Bulletin of the American Physical Society
2005 58th Annual Meeting of the Division of Fluid Dynamics
Sunday–Tuesday, November 20–22, 2005; Chicago, IL
Session NJ: Granular Media: General II |
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Chair: Igor Aronson, Argonne National Laboratory Room: Hilton Chicago Williford C |
Tuesday, November 22, 2005 11:01AM - 11:14AM |
NJ.00001: Statistical Properties of Granular Solid to Liquid Transition in Small Systems under Shear Martin Melhus, Igor Aranson, Dmitry Volfson, Lev Tsimring The fluidization transition of a dense granular assembly under shear is studied numerically using soft particle molecular dynamics simulations in two dimensions using a previously verified predictor-corrector algorithm. We focus on small systems in a thin Couette cell, examining the bistable region while increasing shear, with varying amounts of random noise, and determine statistics of the shear required for fluidization. We find that variance in the fluidization transition increases with decreasing system size, and discuss their quantative relationship. [Preview Abstract] |
Tuesday, November 22, 2005 11:14AM - 11:27AM |
NJ.00002: Plastic Failure Events in 2D Sheared Granular Systems Trushant Majmudar, Robert Behringer We present experimental measurements of plastic failure events in a two dimensional granular system consisting of polymer photoelastic disks. The particles are confined in a rectangular geometry and placed horizontally. We visualize the formation and breaking up of force chains and measure the stress changes and displacements of particles during failure events. The stress changes are measured with photoleastic images and the displacements are measured by particle tracking. We find that certain regions of the sample remain rigid, but a band of particles undergo maximum irreversible deformation and reduction in stress signifying a shear band. We can extract quantitative information about the elastic as well as inelastic deformations. We compare our observations to the shear transformation zone (STZ) theory. We also report measurements of the normal and tangential forces at the grain scale for sheared systems and characterize the induced anisotropy in contact orientations and forces. We find that spatial correlations of forces serve as an additional distinguishing signature of induced anisotropy. [Preview Abstract] |
Tuesday, November 22, 2005 11:27AM - 11:40AM |
NJ.00003: A Freezing/Melting Transition in a Vibrated and Sheared Granular Material Robert Behringer, Karen Daniels We describe experiments on an annular layer of granular material that is sheared from above and vibrated from below. Key control parameters are the shear rate, $\Omega$ and the dimensionless acceleration, $\Gamma = A\omega^2/g$, where $A$ and $\omega$ are respectively the amplitude and frequency of shaking. We measure the pressure, $P$, at the base of the layer, and volume, $V$, hence the mean packing fraction of the layer. The outer sidewall is transparent, and we image/characterize the particles in the outer layer. We find a hysteretic transition from a state with 3D order to a disordered state as the shear rate, $\Omega$, is increased. The boundary between these two phases corresponds to equal energy inputs from shearing and shaking. We also characterize distributions for $P$ and $V$. These are strongly fluctuating quantities, with broad distributions. The Kurtosis of the distributions for $P$ and $V$ are strongly cusped at the transition. This striking behavior suggests that a temperature-like variable may control the transition between the two states. We propose that the non-equilibrium fluctuation-dissipation theorem may provide such a temperature and explore this possibility by measuring the response function, $R$ (for volume) to step changes in $\Omega$. We also determine the volume correlation function, $C$ and use this to determine an effective $kT$ from the slope of the $R$ vs. $C$ curve. [Preview Abstract] |
Tuesday, November 22, 2005 11:40AM - 11:53AM |
NJ.00004: Crystallization of a quasi-two-dimensional granular fluid Rohit Ingale, Pedro Reis, Mark Shattuck We experimentally investigate the structural changes in the crystallization of a uniformly heated quasi-2D granular fluid, as a function of filling fraction, $\phi$. We present a direct mapping between our non-equilibrium experimental granular system and the equilibrium behavior of hard-disks. To quantify this connection we calculate a number of standard measures, namely the radial distribution function, the local bond order parameter and the Lindemann criterion for melting, all of which provide a consistent scenario. The value of the radial distribution function at contact, $g(D)$, closely follows the Carnahan-Starling theoretical prediction for hard spheres up to $\phi\sim0.55$. In an intermediate region, $0.652<\phi<0.719$, there is a qualitative change in behavior which has the characteristics of a hexactic phase. At $\phi_s=0.719\pm0.007$ crystallization occurs, in excellent accord with theoretical and numerical results for hard-disks. In addition to these standard measures we have calculated the \emph{Shape Factor}, $\zeta$, which is a detailed measure of the topology of Voronoi cells and was recently introduced in the context of Monte-Carlo simulations of hard-disks. Remarkably good agreement is found between the experimental and numerical probability density functions, $P(\zeta,\phi)$. Detailed analysis of $P(\zeta,\phi)$, provides a great deal of insight into the physical nature of the intermediate phase, where a coexistence of topologically distinct Voronoi cells occurs. [Preview Abstract] |
