Bulletin of the American Physical Society
APS March Meeting 2014
Volume 59, Number 1
Monday–Friday, March 3–7, 2014; Denver, Colorado
Session J17: Granular Materials |
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Sponsoring Units: GSNP Chair: Robert Behringer, Duke University Room: 402 |
Tuesday, March 4, 2014 2:30PM - 2:42PM |
J17.00001: Developing a Magnetic Resonance Imaging measurement of the forces within 3D granular materials under external loads Stefan Elrington, Thibault Bertrand, Merideth Frey, Mark Shattuck, Corey O'Hern, Sean Barrett Granular materials are comprised of an ensemble of discrete macroscopic grains that interact with each other via highly dissipative forces. These materials are ubiquitous in our everyday life ranging in scale from the granular media that forms the Earth's crust to that used in agricultural and pharmaceutical industries. Granular materials exhibit complex behaviors that are poorly understood and cannot be easily described by statistical mechanics. Under external loads individual grains are jammed into place by a network of force chains. These networks have been imaged in quasi two-dimensional and on the outer surface of three-dimensional granular materials. Our goal is to use magnetic resonance imaging (MRI) to detect contact forces deep within three-dimensional granular materials, using hydrogen-1 relaxation times as a reporter for changes in local stress and strain. To this end, we use a novel pulse sequence to narrow the line width of hydrogen-1 in rubber. Here we present our progress to date, and prospects for future improvements. [Preview Abstract] |
Tuesday, March 4, 2014 2:42PM - 2:54PM |
J17.00002: Imaging Forces in a Three-Dimensional Granular Material Joshua Dijksman, Nicolas Brodu, Hu Zheng, Robert Behringer We experimentally study the quasi-static deformation of three-dimensional sphere packings subjected to macroscopic deformation. We perform these experiments on slightly polydisperse, nearly frictionless soft hydrogel spheres in a modified tri-axial shear apparatus. We resolve the microscopic force network in a this three dimensional packing of spheres through imaging the entire packing. By resolving particle deformations via custom written image analysis software, we extract all particle contacts and contact forces. In addition, we measure boundary stresses during compression and shear. We address the non-linear force response of a disordered packing under compression, force network dynamics and explore the plastic rearrangements inside cyclically sheared and compressed packings. [Preview Abstract] |
Tuesday, March 4, 2014 2:54PM - 3:06PM |
J17.00003: Quantitative DEM of granular packings Nicolas Brodu, Joshua Dijksman, Robert Behringer We introduce a new model for simulating granular assemblies. This model explicitely accounts for the cross-influence of multiple contacts on grains. It maintains the surface deformations of the grains induced by the contacts, improving on the classical non-deformable interpenetrable spheres model, for a reasonable computational cost. We show that both multiple contacts and surface deformations are necessary for reproducing quantitatively the 3D force measurements we recently demonstrated. We also show that friction has a dramatic effect on the forces and number of contacts, so it cannot be ignored even for very small values. [Preview Abstract] |
Tuesday, March 4, 2014 3:06PM - 3:18PM |
J17.00004: Collisional Model for Granular Impact Dynamics Alec Petersen, Abram Clark, Robert Behringer When an intruder collides with a granular material, the grains exert a stopping force which decelerates the intruder. A macroscopic force law, dominated by a $v^2$ drag term, is often used to characterize this decelerating force. However, a description which connects this drag force to grain-scale dynamics is still lacking, due in part to difficulty in obtaining sufficiently fast data at the grain scale. We present experiments using photoelastic particles and a high-speed camera, which capture the intruder dynamics and local granular force response at fast time scales. This allows us to analyze our experiments using both the macroscopic force law, and microscopically, where we observe large fluctuations at small space and time scales. Thus the intruder deceleration is not smooth and steady, but dominated by intermittent collisions with clusters of grains. Based on this, we present a model for the velocity-squared drag force in terms of these intermittent collisions we observe. We show that this model captures the shape-dependence of the $v^2$ drag force, as well as off-axis rotation. Therefore the microscopic assumptions of our model are confirmed, and may provide insight into other dense, driven granular flows. [Preview Abstract] |
Tuesday, March 4, 2014 3:18PM - 3:30PM |
J17.00005: Effect of Mach number on granular impacts Abe Clark, Alec Petersen, Lou Kondic, Robert Behringer When an object strikes a granular material, its momentum and energy are transferred to the grains and dissipated. An important dimensionless parameter in such impacts is $M$, the ratio of the intruder speed, $v_0$, to a typical granular sound speed, $c$. In many previous studies, $M$ has been very small, $M\sim 10^{-2}$. In this regime, the granular force on the intruder is dominated by a $v^2$ drag term, leading to a smooth, monotonic deceleration of the intruder. To probe the regime closer to $M\sim 1$, we perform experiments (and matching simulations) with granular materials comprised of photoelastic disks of varying stiffness, where softer particles allow us to reduce the granular sound speed. As we increase $M$, we reach a regime for which the intruder dynamics are no longer described by $v^2$ drag, but rather show a shock-like front which behaves elastically in response to the impact. Surprisingly, for the higher $M$ impacts ($M\sim 10^{-1}$), penetration depth is greatly reduced compared to the smaller $M$ impacts ($M\sim 10^{-2}$), and the intruder typically rebounds temporarily, before coming to rest. We understand the transition from $v^2$ drag to damped elastic behavior in terms of grain-grain collision time compared to the time for the intruder to move one grain size. [Preview Abstract] |
