Transport Far From Equilibrium --- Uniform Shear Flow

TL;DR

This paper uses the BGK kinetic model to analyze states far from equilibrium under uniform shear flow, deriving exact distribution functions, transport coefficients, and studying stability and spectrum of fluctuations.

Contribution

It provides an exact first-order solution for the distribution function and explicit shear-rate-dependent transport coefficients in far-from-equilibrium shear flows.

Findings

Transport coefficients depend explicitly on shear rate.

Spectrum of fluctuations shows qualitative differences from equilibrium.

Conditions for long-wavelength instabilities are identified.

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.