Comment on "nonlinear viscosity and Grad's method".

Abstract

In their recent paper [Phys. Rev. E 60, 4052 (1999)] Uribe and García-Colín suggest that the stress tensor associated with the nonlinear viscosity formula eta=eta(0)sinh (-1)kappa/kappa (kappa=a Rayleigh dissipation function) vanishes asymptotically as the magnitude of the velocity gradient increases. In this Comment, it is pointed out that their remark is invalid, because the stress tensor asymptotically exhibits a logarithmic kappa dependence. It is also pointed out that their evolution equations for the stress tensor components are missing the terms containing the velocity gradients in the transversal directions and, as a consequence, give rise to a vanishing shear stress, contrary to the experimental evidence of gas flow in a tube.