Controlling Rheology via Boundary Conditions in Dense Granular Flows

EXECUTIVE SUMMARY
In the field of granular rheology, one of the most promising advances of the past decade has
been the development of various nonlocal rheologies [1–7]. These constitutive models hold the
promise of permitting the determination of a small number of empirical parameters for a particular
set of particles, which then can be used to predict flow fields and stresses over a large range of
intermittent, creeping, quasi-static, and intermediate flows. In order for these models to be useful,
the aim is to make a set of flow measurements for a set of particles in one geometry, and then
determine the constitutive parameters for use in predicting flows in other geometries (for the same
particles). Doing this requires a quantitative understanding of which properties are set by both the
particle properties, and the boundary conditions at the walls.
In Years 1-3, we established that NLR successfully models granular flows across different
packing densities, particle sizes and shapes, and shear rates, using just 3 constitutive properties
(A; b; s), but that we must know the amount of slip at the wall from geometry-dependent measurements.
In Years 4-6 of this project, we aim to address current shortcomings in how to calibrate
and apply NLR to real granular systems. We aim to establish that, for a given set of particles,
can we (1) make flow measurements in one geometry which determine the constitutive parameters
and (2) use these parameters to predict flows in other geometries. Thus, our current work focuses
on separating which flow properties are set by the particle properties, versus those set by the wall
properties.
As Year 6 comes to a close, we have used fully-developed experimental protocols to measure
both particle-dynamics and stress fields under controlled conditions for six different-roughness
boundaries. This allowed us to measure the 3 nonlocal constitutive parameters (A; b; s) for a
given set of particles, and test whether they were constant across use under different boundary
conditions. After resolving some issues with sensitivity to changes in humidity, we have found
this to be true. We have further observed that we can associate different amounts of wall slip to
not only the roughness/smoothness of the wall (as expected), but also to the magnitude of force
fluctuations emanating from the outer wall. Finally we have repaired and modified the IFPRIfunded
Behringer hopper for use in future experiments to test these observations in a very different
geometry, where faster flows will be possible.
2