Nonlocal Rheology of Grannular 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.
Through the three years of this project, we have have conducted laboratory testing of one
nonlocal theory [cooperative model, Kamrin and Koval 2012], and added a comparison to a second
model [gradient model, Bouzid et al. 2013]. To validate the efficacy of these two models across
different packing fractions, shear rates, and particle properties, we performed experiments in a
quasi-2D annular shear cell with a fixed outer wall and a rotating inner wall, including using
photoelastic particles.
The apparatus is designed to measure both the stress ratio (the ratio of shear to normal stress)
and the inertial number I through the use of a torque sensor, laser-cut leaf springs, and particletracking.
We obtain (I) curves for several different packing fractions and rotation rates, and
successfully find that a single set of model parameters is able to capture the full range of data
collected once we account for frictional drag with the bottom plate. Our measurements confirm
the prediction that there is growing lengthscale at a finite value s, associated with a frictional
yield criterion. Finally, we newly identify the physical mechanism behind this transition at s by
observing that it corresponds to a drop in the susceptibility to force chain fluctuations.
We have successfully performed experiments to test how the particle properties affect the model
parameters, using particles of three different shapes (circles, ellipses, and pentagons), materials
with three different elastic moduli, and small range of particle sizes. We have observed that the
shape of the interparticle contacts (rounded vs. angular) is an important control on s, separate
from material properties such as the coefficient of friction or elastic modulus. We observe that
while the local rheological parameter is largely independent of particle-shape, the nonlocal parameter
depends on both the particle shape and material.