Inherent Rheology of a Granular Fluid in Uniform Shear Flow

TL;DR

This paper investigates the unique steady-state behavior of granular fluids under shear, revealing their inherently non-Newtonian rheology and the limitations of traditional viscosity measurements.

Contribution

It demonstrates that granular fluids exhibit non-Newtonian rheology in steady shear flow and clarifies the hydrodynamic description using Chapman-Enskog and Grad's methods.

Findings

Granular fluids support steady states with uniform temperature and density.

Shear viscosity depends nonlinearly on shear rate and inelasticity.

Newtonian shear viscosity cannot be obtained from uniform shear flow experiments.

Abstract

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