is identified as the source of inconsistency.

An unsteady flow solution from the Boltzmann equation is provided.

Abstract

It is shown that the steady unidirectional flow with vanishing heat flux considered by B. C. Eu [Phys. Rev. E 65, 031202 (2002)], and earlier by Uribe and Garcia--Colin [Phys. Rev. E 60, 4052 (1999)], is inconsistent with the exact conservation laws of mass, momentum, and energy. The inconsistency does not lie in the assumed symmetry properties of the flow but in the stationarity assumption. The unsteady problem is considered and its solution from the Boltzmann equation for Maxwell molecules is given.