Non-Local Rheology of Intermediate Granular Flows
EXECUTIVE SUMMARY
Currently, there is no first-principles, general theory of intermediate dry granular flow that predicts its rheological response as a function of particle size, shape, and friction (even leaving aside adhesion, which is more challenging still). It is an open question what constitutive equations best describe such flows. Therefore, there is a need for experimental data which tests these theories, and thereby provides an improved understanding of how particle properties control the rheology of granular materials, independent of the flow geometry. Rather than using empirical relations fit to bulk data for a particular flow geometry and particles, we aim to connect grain-scale parameters to macroscale behaviors.
In this initial year of effort, we have focused on testing the Kamrin nonlocal theory [Kamrin and Koval 2012] in experiments. Our apparatus is a modification of a 2D annular shear apparatus capable of providing much better measurements of local boundary forces than has previously been possible, in addition to providing conventional particle-tracking. A key upgrade to the apparatus was the development of a circle of leaf springs as the outer wall. We have calibrated these to provide measurements of both normal and tangential forces at the outer boundary; torque values at the inner boundary are known from an in-line torque sensor. We have run the experiment under continuous shear, allowing us to obtain high-quality measurements of the velocity profile, the internal stress field, and the fluidity field. These experiments were done with a 60-40 mix of circular and elliptical disks at four rotation rates and two packing fractions. We find that there is a single set of parameters (similar to those found by Kamrin) which provide good agreement with the model and do not need to be adjusted in order to cover wide range of shear rates and packing fractions.
By analyzing the positions of the leaf springs, we have successfully observed fluctuations in the boundary forces which arise due to the buckling of force chains. Importantly, this new technique will allow for measuring shear forces even for non-photoelastic particles. We have also installed a polariscope within the apparatus, allowing for future work on internal forces using photoelastic particles.