Transport far from equilibrium: Uniform shear flow

Abstract

The BGK model kinetic equation is applied to spatially inhomogeneous states near steady uniform shear flow. The shear rate of the reference steady state can be large so the states considered include those very far from equilibrium. The single particle distribution function is calculated exactly to first order in the deviations of the hydrodynamic field gradients from their values in the reference state. The corresponding non-linear hydrodynamic equaitons are obtained and the set of transport coefficients are identified as explicit functions of the shear rate. The spectrum of the linear hydrodynamic equation is studied in detail and qualitative differences from the spectrum for equilibrium fluctuations are discussed. Conditions for instabilities at long wavelengths are identified and disccused.