Bulletin of the American Physical Society
62nd Annual Meeting of the APS Division of Fluid Dynamics
Volume 54, Number 19
Sunday–Tuesday, November 22–24, 2009; Minneapolis, Minnesota
Session AU: Granular I: Jamming I |
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Chair: Robert Behringer, Duke University Room: 200I |
Sunday, November 22, 2009 8:00AM - 8:13AM |
AU.00001: Jamming of Granular Materials in Wedge Hoppers Summer Saraf, Scott Franklin We study the jamming of ordinary and rod-like granular materials in wedge-shaped hoppers and compare the probability distributions for exit mass with those obtained from cylindrical hoppers. While cylindrical hoppers show an exponential probability distribution, we find that the rectangular exit aperture of wedge-shaped hoppers exhibit a power law decay for both spheres and rods. This behavior can be explained with a model of the rectangular exit aperture as composed of a series of round, adjacent apertures each with a statistically independent jamming probability. We speculate that the spatially varying jamming probability results from inhomogeneities in the granular material, with regions of the material more tightly packed than others, and thus more likely to jam. [Preview Abstract] |
Sunday, November 22, 2009 8:13AM - 8:26AM |
AU.00002: Jamming of Granular Flow in a Two-Dimensional Hopper Junyao Tang, Sepehr Sadighpour, Robert Behringer We seek an understanding of the physics of jamming in flow from a hopper. Using spatio-temporal video data for photoelastic disks (mean diameter $d$) flowing through a two-dimensional hopper (opening size $D$.), we have found experimental support for the hypothesis that the probability of flow surviving until time $t$ without jamming has the form $P_s(t) = \exp (-t/\tau)$. The important physics is encapsulated in $\tau$, and how that depends on the ratio $D/d$. Estimates of $\tau$ vary as a power-law or an exponential in $D/d$ for a jamming model and an arch formation model. Through particle tracking we conclude that jamming requires both a high packing fraction and a stable force chain arch at the outlet. Work in progress is yielding data for $\tau$ vs. the hopper angle as well as $D/d$. [Preview Abstract] |
Sunday, November 22, 2009 8:26AM - 8:39AM |
AU.00003: Two-dimensional dense granular material subject to uniform simple shear Jie Ren, R. Behringer We have performed 2D shear experiments using photoelastic particles and a novel apparatus to investigate the role of shear strain on the jamming of a dense granular material. The goal of this work is to explore the shear stress axis in the jamming phase diagram proposed by Liu and Nagel. The experiments are carried out using a 2D simple shearing apparatus, whose base is specifically designed to perform nearly uniform shear at the particle scale across the shearing area. By using photoelastic particles, we can measure stresses, strains, contact forces, and particle displacements while shearing. We note two important observations from this work: 1) for densities that are below the value for isotropic jamming, the system jams when subject to shear strain; 2) starting from jammed isotropic states at higher densities, the application of quasi-static shear at constant density does not lead to failure, but rather a strengthening of the system. [Preview Abstract] |
Sunday, November 22, 2009 8:39AM - 8:52AM |
AU.00004: Topology of force chains in dense granular materials Lou Kondic, Yiguang Yan, Miroslav Kramar, Konstantin Mischaikow Force chain structures are well known and well researched due to their importance in determining static and dynamic features of dense particulate systems. However, so far there is no well defined approach towards understanding properties of these structures and distinguishing them in different systems. In this talk, we will present novel approach based on algebraic topology techniques that will be used to analyze and quantify force chain structures. In particular, we will discuss how these properties differ for the systems exposed to shear versus compression, and correlate the topological measures to the phenomena such as jamming. While the present talk will concentrate on the results of discrete element simulations, we will see that this new approach has a significant potential in comparing experimental and theoretical results in a well defined and precise manner. [Preview Abstract] |
Sunday, November 22, 2009 8:52AM - 9:05AM |
AU.00005: Friction-induced hysteresis in quasi-static granular jamming Mahesh Bandi, Andras Libal, Michael Rivera, Robert Ecke Static granular packings are usually interrogated via quasi-static measurements where the packing fraction serves as the control parameter to study the pack evolution. In the absence of externally induced vibrations (effective granular temperature), quasi-static measurements are justified because the system in question is athermal. Whereas this is true for frictionless granular packings, we experimentally demonstrate the failure of quasi-staticity for frictional packings in a quasi two-dimensional system of disks. This failure is traced to hysteretic responses in the system which shifts the critical packing fraction at which the system jams to progressively higher values as the system is repeatedly jammed and un-jammed. The shift in critical packing fraction marks the system's evolution from a Random Loose Packed (RLP) to a Random Close Packed (RCP) density. This rate of evolution is experimentally determined to depend upon the quasi-static step size and the static friction coefficient of the constituent disks in the system. [Preview Abstract] |
