Bulletin of the American Physical Society
2007 APS March Meeting
Volume 52, Number 1
Monday–Friday, March 5–9, 2007; Denver, Colorado
Session B29: Dense Granular Flows and Jamming |
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Sponsoring Units: DFD Chair: Martin van Hecke, University of Leiden Room: Colorado Convention Center 303 |
Monday, March 5, 2007 11:15AM - 11:27AM |
B29.00001: Affine and Non-Affine motion in a Granular Couette Experiment Brian Utter, Robert Behringer We characterize local motion of grains in a 2D granular Couette shear. In steady state, grains exhibit a shear band, where the grains are dilated near the shearing surface, $r = 0$. The mean velocity is in the tangential direction, and decays somwhat faster than exponentially. We characterize the local motion by tracking small clusters of particles. The overall motion of the cluster can be described in terms of a smooth affine part, and a non-affine part that is not captured by the smooth deformation. We determine the measure of non-affine motion, $D^2_{min}$ of Falk and Langer. This quantity shows characteristic distributions that initially grow roughly as power laws, but are then cut off exponentially. Distributions of non-affine displacements for individual particles are roughly guassians. The width of these distributions, the widths of the distributions for $D^2_{min}$ and previously measured diffusivities show essentially identical variation with local shear rate. We understand the formation of the shear band from an initially homogeneous packing in terms of outwardly directed diffusion next to the shearing surface. In the steady state, there is a balance between inward diffusion from a density gradient, and ourward diffusion driven by the shearing. [Preview Abstract] |
Monday, March 5, 2007 11:27AM - 11:39AM |
B29.00002: Nonlinear elastic stress response in granular materials Brian Tighe, Joshua Socolar We study the response of two-dimensional granular materials to a local boundary force, for which classical elasticity predicts identical stress states in the cases of isotropic and hexagonally anisotropic materials. We probe the differences in these two cases by including corrections from the full nonlinear elasticity theory. Additionally, we model the effect of discrete microstructure by taking the magnitude of multipole stress response terms, which are induced in the nonlinear system, as material parameters. By so incorporating both anisotropy and microstructure, reasonable fits are obtained for experimental stress response profiles in hexagonal packings of photoelastic grains, while either correction alone is insufficient. [Preview Abstract] |
Monday, March 5, 2007 11:39AM - 11:51AM |
B29.00003: Upward penetration through a granular medium D. Costantino, T.J. Sheidemantel, M.B. Stone, J. Cole, C. Conger, K. Klein, M. Lohr, W. McConville, Z. Modig, P. Schiffer We measure the force needed to push a flat plunger upwards through a granular medium. The plunger begins flush with the base of the grains' container, and we focus upon the force necessary to initiate motion.~The data show that this break-out force increases monotonically with plunger diameter and pile height as expected.~In contrast to previous measurements of the force needed for vertical penetration from above and of the horizontal drag force, this break-out force has a strong dependence on the diameter of beads making up the pile.~The nature of this bead size dependence can be altered by using different methods to form the grain pile.~Implications for the relevant force chain network will be discussed.~Research supported by NASA grant NAG3-2384 and the NSF REU program. [Preview Abstract] |
Monday, March 5, 2007 11:51AM - 12:03PM |
B29.00004: Sound and Force Propagation in Granular Materials Clifford E. Chafin, Karen E. Daniels A characteristic of granular materials under stress is a highly nonuniform distribution of forces. These localized force chains are prominent of 2-D packings of photoelastic particles, but their role in sound propagation is unclear. We mechanically excite 100 $\mu$s square wave pulses and periodic waveforms through such packings. We report optical measurements of changes in the force chain network using a high speed camera, and simultaneous acoustic measurements from biaxial accelerometers of similar size and mass to the photoelastic particles. These measurements provide amplitude and speed (time of flight and group velocities) of the response both on and off the force chain network. [Preview Abstract] |
Monday, March 5, 2007 12:03PM - 12:15PM |
B29.00005: Testing the equal-probability assumption of jammed particle packings Guo-Jie Gao, Jerzy Blawzdziewicz, Corey O'Hern The Edwards' entropy formalism provides a statistical mechanical framework for describing dense granular systems. In addition, experiments on vibrated granular columns and numerical simulations of quasi-static shear flow of dense granular systems have provided evidence that the Edwards' theory may accurately describe certain aspects of these systems. However, a fundamental assumption of the Edwards' description---that all mechanically stable (MS) granular packings at a given packing fraction are equally likely---has not been explicitly tested in dense granular systems. We investigate this assumption by generating all mechanically stable hard disk packings in small systems using a protocol in which we successively compress or decompress the system followed by energy minimization. We then apply quasi-static shear flow at fixed pressure to these MS packings to study the frequency with which MS packings occur during the shear flow. We find that the MS packings do not occur with equal probability during the shear flow, in fact, there is a significant reduction in the number of accessible MS packings at large shear strain. Thus, the Edwards' entropy formalism should be re-examined in light of our findings. [Preview Abstract] |
