Abstract
Considering a granular fluid of inelastic smooth hard spheres, we discuss the conditions delineating the rheological regimes comprising Newtonian, Bagnoldian, shear thinning, and shear thickening behavior. Developing a kinetic theory, valid at finite shear rates and densities around the glass transition density, we predict the viscosity and Bagnold coefficient at practically relevant values of the control parameters. The determination of full flow curves relating the shear stress σ to the shear rate γ[over ˙] and predictions of the yield stress complete our discussion of granular rheology derived from first principles.
Highlights
Predicting and understanding granular flow is desirable for safety and efficiency
At small volume fractions φ ≪ 1 and infinitesimal shear rates γ_ → 0 standard procedures starting from the Boltzmann or Enskog equation predict a Newtonian rheology for granular particles
One of the earliest results of granular physics by Bagnold [21]— commonly referred to as Bagnold scaling—is the observation that granular fluids do not follow a Newtonian rheology, but that the shear stress shows a quadratic dependence on the shear rate, σ 1⁄4 Bγ_2, instead
Summary
Predicting and understanding granular flow is desirable for safety and efficiency. Many geophysical flows from avalanches to landslides involve macroscopic particles and potentially threaten lives all around the planet [1,2]. W. Till Kranz,1,2,* Fabian Frahsa,3 Annette Zippelius,4 Matthias Fuchs,3 and Matthias Sperl1,2 Considering a granular fluid of inelastic smooth hard spheres, we discuss the conditions delineating the rheological regimes comprising Newtonian, Bagnoldian, shear thinning, and shear thickening behavior.
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