Granular materials and ordinary fluids react differently to shear stresses. Rather than deforming uniformly, materials such as dry sand or cohesionless powders develop shear bands1,2,3,4,5—narrow zones of large relative particle motion, with essentially rigid adjacent regions. Because shear bands mark areas of flow, material failure and energy dissipation, they are important in many industrial, civil engineering and geophysical processes6. They are also relevant to lubricating fluids confined to ultrathin molecular layers7. However, detailed three-dimensional information on motion within a shear band, including the degree of particle rotation and interparticle slip, is lacking. Similarly, very little is known about how the microstructure of individual grains affects movement in densely packed material5. Here we combine magnetic resonance imaging, X-ray tomography and high-speed-video particle tracking to obtain the local steady-state particle velocity, rotation and packing density for shear flow in a three-dimensional Couette geometry. We find that key characteristics of the granular microstructure determine the shape of the velocity profile.

Signatures of granular microstructure in dense shear flows

Predicting the flow mode from hoppers using the discrete element method

The thickness of the shear zone of flowing granular materials

We measure the flow of granular materials inside a quasi-two-dimensional silo as it drains and compare the data with some existing models. The particles inside the silo are imaged and tracked with unprecedented resolution in both space and time to obtain their velocity and diffusion properties. The data obtained by varying the orifice width and the hopper angle allow us to thoroughly test models of gravity driven flows inside these geometries. All of our measured velocity profiles are smooth and free of the shock-like discontinuities ('rupture zones') predicted by critical state soil mechanics. On the other hand, we find that the simple kinematic model accurately captures the mean velocity profile near the orifice, although it fails to describe the rapid transition to plug flow far away from the orifice. The measured diffusion length b, the only free parameter in the model, is not constant as usually assumed, but increases with both the height above the orifice and the angle of the hopper. We discuss improvements to the model to account for the differences. From our data, we also directly measure the diffusion of the particles and find it to be significantly less than predicted by the void model, which provides the classical microscopic derivation of the kinematic model in terms of diffusing voids in the packing. However, the experimental data are consistent with the recently proposed spot model, based on a simple mechanism for cooperative diffusion. Finally, we discuss the flow rate as a function of the orifice width and hopper angles. We find that the flow rate scales with the orifice size to the power of 1.5, consistent with dimensional analysis. Interestingly, the flow rate increases when the funnel angle is increased.

/pdf/velocity-profile-of-granular-flows-inside-silos-and-hoppers-33cwv1jwmx.pdf

U. Tüzün

Papers

A kinematic model for the flow of granular materials

An investigation of the flow boundary during steady-state discharge from a funnel-flow bunker

Experimental evidence supporting kinematic modelling of the flow of granular media in the absence of air drag