Monday, March 5, 2007 12:15PM - 12:27PM |
B29.00006: Experimental study of the compaction dynamics for 2D granular pile of spherical and cylindrical grains Geoffroy Lumay, Nicolas Vandewalle, Francois Ludewig We present an experimental study of the compaction dynamics for two-dimensional granular systems. The compaction of a pile of spherical grains and of a pile of cylindrical grains have been studied. Compaction dynamics is measured at three different scales : the macroscopic scale through the normalized packing fraction, the mesoscopic scale through the normalized fraction of ideally ordered domains in the system, and the microscopic scale through the grain mobility. Moreover, the ideally ordered domains are found to obey a growth process dominated by the displacement of domain boundaries. A global picture of compaction dynamics relevant at each scale is proposed. [Preview Abstract] |
Monday, March 5, 2007 12:27PM - 12:39PM |
B29.00007: Packing and segregation in thermally cycled granular materials Ke Chen, John Draskovic, Julia Cole, Andrew Harris, Casey Conger, Matthew Lohr, Kit Klein, Thomas Scheidemantel, Peter Schiffer We have studied the change of packing fraction of granular materials and the displacement of an intruder in a granular pile under thermal cycling. We find that the packing fraction of granular materials increases with thermal cycling, i.e., heating the sample and returning it to ambient temperature. This effect appears to be related to the difference in thermal expansion between the container and the grains, and it increases monotonically with increasing cycle temperature. The packing fraction further increases under multiple thermal cycles and the increasing packing fraction can be fit to a double exponential decay toward the random close packing. We also find that spherical intruders in granular piles can move downward with thermal cycling, and that this effect depends on the relative density of the grains and the intruder as well as the relative thermal expansion of the grains and the container. This research was supported by the NASA through grant NAG3-2384 and the NSF REU program through grant DMR 0305238. [Preview Abstract] |
Monday, March 5, 2007 12:39PM - 12:51PM |
B29.00008: Experimental Characterization of the Jamming Transition in a Granular Material Trushant Majmudar, Robert Behringer We describe experiments to test recent predictions for the jamming transition in disordered solids. Here, our system is a 2D granular material consisting of photoelastic disks. By observing these particles through crossed circular polarizers, it is possible to a) accurately determine particle contacts, b) via an appropriate computational procedure, calculate the vector contact forces between particles, and c) from the contact forces compute the Cauchy stress. Simulations (e.g. by O'Hern et al., Donev et al.) for frictionless particles predict a discontinuous increase in the contact number, $Z$ at the jamming transition, given by a critical packing fraction, $\phi_c$. Above jamming, $Z$ should then increase as a power law in $\phi -\phi_c$ with an exponent of 0.5 to 0.6. The pressure, $P$ is also predicted to grow as a power law. Additionally, Senkes and Chakraborty have predicted the behavior of $P$ and $Z$ using a meanfield entropy-based description. Our experiments support all of these predictions. There is a rapid increase in $Z$ at $\phi_c$, and power law increase of $Z$ and $P$ above the transition. There is also reasonable agreement between the data and the predictions of Senkens and Chakraborty. [Preview Abstract] |
Monday, March 5, 2007 12:51PM - 1:03PM |
B29.00009: Stress, strain rate, and free volume in dense granular flow Chris Rycroft, Ken Kamrin, Martin Bazant There have been many attempts to describe dense granular flow with continuum models, but a complete theory is still lacking. Often, these models make assumptions about microscopic quantities (such as shear stress, strain rate, and local density) and here we present Discrete Element Method (DEM) simulations to directly measure these in a variety of different non-homogeneous granular flows. Motivated by previous work, we compute these quantities on a mesoscopic length scale of several particle diameters, and examine both spatial distributions, and correlations between the variables. We investigate the validity of the commonly-used Mohr-Coulomb incipient yield hypothesis, which states that the ratio of shear stress to normal stress should be everywhere constant in a flowing granular material. Our results also show some striking correlations between strain rate and local density, which suggest a phase transition between static and flowing granular materials. [Preview Abstract] |
Monday, March 5, 2007 1:03PM - 1:15PM |
B29.00010: The force network in emulsions and the role of external stress Jing Zhou, Tim Prisk, Su Long, Habib Skaff, Qian Wang, Todd Emrick, Anthony D. Dinsmore Direct imaging of emulsion droplets labeled with fluorescent nanoparticles using confocal microscopy is a valuable experimental tool for studying granular materials in three dimensions. By measuring individual droplet-droplet contacts inside the frictionless emulsion piles, we visualize the force network and calculate the orientations, positions, and magnitudes of forces and their statistical distributions. We find that large forces are more likely to align parallel to each other, leading to long-range, chain-like correlations of magnitude and direction of contact force. Furthermore, we investigate how the force network evolves with time and how it changes under various external stresses. We also measure the contact force at the bottom of emulsion piles and compare to previous surface measurements and the measurement inside the bulk. This work may shed light on the aging and macroscopic viscoelasticity of granular systems. [Preview Abstract] |
