Bulletin of the American Physical Society
2006 APS March Meeting
Monday–Friday, March 13–17, 2006; Baltimore, MD
Session U8: Granular Materials |
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Sponsoring Units: DFD Chair: Wolfgang Losert, University of Maryland Room: Baltimore Convention Center 314 |
Thursday, March 16, 2006 8:00AM - 8:12AM |
U8.00001: Statistical and dynamical properties of a vibrated granular polymer Arshad Kudrolli, Micah Veilleux, Mehran Kardar We investigate the structure and dynamics of granular polymers on a vibrated bed to test the applicability of models of self-avoiding random walks. The granular polymer is composed of a chain of hollow 3~mm steel beads connected by flexible links, and moves on a 30 cm diameter flat circular bed which is roughened by gluing a layer of 1 mm steel beads in order to give the chain random kicks in the vertical and horizontal directions. High speed digital imaging is used to track the position of the particles to a fraction of the bead diameter using a centroid technique. Using the identified bead positions, we analyze the motion of the center of mass over a time interval $\Delta t$, and its standard deviation as a function of chain length $L$. The standard deviation is consistent with a scaling of $\sqrt{\Delta t / L}$. The chain end-to-end distance scales as $L^\nu$, with $\nu\approx 3/4$ as for self-avoiding walks. The evolution of the scattering functions and the effect of the size of the container on the observed scaling will be also discussed. [Preview Abstract] |
Thursday, March 16, 2006 8:12AM - 8:24AM |
U8.00002: Power Spectra of Force Fluctuations in Granular Materials Under Shear Eric Corwin, Heinrich Jaeger, Sidney Nagel We measure the time-varying forces at the bottom surface of a granular system sheared at the top. The shear is applied by rotating a roughened piston while maintaining a constant, uniaxial compressive force. We report on the force autocorrelation and the corresponding power spectrum $S$ of the variation of force on individual grains at the bottom surface. These forces are obtained from video tracking of imprints in a pressure-sensitive birefringent layer across the bottom surface. Averaging over concentric annuli we find power-law behavior $S \sim 1/f^{\alpha}$ over several orders of magnitude in each annulus. The power law exponents $\alpha$ appear to be correlated with the in-plane shear strain rate. In our system friction with the stationary side walls introduces a radial gradient in the shear rate, which is maximum at the outer edge and zero at the center. The corresponding power law exponents suggest strict $1/f$ noise ($\alpha = 1$) at the outer, shearing edge and an increasing index as one approaches the center and the shear rate vanishes. [Preview Abstract] |
Thursday, March 16, 2006 8:24AM - 8:36AM |
U8.00003: Self-diffusion of particles in gas-driven granular layers with periodic flow modulation Carlos Orellana, Igor Aranson, Wai Kwok, Sergio Rica We study particles self-diffusion in gas-driven granular layers by high-speed fluorescent video-microscopy. We show that periodic flow modulation results in an enhancement of the particle's diffusion. The diffusion enhancement, which in turn is an indication of more efficient fluidization of the granular layer, is associated with the onset of disordered sub-harmonic patterns. Our measurements provide a sensitive characterization method of the fluidization properties of particulate/gas systems. [Preview Abstract] |
Thursday, March 16, 2006 8:36AM - 8:48AM |
U8.00004: Free cooling of the one-dimensional wet granular gas Vasily Zaburdaev, Martin Brinkmann, Stephan Herminghaus In the present work we consider a one-dimensional gas of hard balls covered with a thin liquid film. A liquid bridge, formed at each collision, is responsible for the hysteretic and dissipative interaction. Each rupture of a liquid bridge requires a fixed amount of energy, and thus determines a threshold of relative velocities below which the two colliding particles form a bounded state loosing their relative kinetic energy. We aim to study the cluster formation process in the free cooling system. Macroscopic laws of energy dissipation and cluster growth are studied in this model on the basis of numerical simulations supported by a scaling-like system of equations. We show that the sticky gas regime is an attracting asymptotic limit of the wet granular gas and does not dependent on the liquid bridges strength. The next neighbor velocities correlations play the key role in the establishing of this regime. [Preview Abstract] |
Thursday, March 16, 2006 8:48AM - 9:00AM |
U8.00005: A Theory of Stochastic Plasticity in Dense Granular Flow Ken Kamrin, Martin Bazant There have been many attempts to derive continuum models for dense granular flow, but a general theory is still lacking, which can describe different flow conditions, such as gravity-driven silo drainage and forced shear cells. Here, we start with Mohr-Coulomb plasticity for quasi-2d granular materials to calculate stresses and slip planes, but we propose a simple ``stochastic flow rule'' to replace the principle of co-axiality in classical plasticity. This formulation takes into account two crucial features of granular materials -- discreteness and randomness at the scale of a continuum element -- via diffusing ``spots'' which cause chain-like cooperative particle displacements, as in recent simulations of silo drainage. We postulate that spots perform random walks along slip lines, biased by body forces (gravity) and local fluidization (switch from static to dynamic friction). Stochastic plasticity allows a natural description of dense granular flows in silos and shear cells within a single theory, rooted in classical mechanics. [Preview Abstract] |
