Fluidity, anisotropy, and velocity correlations in frictionless, collisional grain flows

We show that the fluidity, made dimensionless by the square root of the granular temperature, measured in numerical simulations of granular shearing flows of frictionless spheres, may be predicted over a wide range of volume fractions using existing kinetic theories. We also show that the departure of these predictions from the measurements in the limit of random close packing is due to the reduction of the dissipation because of velocity correlations and the contribution of the anisotropy of the second moment of the velocity fluctuations to the shear stress. The former causes the granular temperature to increase without bound, the latter ensures that the pressure and shear stress behave in the same way with temperature. This combination of mechanisms may also be relevant to the shearing of emulsions, dense colloids, and non-Brownian suspensions.

Figure 1

Dimensionless fluidity as a function of the solid volume fraction in steady, homogeneous shearing flows of frictionless spheres with a coefficient of normal restitution equal to 0.7: measurements in event-driven (circles, [17]) and soft-sphere (squares, [18]; triangles, [19]) molecular dynamics simulations, predictions of kinetic theory at the isotropic Navier-Stokes order (dashed line, [20]), and the anisotropic higher-order kinetic theory (solid line, [16]).

Figure 2

Measured (symbols, [17, 18]) and predicted [lines, Eqs. (15) and (16)] dimensionless fluidity as a function of the solid volume fraction in steady, homogeneous shearing flows of frictionless spheres with coefficient of collisional restitution equal to 0.7 (circles and solid line), 0.8 (squares and dashed line), 0.9 (diamonds and dot-dashed line), and 0.95 (triangles and dotted line).