Propagating Waves in a Monolayer of Gas-Fluidized Rods

We report on an observation of propagating compression waves in a quasi-two-dimensional monolayer of apolar granular rods fluidized by an upflow of air. The collective wave speed is an order of magnitude faster than the speed of the particles. This gives rise to anomalously large number fluctuations dN ~ $N^{0.72 \pm 0.04}$, which are greater than ordinary number fluctuations of N^{1/2}. We characterize the waves by calculating the spatiotemporal power spectrum of the density. The position of observed peaks, as a function of frequency w and wavevector k, yields a linear dispersion relationship in the long-time, long-wavelength limit and a wavespeed c = w/k. Repeating this analysis for systems at different densities and air speeds, we observe a linear increase in the wavespeed with increasing packing fraction with no dependence on the airflow. Although air-fluidized rods self-propel individually or in dilute collections, the parallel and perpendicular root-mean-square speeds of the rods indicate that they no longer self-propel when propagating waves are present. Based on this mutual exclusivity, we map out the phase behavior for the existence of waves vs self-propulsion as a function of density and fluidizing airflow

Flow-induced Agitations Create a Granular Fluid

We fluidize a granular medium through localized stirring and probe the mechanical response of quiescent regions far away from the main flow. In these regions the material behaves like a liquid: high-density probes sink, low-density probes float at the depth given by Archimedes' law, and drag forces on moving probes scale linearly with the velocity. The fluid-like character of the material is set by agitations generated in the stirred region, suggesting a non-local rheology: the relation between applied stress and observed strain rate in one location depends on the strain rate in another location

Solid-fluid transition in a granular shear flow

The rheology of a granular shear flow is studied in a quasi-2d rotating cylinder. Measurements are carried out near the midpoint along the length of the surface flowing layer where the flow is steady and non-accelerating. Streakline photography and image analysis are used to obtain particle velocities and positions. Different particle sizes and rotational speeds are considered. We find a sharp transition in the apparent viscosity ($\eta$) variation with rms velocity ($u$). In the fluid-like region above the depth corresponding to the transition point (higher rms velocities) there is a rapid increase in viscosity with decreasing rms velocity. Below the transition depth we find $\eta \propto u^{-1.5}$ for all the different cases studied and the material approaches an amorphous solid-like state deep in the layer. The velocity distribution is Maxwellian above the transition point and a Poisson velocity distribution is obtained deep in the layer. The observed transition appears to be analogous to a glass transition.Comment: 4 pages, 4 figures, submitted to Phys. Rev. Let

Force Chains, Microelasticity and Macroelasticity

It has been claimed that quasistatic granular materials, as well as nanoscale materials, exhibit departures from elasticity even at small loadings. It is demonstrated, using 2D and 3D models with interparticle harmonic interactions, that such departures are expected at small scales [below O(100) particle diameters], at which continuum elasticity is invalid, and vanish at large scales. The models exhibit force chains on small scales, and force and stress distributions which agree with experimental findings. Effects of anisotropy, disorder and boundary conditions are discussed as well.Comment: 4 pages, 11 figures, RevTeX 4, revised and resubmitted to Phys. Rev. Let

Continuum approach to wide shear zones in quasi-static granular matter

Slow and dense granular flows often exhibit narrow shear bands, making them ill-suited for a continuum description. However, smooth granular flows have been shown to occur in specific geometries such as linear shear in the absence of gravity, slow inclined plane flows and, recently, flows in split-bottom Couette geometries. The wide shear regions in these systems should be amenable to a continuum description, and the theoretical challenge lies in finding constitutive relations between the internal stresses and the flow field. We propose a set of testable constitutive assumptions, including rate-independence, and investigate the additional restrictions on the constitutive relations imposed by the flow geometries. The wide shear layers in the highly symmetric linear shear and inclined plane flows are consistent with the simple constitutive assumption that, in analogy with solid friction, the effective-friction coefficient (ratio between shear and normal stresses) is a constant. However, this standard picture of granular flows is shown to be inconsistent with flows in the less symmetric split-bottom geometry - here the effective friction coefficient must vary throughout the shear zone, or else the shear zone localizes. We suggest that a subtle dependence of the effective-friction coefficient on the orientation of the sliding layers with respect to the bulk force is crucial for the understanding of slow granular flows.Comment: 11 pages, 7 figure

Unjamming due to local perturbations in granular packings with and without gravity

We investigate the unjamming response of disordered packings of frictional hard disks with the help of computer simulations. First, we generate jammed configurations of the disks and then force them to move again by local perturbations. We study the spatial distribution of the stress and displacement response and find long range effects of the perturbation in both cases. We record the penetration depth of the displacements and the critical force that is needed to make the system yield. These quantities are tested in two types of systems: in ideal homogeneous packings in zero gravity and in packings settled under gravity. The penetration depth and the critical force are sensitive to the interparticle friction coefficient. Qualitatively, the same nonmonotonic friction dependence is found both with and without gravity, however the location of the extrema are at different friction values. We discuss the role of the connectivity of the contact network and of the pressure gradient in the unjamming response.Comment: 12 pages, 13 figure

Diffusion and mixing in gravity-driven dense granular flows

We study the transport properties of particles draining from a silo using imaging and direct particle tracking. The particle displacements show a universal transition from super-diffusion to normal diffusion, as a function of the distance fallen, independent of the flow speed. In the super-diffusive (but sub-ballistic) regime, which occurs before a particle falls through its diameter, the displacements have fat-tailed and anisotropic distributions. In the diffusive regime, we observe very slow cage breaking and Peclet numbers of order 100, contrary to the only previous microscopic model (based on diffusing voids). Overall, our experiments show that diffusion and mixing are dominated by geometry, consistent with fluctuating contact networks but not thermal collisions, as in normal fluids

Phase transition in a static granular system

We find that a column of glass beads exhibits a well-defined transition between two phases that differ in their resistance to shear. Pulses of fluidization are used to prepare static states with well-defined particle volume fractions $\phi$ in the range 0.57-0.63. The resistance to shear is determined by slowly inserting a rod into the column of beads. The transition occurs at $\phi=0.60$ for a range of speeds of the rod.Comment: 4 pages, 4 figures. The paper is significantly extended, including new dat

Universal and wide shear zones in granular bulk flow

We present experiments on slow granular flows in a modified (split-bottomed) Couette geometry in which wide and tunable shear zones are created away from the sidewalls. For increasing layer heights, the zones grow wider (apparently without bound) and evolve towards the inner cylinder according to a simple, particle-independent scaling law. After rescaling, the velocity profiles across the zones fall onto a universal master curve given by an error function. We study the shear zones also inside the material as function of both their local height and the total layer height.Comment: Minor corrections, accepted for PRL (4 pages, 6 figures

Forces on Bins - The Effect of Random Friction

In this note we re-examine the classic Janssen theory for stresses in bins, including a randomness in the friction coefficient. The Janssen analysis relies on assumptions not met in practice; for this reason, we numerically solve the PDEs expressing balance of momentum in a bin, again including randomness in friction.Comment: 11 pages, LaTeX, with 9 figures encoded, gzippe