Sunday, November 22, 2009 9:05AM - 9:18AM |
AU.00006: Is random close packing of beads well defined? Frank Rietz, Charles Radin, Harry L. Swinney, Matthias Schroeter The name random close packing refers to the experimental observation that some ways of packing of monodisperse beads (like vertical vibration or sedimentation) can't exceed a volume fraction of $\approx $64{\%}. There are several competing theories for this phenomenon [1-3]. However, it is possible to surpass the random close packing limit by cyclic shearing [4]. We investigate the three-dimensional distribution of particles in such a shear cell. Index matching of the surrounding liquid provides access to the interior of the granular bed. A laser sheet is scanned through the sample and by adding a fluorescent dye to the liquid we can determine the particle positions. The experiment starts at packing fractions well below random close packing. After a few thousand cycles packing fractions above 64{\%} are achieved. By determination of Voronoi cells we characterize the local packing densities and measure order parameters around the onset of random close packing. This allows us to comment on the question if random close packing is well defined. [1] Torquato; Phys. Rev. Lett. 84, 2064 (2000). [2] Kamien; Phys. Rev. Lett. 99, 155501 (2007). [3] Radin; J. Stat. Phys. 131, 567 (2008). [4] Nicolas; Eur. Phys. J. E 3, 309 (2000). [Preview Abstract] |
Sunday, November 22, 2009 9:18AM - 9:31AM |
AU.00007: Random Packings of Rod-like Granular Materials Scott Franklin Piles of large aspect ratio granular materials are known to form solid plugs, significantly more rigid than piles of ordinary sand or rice. We create random, jammed packings of spherocylinders --- cylinders with hemispherical endcaps --- using energy minimization techniques. The packing fraction at high aspect ratios agrees with a mean-field model that scales as the inverse of excluded volume, implying that that contact number is constant even for very long, thin particles. This is confirmed by a direct analysis of the average contact number at large aspect ratios. The structure of the jammed state can be investigated through the dynamical matrix of elastic modes. In contrast with other work on ellipsoids, our packings show low energy translational modes and higher energy rotational modes, which we explain as resulting due to the absence of particle curvature. [Preview Abstract] |
Sunday, November 22, 2009 9:31AM - 9:44AM |
AU.00008: Jamming of granular materials under shear Jie Zhang, Robert Behringer We probe the transition of a disordered system between an unstable (e.g. fluid-like) state and a stable (e.g. solid-like or jammed) state. Examples of relevant systems include glasses, foams, colloids and granular materials. Liu and Nagle proposed a jamming diagram with axes of inverse density, temperature and shear stress, and a region near the origin was proposed to encompass the jammed states. Point J on the diagram, (isotropic jamming) was thought to be the lowest possible jammed density, and for denser systems, shear stress was thought to lead to unjamming. Recent work has focusd on isotropic jamming. Here, we explore the effect of shear on jamming. We have carried out experiments using quasi-2D systems of photoelastic disks subject to pure shear. We obtain inter-particle contact forces as well as other key information. From this data we compute stresses, densities, etc. Contrary to the above picture, we find that the application of shear to densities lower than that at point J can lead to jammed states. Shear applied to isotropic jammed states does not lead to unjamming, but rather to an increase in all stresses. These data, which obviously pertain to frictional particles, suggest a jamming diagram given by shear stress, pressure and inverse density. [Preview Abstract] |
Sunday, November 22, 2009 9:44AM - 9:57AM |
AU.00009: A kinetic theory of plastic flows in jammed materials Lyderic Bocquet, Annie Colin, Armand Ajdari Amorphous jammed materials of diverse nature display complex flow properties intermediate between solid and liquid, as characterized by the existence of a yield stress. Furthermore flows in such systems usually exhibit spatial inhomogeneities, which cannot be reconciliated with classical rheological descriptions. We present a novel kinetic approach for the elasto-plastic flow dynamics of jammed materials, describing the spatio-temporal collective dynamics of the localized plastic events occuring during the flow [1]. This description yields a non-local constitutive law for the flow, introducing as a key dynamic quantity the local rate of plastic events. This quantity, interpreted as a local fluidity, is spatially correlated with a correlation length diverging in the quasistatic limit, i.e., close to yielding. In line with recent experimental [2] and numerical observations, we predict finite size effects in the flow behavior, as well as the absence of an intrinsic local flow curve.\\[4pt] [1] L. Bocquet, A. Colin, A. Ajdari, {\it Phys. Rev. Lett.} (2009) in press\\[0pt] [2] J. Goyon, A. Colin, G. Ovarlez, A. Ajdari, L. Bocquet, {\it Nature} {\bf 454} 84 (2008) [Preview Abstract] |
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