Tuesday, March 4, 2014 3:30PM - 3:42PM |
J17.00006: Velocity Regimes for Sphere Penetration of Granular Materials Mehdi Omidvar, Stephan Bless, Ivan Guzman, Magued Iskander Penetration of granular materials as a function of velocity is made complex by transitions where one or another physical process is dominant. At the lowest velocity, bearing resistance (which depends on friction and depth) is dominant, then dynamic Coulomb friction, then inertial resistance, then particle crushing. There is also a special regime where resistance is very high during the first radius of penetration, probably due to shock wave effects. These transitions are very evident in penetration of dry sand, between 0 and 300 m/s, as revealed by measurements of deceleration and the final depth of penetration. With crushed quartz particles, the particle crushing regime is not observed. Additionally, in saturated sand, the crushing regime appears to be suppressed. The regime where particles are crushed corresponds to an increase in penetration resistance, and this plays a large role in the relative difficulty in penetration of dry as opposed to wet materials. Measurements of deceleration give rise to estimates of average stress in the granular materials. For the case of sand, the threshold for comminution is at about 100 MPa, and this is also where significant crushing of sand is seen in triaxial compression experiments. [Preview Abstract] |
Tuesday, March 4, 2014 3:42PM - 3:54PM |
J17.00007: Impact and crater formation in an inhomogeneous granular medium Philip Drexler, Nathan Keim, Paulo Arratia Non-circular impact crater shapes, including polygons, have been observed on many terrestrial planets as well as moons and asteroids. In this talk, we investigate how the impact of a spherical projectile on a granular bed (sand) is affected by inhomogeneity of the bed. To create inhomogeneity, we locally inject nitrogen gas beneath the bed to balance the hydrostatic pressure of the sand. Our experimental results show that in low energy impacts and when the inhomogeneity is within two ball diameters of the impact, the sphere is deflected and rotated, and the resulting crater is non-circular. We characterize these behaviors as a function of drop height and location of the impact relative to the inhomogeneity, and we relate our findings to a model of forces in granular impact. [Preview Abstract] |
Tuesday, March 4, 2014 3:54PM - 4:06PM |
J17.00008: Dense Suspension Splash Wendy Zhang, Kevin M. Dodge, Ivo R. Peters, Jake Ellowitz, Martin H. Klein Schaarsberg, Heinrich M. Jaeger Upon impact onto a solid surface at several meters-per-second, a dense suspension plug splashes by ejecting liquid-coated particles. We study the mechanism for splash formation using experiments and a numerical model. In the model, the dense suspension is idealized as a collection of cohesionless, rigid grains with finite surface roughness. The grains also experience lubrication drag as they approach, collide inelastically and rebound away from each other. Simulations using this model reproduce the measured momentum distribution of ejected particles. They also provide direct evidence supporting the conclusion from earlier experiments that inelastic collisions, rather than viscous drag, dominate when the suspension contains macroscopic particles immersed in a low-viscosity solvent such as water. Finally, the simulations reveal two distinct routes for splash formation: a particle can be ejected by a single high momentum-change collision. More surprisingly, a succession of small momentum-change collisions can accumulate to eject a particle outwards. [Preview Abstract] |
Tuesday, March 4, 2014 4:06PM - 4:18PM |
J17.00009: Quasi-2D dynamic jamming of cornstarch suspensions Ivo Peters, Heinrich Jaeger A dense suspension of cornstarch in water has the extraordinary behavior that, when perturbed lightly, it behaves like a liquid, but, when impacted at high velocities, the material solidifies. Waitukaitis et al. (Nature, 2012) have shown that this behavior is due to a dynamic jamming front that propagates through the system. The details of this jamming front, however, are obscured by the surrounding suspension in a 3-dimensional system. In our current experiment, we prepare a layer (thickness order 1 cm) of the cornstarch suspension, which floats on a dense, low-viscosity liquid. This setup provides a stress-free boundary condition on the bottom and upper surface of the suspension. The floating suspension is bounded at three sides by solid walls, and on one side by a thin rubber sheet. We perturb the system by impacting an object horizontally on one side at a controlled velocity using a linear actuator. Tracer particles sitting on the top surface of the suspension allow us to perform PIV on the perturbed suspension. From the PIV analysis we determine the shape of the jammed region, the growth rate, shear rates, and the expected force response due to the added mass. We compare this to direct force measurements and determine which components make up the total force response. [Preview Abstract] |
Tuesday, March 4, 2014 4:18PM - 4:30PM |
