Inherent rheology of a granular fluid in uniform shear flow

In contrast to normal fluids, a granular fluid under shear supports a steady state with uniform temperature and density since the collisional cooling can compensate locally for viscous heating. It is shown that the hydrodynamic description of this steady state is inherently non-Newtonian. As a consequence, the Newtonian shear viscosity cannot be determined from experiments or simulation of uniform shear flow. For a given degree of inelasticity, the complete nonlinear dependence of the shear viscosity on the shear rate requires the analysis of the unsteady hydrodynamic behavior. The relationship to the Chapman-Enskog method to derive hydrodynamics is clarified using an approximate Grad's solution of the Boltzmann kinetic equation.