Tuesday, November 22, 2005 11:53AM - 12:06PM |
NJ.00005: Granular Flow in Narrow Channels K.M. Hill, S.A. McGough, J. Zhang We experimentally investigate the effect of channel thickness on monodisperse spherical particles in thin drums of different widths. We find the velocities and velocity fluctuations to be strongly dependent on the width of the drum, but that relationship is not monotonic. As the ratio of the drum width to particle diameter increases, the velocity and velocity fluctuations oscillate, and the amplitude of oscillations decrease as the width of the drum increases. This phenomenon appears to be governed by the level of disorder in the allowed packing structure. That is, the velocities and velocity fluctuations are maximized where the drum widths forces a more disordered packing and minimized for drum widths where, for example, hexagonal close packing is allowed. Measurements of the pair correlation function also indicate that the particles are hexagonally packed in planes parallel to the sidewalls for drum widths where the velocities are slowest, and that the packing is more disordered for widths where the velocities are faster. [Preview Abstract] |
Tuesday, November 22, 2005 12:06PM - 12:19PM |
NJ.00006: Dense free surface flow in granular mixtures J. Zhang, K.M. Hill When the surface of a sandpile is tipped beyond the angle of repose, the particles will start to flow, but only in a thin surficial boundary layer. The flow of monodisperse spherical particles is laminar-like, with the particles moving primarily in layers parallel to the free surface. This laminar structure has been recently shown to determine certain details of the volume fraction and particle velocities. Further, a simple ``slip and shake'' model based on the laminar structure has been shown to describe well the nature of the diffusion and the velocity fluctuations. We test the applicability of these results for a broader range of granular systems, specifically, for mixtures of particles. As is typically observed, smaller (or, alternatively, denser) particles segregate to the bottom of the boundary layer; measurements are taken before, during, and after segregation. We find a similar stratified structure in these mixtures, though the structure is less distinct in the pre-segregated state for the different sized particles. Nevertheless, we find the laminar structure has similar significance for kinematic details in granular mixtures at every stage of segregation. [Preview Abstract] |
Tuesday, November 22, 2005 12:19PM - 12:32PM |
NJ.00007: Discrete Element Simulation of Granular Flow in a Modified Couette Cell Jeremy B. Lechman, Gary S. Grest Slow, dense granular flows often exhibit thin, localized regions of particle motion, called shear bands, separating largely solid-like regions. Recent experiments using a split-bottom Couette cell found that the width of the shear zone grew as the pack height increased and the azimuthal velocities when rescaled fall on a universal curve regardless of the particle properties. Here we present large-scale Discrete Element simulations of a similar system for packs of varying height up to 180,000 monodisperse spheres. The onset and evolution of granular shear flow is investigated as a function of height. We find a transition in the nature of the shear as a characteristic height is exceeded. Below this height there is a central quasi-solid core; above this height we observe the onset of additional axial shear associated with a torsional failure mode of the inner core. Radial and axial shear profiles are qualitatively different: the radial extent is wide and increases with height while the axial width remains narrow and fixed. [Preview Abstract] |
Tuesday, November 22, 2005 12:32PM - 12:45PM |
NJ.00008: Velocity Depth Profile of Granular Media in a Horizontal Rotating Drum Lori Sanfratello, Arvind Caprihan, Eiichi Fukushima, Christian Heine We report on the velocity depth profile of granular materials within the lens-shaped flowing region of a horizontal rotating drum. Using MRI velocimetry, we found that the velocity profile of the flowing layer near the axial center of a half-filled 3D drum has the form Vm[1-(r/r0)\^{}2]-$\Omega $r, where r is the depth measured from the cylinder center, except very close to the free surface where it lies below the quadratic form. We propose that this deviation is due in part to particles reaching the surface with components of their velocity in the azimuthal direction. To test this we used a 3D cylinder with a radial ``paddle'' placed approximately at the dynamic angle of repose, covering the top $\raise.5ex\hbox{$\scriptstyle 1$}\kern-.1em/ \kern-.15em\lower.25ex\hbox{$\scriptstyle 4$} $ of the flow, so as to direct the particles immediately into the flow upon reaching the surface. Data taken with the paddle at the free surface fit the quadratic better than without the paddle at all rotation rates observed. Thus, we conclude that the quadratic form is intrinsic to this flow geometry. [Preview Abstract] |
