Steady shearing flows of deformable, inelastic spheres

Abstract

We extend models for granular flows based on the kinetic theory beyond the critical volume fraction at which a rate-independent contribution to the stresses develops. This involves the incorporation of a measure of the duration of the particle interaction before and after this volume fraction. At volume fractions less than the critical, the stress components contain contributions from momentum exchanged in collisions that are influenced by the particle elasticity. At volume fractions greater than the critical, the stress components contain both static contributions from particle elasticity and dynamic contributions from the momentum transfer associated with the release of elastic energy by the breaking of force chains. A simple expression for the duration of a collision before and after the critical volume fraction permits a smooth transition between the two regimes and predictions for the components of the stress in steady, homogeneous shearing that are in good agreement with the results of numerical simulations. Application of the theory to steady, inhomogeneous flows reproduces the features of such flows seen in numerical simulations and physical experiments.

Microscopic Description of the Granular Fluidity Field in Nonlocal Flow Modeling

“…Even though our formula for g agrees with the functional scaling from kinetic theory, we find, contrary to the kinetic theoretical picture, that the individual forms for pressure and viscosity (Eq 4) are actually not well satisfied in our data beyond Φ = 0.57; see Supplemental Material [37] for additional data comparisons and more discussion relating to models in [39,41,42]. The pressure may collapse better if permitted to depend on additional fields, like gradients of strain-rate, or on particle properties such as stiffness [43]. Since Eq 2 evolves g as a single state variable, it is natural to ask if the observed relation g(δv, Φ) can be reduced to depend on only one state variable rather than two.…”

Stresses and orientational order in shearing flows of granular liquid crystals

“…Building a theory based on first principles for flows of more realistic particles has proved a difficult task. Hence, ad hoc, but physically sound, modifications of classic kinetic theory have been proposed to take into account velocity correlation among the particles at large solid volume fractions [6][7][8][9][10][11][12], particle surface friction [13,14], and finite stiffness [15]. Recently [16,17], discrete element simulations on simple shear flows of cylinders at different solid volume fractions have been performed to study the influence of length-to-diameter (aspect) ratio, coefficient of collisional restitution, surface friction, and stiffness on the stresses, highlighting differences and similarities with the predictions of the kinetic theory for spheres.…”

Virtual Characterization of Dense Granular Flow through a Vertically Rotating Feeding Experiment

“…This leads to the splitting of the stresses into a rate-dependent and a rate-independent term, a common approach also used [6][7][8][9][10]. One main difference between those models and the model of Latz and Schmidt lies in the singularity of the radial distribution function at contact between the model: The rate-independent term diverges in the model of Latz and Schmidt, ensuring numerical stability in the dense regime, whereas it does not diverge in [9,10]. A direct comparison between these different rheological models in the rotating feeding device would be interesting, but is out of the scope of this work.…”

“…Therefore, there is no assumption about microscopic particle behavior like particle shape, particle size distribution, or restitution coefficient. On the other hand, since the model is also correct in the dilute regime, it is possible, but not necessary, to use the kinetic theory for mono disperse granular balls to relate the transport coefficients h 0 , z 0 , l 0 , and e 0 to the particle diameter and restitution coefficient for this specific case via a relation of the form [10]:…”