Nonlocal rheology of dense granular flow in annular shear experiments

Abstract

The flow of dense granular materials at low inertial numbers cannot be fully characterized by local rheological models; several nonlocal rheologies have recently been developed to address these shortcomings. To test the efficacy of these models across different packing fractions and shear rates, we perform experiments in a quasi-2D annular shear cell with a fixed outer wall and a rotating inner wall, using photoelastic particles. The apparatus is designed to measure both the stress ratio μ (the ratio of shear to normal stress) and the inertial number I through the use of a torque sensor, laser-cut leaf springs, and particle-tracking. We obtain μ(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 a growing lengthscale at a finite value μs, associated with a frictional yield criterion. Finally, we newly identify the physical mechanism behind this transition at μs by observing that it corresponds to a drop in the susceptibility to force chain fluctuations.

Viewing Earth’s surface as a soft-matter landscape

“…Two primary challenges to rheological descriptions of these particulate systems are: (1) accounting for sub-yield creep, which is ubiquitous in granular materials [29,32,86,88,101,[107][108][109]; and (2) how to correctly couple rheological models to the boundaries. Recently, nonlocal constitutive relations have been proposed that successfully explain the extension of above-yield flow into sub-yield regions for many flow configurations [110][111][112][113]. Such models cannot, however, account for purely subyield creep that occurs even in the absence of any flowing layer [88,101], slip near solid boundaries, the geometry of shear bands [63,114], the transition from inertial to creeping flow [115], or fluidization at distances far from disturbance [107,116].…”

Non-locality in Granular Flow: Phenomenology and Modeling Approaches

“…The diverging of the correlation length, ξ , where µ = µ s has been shown directly in simulations [51,56] and experiments [23], with…”

“…However, slow, creeping flow is seen throughout the entire geometry. The velocity field has an exponential-type decay moving away from the rapid flow zone, with decay length governed by the grain size [20][21][22][23].…”

“…NGF, with its own dedicated numerical solver [68], has been validated in the most geometries and conditions [78]. The NGF and the I−gradient models have each shown quantitative agreement with non-local creep in multiple 2D experiments [23,51,62], capturing proper flow spreading and the emergence of rate-independence. NGF also produces quantitative predictions in 3D cases such as flows in split-bottom cells [56] and wall-bounded heap flows [79].…”

Measurements of the velocity distribution for granular flow in a Couette cell

“…In a Couette geometry, the visco-plastic model predicts the formation of shear bands approximately at the transition between the granular liquid and granular solid [8]. However, experimental observations indicate that the size of the shear bands are largely independent of the shear velocity while visco-plastic rheology models suggest a dependence on shear velocity [9].…”