Non-Local Rheology of Intermediate Granular Flows

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Author Last Name: 
Karen E. Daniels
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Research Area: 
Powder Flow
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United States


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


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