Granular packing in complex flow geometries

Granular packing is often characterized by a linear relationship between packing fraction phi and dimensionless shear rate. We examine this relationship in simple and complex heterogeneous flow geometries. At high inertial number (I), we observe that the packing fraction depends approximately linearly on I and is seemingly independent of the geometry. However, at low I the packing fraction varies nonlinearly with I and this variation is dependent on the specific geometry and conditions. This response is analogous to the behavior of the stress ratio (mu), where, at low I, mu depends on the geometry of the system, an effect that is often attributed to nonlocal effects of the granular rheology. We demonstrate that, in steady isochoric flow geometries, the phi and mu responses are equivalent and phi may be determined locally from mu, even at low I. However, in a more complex, nonisochoric geometry, such as a pseudo-two-dimensional hopper, this phi(mu) relationship is not recovered in dense regions. We show that during transient startup in a shear cell phi and mu follow a similar response to that seen in these nonisochoric flows. Hence we conclude that the observed discrepancy arises because the hopper is transient in a Lagrangian sense. The simple phi(mu) relationship seen in isochoric flows is insufficient in these more complex systems because of differences in the temporal evolution of the stress and packing fraction.

Automated summary

Granular packing is characterized by a linear relationship between packing fraction and dimensionless shear rate. This relationship is observed in simple and complex heterogeneous flow geometries. However, at low inertia, the relationship becomes nonlinear and dependent on the specific geometry and conditions. The response of packing fraction is analogous to the behavior of stress ratio, suggesting nonlocal effects of granular rheology.