Thursday, March 16, 2006 9:00AM - 9:12AM |
U8.00006: The Solitary Wave Collision Problem in Granular Alignments Edgar Avalos, Surajit Sen, Jan Pfannes, T.R. Krishna Mohan Any impulse travels as a solitary wave in an alignment of spherical elastic grains where the system grains are barely in contact. These solitary waves are about 7 grain diameters wide. Their speeds depend upon the maximum displacement amplitudes associated with these waves. We focus on the dynamical problem associated with the collision of two identical and opposite propagating solitary waves. Interface and grain center collisions reveal markedly different dynamics. Solitary wave collisions lead to the destruction of the original waves and the subsequent creation of new smaller waves along with ``baby" or secondary solitary waves. In the absence of dissipation, these granular systems point towards the existence of a generalized equilibrium phase that involves Maxwellian distribution of velocities with no depedence on initial conditions but one that violates the equipartition theorem. [Preview Abstract] |
Thursday, March 16, 2006 9:12AM - 9:24AM |
U8.00007: Toward Zero Surface Tension Limit: Granular Fingering Instability in a Radial Hele-Shaw Cell Xiang Cheng, Lei Xu, Aaron Patterson, Heinrich Jaeger, Sidney Nagel Because of the absence of cohesive forces between grains, dry granular material can, in many respects, be thought of as a fluid with zero surface tension. In the zero surface-tension limit, viscous fingering is known to possess singular behavior. We have studied the viscous fingering instability in such a granular ``fluid.'' In our experiment, we use a conventional radial Hele-Shaw cell consisting of two parallel glass plates separated by a gap. Gas with controlled pressures is blown through a hole at the center of one glass plate and displaces the surrounding dry granular material. We have systematically studied the fingering pattern as a function of gas pressure, gap thickness, and grain size. Two stages are observed during pattern growth. In the first stage, we find fluid-like fingering. However, as opposed to normal fluids, the pattern is more ramified at low pressure. In the second stage, we find several new behaviors in the system such as merging and pinching off of fingers and the existence of satellite bubbles. [Preview Abstract] |
Thursday, March 16, 2006 9:24AM - 9:36AM |
U8.00008: Force fluctuations in collisional and frictional granular flows Emily Gardel, Efrosyni Seitaridou, Ellen Keene, Nalini Easwar, Narayanan Menon We make measurements of the force delivered to the wall in 2D and 3D flow geometries to explore the difference between collisional and frictional flows, and between flow geometries with and without velocity gradients in the flow direction. The distribution of force fluctuations has an exponential tail at large force in collisional flows, but falls off slower than an exponential in frictional flows. We do not see a clear signature in the force distribution of the approach to jamming and therefore the connection to force distributions in quasistatic flows remains to be understood. However, the temporal characteristics of the force fluctuations do show the approach to jamming. As reported earlier, the distribution of collision times tends to a power law in collisional flows. Similarly, the power spectrum of forces in frictional flows develops power-law behaviour at low frequencies as jamming is approached. Supported by NSF DMR 0305396 and NSF MRSEC DMR 0213695 [Preview Abstract] |
Thursday, March 16, 2006 9:36AM - 9:48AM |
U8.00009: Thermal collapse of a granular gas under gravity Lev S. Tsimring, Dmitri Volfson, Baruch Meerson Free cooling of a gas of inelastically colliding hard spheres is a central paradigm of the kinetic theory of granular gases. At zero gravity the temperature of a freely cooling homogeneous granular gas follows a power law in time. How does gravity affect the cooling? We consider a semi-infinite layer of granular gas bounded from below by an elastic wall. An initially isothermal dilute granular gas is prepared in the state of hydrostatic equilibrium with barometric density distribution. We combine molecular dynamics simulations, a numerical solution of granular hydrodynamic equations and an analytic theory to show that the cooling gas undergoes thermal collapse: it condenses on the bottom of the container and cools down to zero temperature in a finite time $t_c$ as $T\sim (t_c-t)^2$. The cooling scenraio is determined by the interplay between the collisional energy loss and heat conduction, while the collapse time $t_c$ is much longer than the typical free fall time of the grains if the inelasticity of the particle collisions is small. The hydrodynamic description is found to be in excellent agreement with molecular dynamics simulations until very close to $t_c$. [Preview Abstract] |
Thursday, March 16, 2006 9:48AM - 10:00AM |
