Session R29: Granular Materials: Phases, Flow, and Rheology

Study on a 2D system of granular particles under a cyclic shear

Recent computer simulations of granular material under cyclic shear revealed an interesting phase diagram with ordered and disordered spatial and/or temporal patterns. The transition from reversible to irreversible dynamics in systems of many interacting particles is of a fundamental importance to many-body physics. To investigate these effects experimentally we built a two dimensional version where mono-disperse and poly-disperse disks are periodically driven in a parallelepiped shear cell. We track the particle dynamics and measure local packing changes as a function of shear amplitude and find diffusive behavior, localization of motion, reversibility, and macroscopic and microscopic limit cycles.   

Avalanche Statistics in a Rotating Drum.

We perform experiments in a quasi-two dimensional rotating drum. Two glass plates separated by about one particle diameter confine mono-disperse stainless-steel spheres to a cylindrical region. We rotate the system about the cylinder axis, which is perpendicular to gravity. Using high speed video up to 1000 fps we measure the particle positions during very slow rotation in which the flow is dominated by discrete avalanche events. We measure the avalanche size, duration, and time evolution (shape) for up to $10^{5}$avalanches and compare with DEM simulation and a mean field theory that predicts avalanche shape and a power-law distributions of size and duration.   

Granular gases of rodlike grains in micro-gravity experiments

Understanding the dynamics of granular materials is relevant both in fundamental physics and from the technological point of view, but many well-known phenomena are still insufficiently understood. Granular gases are dilute ensembles of macroscopic grains, interacting by inelastic collisions. Permanent energy supply is required to maintain dynamic equilibrium. Granular gases of spherical grains have been widely investigated theoretically and in experiments in 2 dimensions. Microgravity is necessary for maintaining such a gas in 3 dimensions (3D). Only dynamics in the Knudsen-regime and clustering instabilities were accessible in previous experiments. Our experiment with rodlike grains offers access to statistical dynamics in the rod-rod collision dominated regime as well as the oppotunity to measure the rotational degrees of freedom of the particles. We present recent results from sounding rocket and drop-tower experiments. Ensembles of rods are confined in a 3D container, monitored by video cameras. Individual rods are tracked in consecutive frames. We analyse spatial and temporal density fluctuations, translational and rotational velocity distributions, the partition of kinetic energy and the influence of different experimental parameters.   

Critical Phase Transitions in Vibrated Granular Media

Granular media, such as sand, jam under low stresses but yield and flow when stressed sufficiently. We present experiments that uncover that weak vibrations qualitatively modify the nature of this yielding transition from 1st to 2nd order: when the vibration strength, which plays a role similar to temperature, is raised sufficiently, the yielding transition becomes continuous. At the critical point, we find diverging fluctuations, growing timescales and the emergence of a length scale: hallmarks of criticality never seen before in sand.   

Collision Dynamics of Levitated Granular Clusters

In a granular gas, inelastic collisions cause an initially homogeneous density of particles to evolve into discrete clusters consisting of many particles [1,2]. Further evolution of the system results from the collisions of particles within the clusters and from collisions between the separate clusters. In all of these regimes, however, experimental data is nearly non-existent due to the difficulty of creating a free gas of particles in a terrestrial environment. Here we report experiments of $\sim$ 200 particles moving on a two-dimensional, 90 x 90 cm, anodized aluminum plate. Our particles are composed of solid CO$_2$ disks with diameter $\sim$ 1.0 cm. When placed on a heated flat surface, the disks float on a cushion of sublimated gas, so that they move essentially without friction. The experiment is filmed from above so that particle velocities can be tracked. Our analysis from the collision of two clusters of particles reveals a sharp decrease in the total kinetic energy, which is weakly dependent on the restitution coefficient, and different velocity distributions parallel and perpendicular to the direction of impact.\newline\newline [1] I. Goldhirsch and G. Zanetti, Phys. Rev. Lett. 70, 1619 (1993).\newline [2] S. McNamara and W.R. Young. Phys. Rev. E 50, R28 (1994).   

The relationship between mechanically stable packings of frictional particles and low-dimensional saddle points of frictionless particles

We perform computational studies of static packings of bidisperse frictionless and frictional disks. We show that there is a one-to-one correspondence between highly probable mechanically stable packings of frictional disks and low-dimensional saddle points for hard frictionless disks. To show this, we enumerate static packings of frictionless disks with one less contact than that required for mechanical stability $N_c = N_c^{\rm iso} - 1$. We find that the collection of these states forms lines in configuration space that emanate from the mechanically stable packings. Saddles with two missing contacts form branches that emanate from the one-missing-contact lines, and so on. For each saddle point, we calculate the minimum static friction coefficient $\mu_{\rm min}$ required to make each one mechanically stable. These studies allow us to calculate the allowed mechanically stable packings of frictional particles using MS packings of frictionless particles as a reference.   

Extensional Rheology of Granular Staples

Collections of U-shaped granular materials (e.g. staples) show a surprising resistance to being pulled apart. We conduct extensional stress-strain experiments on staple piles with vary arm/spine (barb) ratio. The elongation is not smooth, with the pile growing in bursts, reminiscent of intruder motion through ordinary and rod-like granular materials. The force-distance curve shows a power-law scaling, consistent with previous intruder experiments. Surprisingly, there is significant plastic creep of the pile as particles rearrange slightly in response to the increasing force. There is a broad distribution of yield forces that does not seem to evolve as the pile lengthens, suggesting that each yield event is independent of the pile's history. The distribution of yield forces can be interpreted in the context of a Weibullian weakest-link theory that predicts the maximum pile strength to decrease sharply with increasing pile length. From this interpretation arise length and force scales that may be used to characterize the sample.   