Tuesday, November 22, 2005 12:45PM - 12:58PM |
NJ.00009: Model system to study polymer folding in poor solvents Ben Bammes, Jeffrey Olafsen The dynamics of a chain of stainless steel monomers partially submerged in a thin layer of water that is vertically oscillated on a horizontal plate have been observed to be visually similar to that of polymer collapse in a poor solvent.\footnote{B. Bammes and J. S. Olafsen, Chaos, \textbf{14}, S9 (2004).} In this experiment, the model `polymer' is composed of 25 to 250 loosely connected spheres that allows the chain to bend but also limits the smallest circle into which the chain can be folded (a persistence length). The surface tension plays the role of the long-ranged potential that is minimized during the folding process and the surface excitations of the thin fluid layer play the role of the Brownian noise that drives the system stochastically. In addition to the folding of a single chain, we examine the interactions between multiple chains to better detail the total potential that is minimized in the folding process. We are attempting to model the folding in this 2D system using a Langevin equation to describe the dynamic evolution. Once a simulation can be built to using this 2D model, it can be generalized to predict folding in 3D. This system is advantageous for studying polymer folding in poor solvents in the absence of many of the electrical and chemical details in real polymers. [Preview Abstract] |
Tuesday, November 22, 2005 12:58PM - 1:11PM |
NJ.00010: Energy injection in a mechanically thermalized, steady state granular Boltzmann bath. Jeffrey Olafsen, G. William Baxter A variety of experiments in driven granular gases have demonstrated an ability to tune the velocity statistics based upon the details of how energy is injected into the granular gas, the long- and short-ranged forcing of the particles, and the viscosity of the interstitial fluid. In one experiment using a two-layer system, simultaneous non-Gaussian and Gaussian velocity statistics are obtained in two different species of particles corresponding to the two layers. This particular design allows for the creation of a steady state granular Boltzmann bath in which equilibrium-like statistics can be observed for a system that is not in equilibrium. Understanding the details of both the mechanical driving and particle-particle interactions that result in this condition may provide clues for predicting when non-equilibrium dynamics can be expected to demonstrate the thermostatistics seen in equilibrium systems. [Preview Abstract] |
Tuesday, November 22, 2005 1:11PM - 1:24PM |
NJ.00011: Improved Model for Traffic Flow R.M. Velasco, W. Marques Junior A second order phenomenological model is assumed in order to describe the behavior of vehicles in an unidirectional highway. The density and the average velocity of vehicles are considered as the macroscopic variables relevant to study the system. The traffic pressure is obtained by means of an iterative procedure and the corresponding constitutive equation contains the equilibrium pressure as well as a viscosity which depends on the density. The stability conditions, the phase velocity and the attenuation coefficient are studied. Also the numerical solution for the macroscopic variables is obtained. A close comparison with other models in the literature is done. [Preview Abstract] |
Tuesday, November 22, 2005 1:24PM - 1:37PM |
NJ.00012: Velocity statistics in 2D granular fluids M.D. Shattuck, P.M. Reis We report on the experimental velocity statistics in 2D granular fluids for three different geometries: horizontal uniformly heated, vertical heated from below, and rotated. We use stainless steel spheres (diameter D), confined by two glass plates. In the uniformly heated case, the plates are horizontal and separated by 1.6 D with a rough bottom plate which effectively transfers momentum from the vertical shaking into the horizontal plane. This allows us to study a large range of filling fractions. In the vertically heated case, the plates are vertical and separated by 1.05 D with a weight on top and a vertically vibrating bottom. In the rotating case, the wall are vertical with a separation of 1.6D and rotated about the horizontal. We compare and contrast the single particle velocity distributions in the various geometries and with standard kinetic theory assumptions. [Preview Abstract] |
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