Fourier's Law for a Granular Fluid

Newton’ viscosity law for the momentum flux and Fourier’s law for the heat flux define Navier-Stokes hydrodynamics for a simple, one component fluid. There is ample evidence that a hydrodynamic description applies as well to a mesoscopic granular fluid with the same form for Newton’s viscosity law. However, theory predicts a qualitative difference for Fourier’s law with an additional contribution from density gradients even at uniform temperature. The reasons for the absence of such terms for normal fluids are indicated, and a related microscopic explanation for their existence in granular fluids is presented.