Particle jamming in the gap between a blade and boundary in a granular mixer

The jamming of particles between the blade of a vertical axis mixer and a cylindrical container wall is examined. A single particle model is developed to understand the factors influencing jamming and experiments are performed to investigate jamming as a function of the mixing blade rotational speed, fill height, and gap width. For the range of angular speeds investigated, the rate at which jamming occurs is independent of the blade speed. The jamming rate is proportional to fill height for level fill heights less than twice the blade height, but remains constant for larger heights. This trend is the result of the blade not being completely covered by the particles for level fill heights less than approximately two blade heights due to the deformation of the surface during operation of the mixer. Jamming is a more complex function of the gap width. For gap widths less than a critical distance, which is a function of the particle-boundary friction coefficient as predicted by the single particle model, no jamming occurs. At the critical width, the rate of jamming increases abruptly to its maximum value. Increasing the gap width further decreases the jamming rate until at a gap width of approximately five particle diameters the jamming rate is zero.   

Orientation Effects for Ellipses Flowing in a 2D Hopper

Hopper flow of disks has been extensively studied in the past decades. In this work, we investigate how ellipses (aspect ratio = 2) flow in a hopper. This study address the fact that many real-word examples of granular materials have ellipsoidal shapes. We use a quasi-two-dimensional hopper system with photoelastic ellipses so we can obtain stress/force information during the flow. Through synchronized data of particle tracking and stress, we can quantify the orientation of the force networks relative to the orientation of ellipses. The analysis shows that the ellipses which form the force chains have a strong orientation preference, particularly for force chains that form across the opening of the hopper and cause a jam. More generally, the relative orientation of ellipses plays an important role in controlling the flow rheology of ellipses.   

Hopper Flow: Experiments and Simulation

Jamming and intermittent granular flow are important problems in industry, and the vertical hopper is a canonical example. Clogging of granular hoppers account for significant losses across many industries. We use realistic DEM simulations of gravity driven flow in a hopper to examine flow and jamming of 2D disks and compare with identical companion experiments. We use experimental data to validate simulation parameters and the form of the inter particle force law. We measure and compare flow rate, emptying times, jamming statistics, and flow fields as a function of opening angle and opening size in both experiment and simulations.   

Clogging in hopper flow and the kinetics of jamming

Understanding the time evolution of a system from an unjammed to a jammed state is a significant and open problem. The clogging of granular materials during hopper discharge is a quintessential example of a system undergoing such a process. When a hopper has a small opening, grains exit until a stable arch forms at the opening and a jamming front propagates up through the system. Conversely, hoppers with large enough openings do not clog. We define the clogging transition as the boundary in parameter space between those systems which can clog and those which will never clog. We have established experimental techniques for locating the clogging transition and describing the grain-scale behavior in hopper flow. We use these methods to study the approach to the clogging transition for a quasi-2D hopper. By tracking particle positions with a high-speed camera, we measure time-averaged velocity fields as well as velocity fluctuations. We have previously shown that systems which can clog exhibit elevated velocity fluctuations. We currently investigate the correlations between velocity fluctuations throughout the hopper as well as the size of dynamical heterogeneties as further promising grain-scale signatures of the approach to the clogging transition and of the kinetics of jamming.   

Jamming to Clogging Transitions for Systems with Obstacle Arrays

Jamming can occur in systems consisting of collections of particles when the response of the system changes from a fluidlike state that can easily flow to a state that acts like a solid. For a loose collection of grains, jamming can occur as a function of density, where the grains readily flow at low densities but with increasing density undergo a transition to a jammed state at point J. Liu and Nagel have proposed that there may be a universal jamming phase diagram as a function of density, load, or temperature that may also include the glass transition. Here we propose that the density of fixed obstacles or quenched disorder can be considered as a new axis for the jamming phase diagram, since the disorder causes the system to jam at densities below point J. For a small number of obstacles, the system exhibits jamming behavior; however, for higher disorder density, there is a crossover to a behavior that we term clogging rather than jamming since the stuck states are highly heterogeneous, fragile, and exhibit memory effects. Our results imply that clogging is a distinct phenomenon from jamming with very different behaviors. These results are of relevance for particle flow in porous media, depinning transitions, and jamming in crowded environments.   

Dynamic Jamming in Granular Polymers

We present an extensive study of jamming behavior of two-dimensional granular polymers. In previous work, we showed that the nature of the jamming in granular polymer systems has pronounced differences from the jamming behavior observed for bidisperse two-dimensional disk systems at point J [1,2]. We found that the jamming density decreases with increasing length of the granular chain due to the formation of loop structures, in excellent agreement with experiments [3]. Now we present the response of the granular polymers to shear. At low densities, the system unjams independently of boundary conditions or shear rate. At high densities, for a slip wall the system develops plug flow with velocity equal to shear rate, while for a non-slip wall, the system develops a shear band and finite stress. We show that the stress asymptotes to a value that increases with increasing density and decreases with increasing shear rate. The latter is attributed to shear band changes from wide and migrating at low load to very narrow and localized at high load. [1] C. J. Olson Reichhardt and L. M. Lopatina, Science 326 (5951), 374 (2009). [2] L. M. Lopatina, C. J. Olson Reichhardt, and C. Reichhardt, Phys. Rev. E 84, 011303 (2011). [3] L.-N. Zou et al, Science 326 (5951), 408 (2009).