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.