Monday, March 5, 2007 1:15PM - 1:27PM |
B29.00011: The packing and compaction dynamics of granular polymers Ling-Nan Zou, Xiang Cheng, Heinrich Jaeger, Sidney Nagel While the packing of hard spheres has been the subject of intense research, the packing of objects with reduced symmetries is far less well-studied, both experimentally and theoretically. Here, we report an experimental study on the packing of a granular polymer analogue --- chains of hollow, spherical brass beads, 1.9 mm in diameter, ranging in length from a 1 to 42 700 beads per chain. In particular, we systematically measure the density $\rho$ of the bead-chain pack as a function of the number of beads per chain $M$ (\textit{i.e.} the molecular weight of the granular polymer). The density decreases from the random close packed density $\rho_{RCP} \approx 0.64$ for single beads to an asymptotic density $\rho_\infty \approx 0.39$ in the limit of very long chains; the form of the density fall-off is rather slow, the effect is noticeable even when $M$ is much larger than the chain persistence length. In terms of dynamics, the compaction of bead-chain packs appears to obey the same logarithmic relaxation form found in the compaction of single bead packs [1], but with a puzzling, $M$-dependent sensitivity to initial conditions. We shall discuss these results in the context of, and attempt to make connections to, the packing of single hard spheres on one hand and the physics of polymer melts on the other. [1] J. B. Knight \textit{et al.}, Phys. Rev. E \textbf{51}, 3957 - 3963 (1995). [Preview Abstract] |
Monday, March 5, 2007 1:27PM - 1:39PM |
B29.00012: The Stochastic Flow Rule and Rate Sensitivity in Dense Granular Flows. Ken Kamrin, Chris H. Rycroft, Martin Z. Bazant The Stochastic Flow Rule (SFR) is a constitutive law which, when used with limit-state Mohr-Coulomb plasticity for stresses, gives predictions for the mean velocity field in quasi-2D dense granular flows. It is based on a simple microscopic flow mechanism, where ``spots'' of free volume perform random walks along slip-lines, biased by stress imbalances upon local fluidization. The SFR has recently been shown to predict dense granular flows in diverse geometries--- e.g. draining silos, annular Couette cells, and plate-dragging experiments--- without the use of fitting parameters. However, a significant rheological change occurs in certain geometries--- e.g. inclined plane flow and gravity-free horizontal shear flow--- where the packing fraction is nearly uniform and a distinct stress/strain-rate relationship arises. In this talk, we review the SFR and propose a simple explanation of when and why rate sensitivity occurs, depending on the slip-line geometry. We also postulate how rate-dependent terms may be combined with the SFR to create a more universal theory of dense flows. [Preview Abstract] |
Monday, March 5, 2007 1:39PM - 1:51PM |
B29.00013: The Dynamics of Sandpile Model and Its Application to Earthquakes Yunfan Gong Just from the simple yet widespread power laws, it seems unlikely to differentiate self-organized criticality (SOC) from other mechanisms proposed for power-law relationships. Here we report SOC phenomenon in a sandpile model driven by chaos. We characterize SOC by analyzing times series from the system. Surprisingly, we find that the microscopic dynamics of the complex sandpile system can be best approximated by a very simple one-order autoregressive (AR) model. Meanwhile, the AR model can well reproduce almost all power-law behaviors of the sandpile model, suggesting a similar dynamics between the complex sandpile system and the simple one-order AR model. Next, real earthquake time series including Harvard catalog and source time functions (STFs) are analyzed along the same lines. The one-order linear dynamics fitted from the STFs is in excellent agreement with that of the sandpile model, whereas the optimal two-order dynamics fitted from the STFs is a false mode and should be rejected. Our results support that earthquakes can be considered as a SOC process and suggest that they may be governed by sandpile models with high order ($\geq 2$) dynamics. [Preview Abstract] |
Monday, March 5, 2007 1:51PM - 2:03PM |
B29.00014: Smoothing a Rock by Chipping Sidney Redner, Paul Krapivsky We investigate an idealized model for the size reduction and smoothing of a polygonal rock due to repeated chipping at corners. Each chip is sufficiently small so that only a single corner and a fraction of its two adjacent sides are cut from the object in a single chipping event. After a large number of chipping events, the shape is not circular, with the distribution of facet lengths and corner angles broadly distributed. In the long-time limit, the shape of the object is not a unique, but rather is characterized by large sample-to-sample fluctuations. [Preview Abstract] |
Monday, March 5, 2007 2:03PM - 2:15PM |
B29.00015: Comparison of the influence of a strong current and of a spark on the distribution of the resistance of a contact between two grains Stephane Dorbolo, Alexandre Merlen, Eric Falcon, Matthieu Creyssels, Bernard Castaing, Nicolas Vandewalle The distribution of the electrical resistance of a contact between two stainless steel beads is a log normal. When a current is injected through a contact, the voltage is not univocally determined. The system exhibits hysteresis. A chain of beads have been used to make some statistic and to determine how a strong current or a electric spark modify the distribution of the resistance. A strong current changes the distribution of resistance into a nearly gaussian distribution. The contacts are soldered by the current. On the other hand, a spark only modifies the highest resistances. The value of the minimum resistance that is modified is determined by the distance between the spark and the bead chains. [Preview Abstract] |
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