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 measurements. During Years 4-7, we extended these measurements to compare which flow properties are set by the particle properties, versus by the wall properties. We performed experiments in both the original annular rheometer, as well as in a vertical hopper, using six different boundary conditions. We found that the roughness and compliance of the boundary strongly controls the amount of wall slip. Nonetheless, we find that we can successfully capture the full flow profile using a single set of empirically determined model parameters, with only the wall slip velocity set by direct observation. Through the use of photoelastic particles, we observed how the internal stresses fluctuate more for rougher boundaries, corresponding to lower wall slip, and connected this observation to the propagation of nonlocal effects originating at the wall. Our measurements indicate a universal relationship between dimensionless fluidity and velocity. The measurements in the annular rheometer are echoed by less-quantitative measurements performed in the vertical hopper. These results have been published in one paper  and one preprint . Two graduate students received their PhDs, and one undergraduate gained research experience.
Three IFPRI collaborations have been supported during this seven year period, with Nathalie Vriend, Karen Hapgood, Prahbu Nott and their research groups. With Vriend, we extended our efforts into a chute flow which provided us data at higher inertial number than was possible in the annular rheometer. We defined a quantitative measure for the rate of generation of new force chains and found that fluctuations extend below the boundary between dense flow and quasi-static layers, as well as evaluating several existing definitions for granular fluidity . With Hapgood, we performed stress visualization within 3d printed particles with realistic shapes, using photoelasticity. We characterized the importance of controlling the relative orientation of the print layers and the loading force, and observed that semi-quantitative measurement of internal stresses is possible, with some caveats . With Nott, we performed laboratory tests of an additional nonlocal model  that incorporates dilatancy as a model variable, and found good agreement. This effort is ongoing, and will continue into the remaining years of his project. More details are provided in IFPRI ARR-106-03.