Annular shear of cohesionless granular materials: From the inertial to quasistatic regime

Abstract

Using discrete simulations, we investigate the behavior of a model granular material within an annular shear cell. Specifically, two-dimensional assemblies of disks are placed between two circular walls, the inner one rotating with prescribed angular velocity, while the outer one may expand or shrink and maintains a constant radial pressure. Focusing on steady state flows, we delineate in parameter space the range of applicability of the recently introduced constitutive laws for sheared granular materials (based on the inertial number). We discuss the two origins of the stronger strain rates observed near the inner boundary, the vicinity of the wall and the heteregeneous stress field in a Couette cell. Above a certain velocity, an inertial region develops near the inner wall, to which the known constitutive laws apply, with suitable corrections due to wall slip, for small enough stress gradients. Away from the inner wall, slow, apparently unbounded creep takes place in the nominally solid material, although its density and shear to normal stress ratio are on the jammed side of the critical values. In addition to rheological characterizations, our simulations provide microscopic information on the contact network and velocity fluctuations that is potentially useful to assess theoretical approaches.

What is fluidity? Designing an experimental system to probe stress and velocity fluctuations in flowing suspensions

“…In Figure 4A, we plot the velocity profiles of the PAAm suspen-sion, showing that the shear band widens as we increase the driving rate of the inner cylinder Ω i , as expected and similar to the findings in Ref. [13,14]. For the gelatin suspension ( Figure 4C), the shear is much more localized; particles in the outer half of the gap show very little movement, even at the highest rates applied.…”

A finite element implementation of the nonlocal granular rheology

“…The stress at a point is no longer given through local constitutive equations involving strain, strain rate, or locally-evolved state variables. As a consequence, flows involving these materials display finite-size effects, in which the ratio of the characteristic size of the flow configuration to the particle size has an important impact on the observed flow fields [1,5,6,7]. This is evidence that the aforementioned size-independent constitutive relations are insufficient for describing inhomogeneous flows, and developing nonlocal, continuum-level constitutive equations has posed a substantial challenge in engineering and condensed matter physics.…”

Local rheological measurements in the granular flow around an intruder

“…This rheology works quite well by rescaling various experimental and numerical data into a consistent picture for parallel flows -such as Couette flows or flows down inclines -or weakly non parallel flows in a wide range of flow rates [1,3,4]. Nevertheless, this local description falls short of describing non-parallel flows where the streamlines are far from parallel and also quasi-static regimes close to the "liquid-solid" transition [5]. Nonlocal effects, where the stress not only depends on the strain rate but also on its spatial variations, have been recently reported both experimentally and numerically [6][7][8].…”