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, µs), but that we must know the amount of slip at the wall from geometry-dependent mea- surements. 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.
During this first year of the renewal grant, we have observed that boundary roughness strongly controls both the flow profile v(r) and shear rate profile γ˙ (r), particularly as measured at the outer wall. This is also the region of the flow most sensitive to nonlocal effects. We also observed that the pressure P , and therefore the stress ratio µ(r), are affected by the roughness of the wall. All of this is expected, and we can now begin a quantitative understanding of these effects during Year 5. We have done significant development work on photoelastic methods to prepare for these studies. In addition, we continued working on the IFPRI-funded collaboration with Nathalie Vriend.
This resulted in measurements taken at faster flow rates than are accessible in this apparatus (I 1), and resulted in a published paper  that included NCSU authors. Along with our other work during Years 1-3, this paper emphasizes the importance of understanding the timescales over which the force chains fluctuate. In performing the next year’s work, will utilize photoelastic methods (both statics and dynamics) as well as our older particle-tracking methods to meet the three aims.