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 [2, 4, 5, 11, 13, 15, 25]. 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 5 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. We have observed that boundary roughness strongly controls both the flow profile
v(r) and shear rate profile _ (r), particularly as measured at the outer wall. This is also the region
of the flow most sensitive to nonlocal effects. Photoelastic techniques provide us full stress profile
of the flow, allowing us to observe that the pressure P and shear stress , measured by photoelastic
techniques, are similarly affected by the roughness and compliance of the wall. Future work will
elucidate the nontrivial connection between these observations, which so far is confounding. Using
data of the type collected here, we will soon be fully able to calculate the fluidity g(r) and the
rheology (I). This will allow us to separately determine constitutive parameters and boundary
conditions for the first time, and address the main Aims.
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