U8.00010: Two particle contact lifetime distribution in gravity driven granular flow Robert Brewster, Leonardo Silbert, Gary Grest, Alex Levine The distribution of two particle contact life times for gravity driven granular flow down an inclined plane are determined from large-scale, three-dimensional discrete element simulations. Results are presented for both cohesive and non-cohesive particles for Hertzian and Hookean contact forces. The distribution of lifetimes is analyzed as a function of height from the surface for different strength $k_n$ of the normal force, coefficient of restitution $e_n$ and coefficient of friction $\mu$. In addition a generalized form of the Bagnold constitutive relation in which the shear stress depends on a sum of terms that are linear and quadratic in the shear rate is proposed for cohesive granular flows. The linear term represents a new mode of momentum transport made possible through the long lived contacts in the network while the quadratic term represents the usual Bagnold contribution from short time scale collisions. For non-cohesive grains, the strength of the linear term disappears as strength of the normal interaction $k_n$ increased. [Preview Abstract] |
Thursday, March 16, 2006 10:00AM - 10:12AM |
U8.00011: Particle collisions in a granular gas Hong-Qiang Wang, Klebert Feitosa, Narayanan Menon We report a study of particle collisions in a 2D granular system vibrated in a vertical plane. We have previously studied this experimental system in a variety of contexts. With improved image analysis algorithms, we are able to locate particles with enough precision to allow detailed tracking of the collision process, when the particles are close to each other. This allows us to better study the role of the vertical walls in the collision process and to place a limit on the dissipation by mechanisms other than inelastic collisions. We report the distribution of collision parameters and comment on violations of molecular chaos resulting from the inelasticity of the system. [Preview Abstract] |
Thursday, March 16, 2006 10:12AM - 10:24AM |
U8.00012: Boltzmann's \textit{stosszahlansatz }generalized for granular contact forces Philip Metzger Is there a valid way to generalize Boltzmann's \textit{stosszahlansatz }(molecular chaos), the assumption that colliding molecules are not statistically correlated before the collision takes place, to the case of granular contact forces in a static packing? In thermal statistical mechanics the assumption produces a transport equation that obtains the density of single particle states and the Maxwell Boltzmann distribution. The problem in generalizing this to granular contact forces is that we must maintain the spatial symmetries of granular packing ensembles, which is not trivial. The essential trick is to sum the density of states over all particle exchanges, which destroys multi particle state information but maintains the distribution of single particle states. This summation transforms the equations into a generalized form of boson statistics. I will show that, in the summation, the first shell approximation of the fabric is transformed into the properly symmetric version of Boltzmann's \textit{stosszahlansatz}. This produces a transport equation that obtains the density of single particle states and hence the distribution of granular contact forces. Granular simulation data will also be presented to validate the theory. [Preview Abstract] |
Thursday, March 16, 2006 10:24AM - 10:36AM |
U8.00013: Dynamical Heterogeneity close to the Jamming Transition in a Sheared Granular Material Olivier Dauchot, Guillaume Marty, Giulio Biroli The dynamics of a bi-dimensional dense granular packing under cyclic shear is experimentally investigated close to the jamming transition. Measurement of multi-point correlation functions are produced. The self-intermediate scattering function, displaying slower than exponential relaxation, suggests dynamic heterogeneity. Further analysis of four point correlation functions reveal that the grain relaxations are strongly correlated and spatially heterogeneous, especially at the time scale of the collective rearrangements. Finally, a dynamical correlation length is extracted from spatio-temporal pattern of mobility. Our experimental results open the way to a systematic study of dynamic correlation functions in granular materials. [Preview Abstract] |
Thursday, March 16, 2006 10:36AM - 10:48AM |
U8.00014: The Decorated Tapered Chain as a Granular Shock Absorber Robert Doney, Surajit Sen, Dorian DiCocco A 1$D$ alignment of progressively shrinking spherical grains (a tapered chain) turns out to be an excellent impulse absorber with rich nonlinear dynamical behavior. Here we discuss a tapered chain with interstitial grains between every sphere of the original tapered chain and demonstrate analytically (using the hard sphere approximation), numerically and experimentally that the shock absorption ability of the ``decorated" system is far superior to that of the system without the interstitial grains. [Preview Abstract] |
Thursday, March 16, 2006 10:48AM - 11:00AM |
U8.00015: Shock Absorption by Small, Scalable, Tapered Granular Chains Jan Pfannes, Adam Sokolow, Robert Doney, Masami Nakagawa, Juan Agui, Surajit Sen Making shock proof layers is an outstanding challenge. Elastic spheres are known to repel softer than springs when gently squeezed but develop strong repulsion upon compression and the forces between adjacent spheres lead to \textit{ballistic-like} energy transfer between them. Here we demonstrate for the first time that a \textit{small alignment} of progressively shrinking spheres of a strong, light-mass material, placed horizontally in an appropriate casing,$^{ }$can absorb $\sim $ 80{\%} ($\sim $90{\%}) of the incident force (energy) pulse. The system can be scaled down in size. Effects of varying the size, radius shrinkage and restitutive losses are shown via computed ``dynamical phase diagrams.'' [Preview Abstract] |
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