J17.00010: Transiently Jammed State in Shear Thickening Suspensions under Shear Shomeek Mukhopadhyay, Benjamin Allen, Eric Brown We examine the response of a suspension of cornstarch and water under normal impact at controlled velocities. This is a model system to understand why a person can run on the surface of a discontinuous shear thickening fluid. Using simultaneous high-speed imaging of the top and bottom surfaces along with normal force measurements allows us to investigate whether the force response is a result of system spanning structures. We observe a shear thickening transition where above a critical velocity the normal force increases by orders of magnitude. In the high force regime the force response is displacement dependent like a solid rather than velocity dependent like a liquid. The stresses are on the order of $10^6$ $Pa$ which is enough to hold up a person's weight. In this regime imaging shows the existence of a solid like structure that extends to the bottom interface. [Preview Abstract] |
Tuesday, March 4, 2014 4:30PM - 4:42PM |
J17.00011: Dilation dynamics of granular suspensions during the shear thickening transition Qin Xu, Sayantan Majumdar, Heinrich Jaeger We experimentally investigate the dilation dynamics of dense granular (non-Brownian) suspensions under shear. We focus on the scenario where the packing fraction is close to the dynamic jamming point and combine oscillatory rheological measurements with \emph{in situ} high-speed imaging to study the particle dynamics throughout the shear-thickening (ST) transition. By visualizing the shear profile at different strain amplitudes, we show that, although frustrated dilation is the dominant factor for ST in granular suspensions, viscous hydrodynamic stress $\tau_\mu$ still plays an important role in determining the velocity profile and shear localization during the dilation process. Moreover, when the suspending liquid becomes highly viscous, $\tau_\mu$ affects the magnitude of the stress increment. By imaging the air-suspension boundary during shear, we demonstrate that the upper stress limit of the observable ST regime in suspensions of hard particles corresponds to the point where the confining pressure due to capillary forces is exceeded, as signaled by movement of the contact line between suspension and substrate. [Preview Abstract] |
Tuesday, March 4, 2014 4:42PM - 4:54PM |
J17.00012: Particle-Laden Liquid Bridge: Simulation and Experiment Mark D. Shattuck, Zhusong Li, Jeffery F. Morris, Marc Miskin, Heinrich Jaeger Particle-laden fluids like pastes are important in many industries, but they are not well understood. We developed coordinated experimental and computational techniques to explore the flow behavior of these systems. Due to surface tension fluids can be suspended between the flat ends of two cylinders in a ``liquid bridge.'' In experiments, we vary the gap height and measure the forces and bridge shape to determine the response of the particle-laden fluid. We simulate the liquid bridge using a new hybrid technique combining direct particle trajectory calculations with a grid based model for the surface of the fluid. The model is appropriate for flows that are slow compared to the speed of sound in the fluid and flows in which the fluid can move freely between the particles. By combining experiments and simulation we have unprecedented access to information on both particle details and overall fluid response to external stress. [Preview Abstract] |
Tuesday, March 4, 2014 4:54PM - 5:06PM |
J17.00013: Onset of motion at the surface of a porous granular bed by a shearing fluid flow Anyu Hong, Mingjiang Tao, Arshad Kudrolli We will discuss an experimental investigation of the onset of particle motion by a fluid flow over an unconsolidated granular bed. This situation arises in a number of natural and industrial processes including wind blowing over sand, sediment transport in rivers, tidal flows interacting with beaches and flows in slurry pipelines and mixing tanks. The Shields criteria given by the ratio of the viscous shear and normal stresses is used to understand the onset of motion. However, reviews reveals considerable scatter while noting broad trends with Reynolds Number. We discuss an idealized model system where fluid flows with a prescribed flow rate through a horizontal rectangular pipe initially fully filled with granular beads. The granular bed height decreases and reaches a constant height when the shear stress at the boundary decreases below a critical value. We compare and contrast the values obtained assuming no-slip boundary conditions with those observed with PIV using florescent tracer particles to measure the actual fluid flow profile near the porous interface. We will also report the observed variation of the Shields criteria with particle Reynolds Number by varying particle size and fluid flow rates. [Preview Abstract] |
Tuesday, March 4, 2014 5:06PM - 5:18PM |
J17.00014: A Microstructural View of Burrowing with Roboclam Kerstin Nordstrom, Dan Dorsch, Wolfgang Losert, Amos Winter, V Roboclam is a burrowing technology inspired by \textit{Ensis directus}, the Atlantic razor clam. The organism only has sufficient strength to burrow a few centimeters into the soil, yet razor clams dig to over 70 cm. The animal uses motions of its valves to contract and thereby locally fluidize the surrounding soil and reduce burrowing drag. Roboclam technology is valuable for subsea applications that could benefit from efficient burrowing, such as anchoring, mine detonation, and cable laying. We directly visualize the movement of soil grains during the contraction of Roboclam, using a novel index-matching technique along with particle tracking. We show that a previously developed mechanical theory for \textit{E. directus} describes the size of the failure zone around contracting Roboclam, provided that the timescale of contraction is sufficiently large. We also show that the nonaffine motions of the grains are a small fraction of the motion within the fluidized zone, affirming the relevance of a continuum model for this system, even though the grain size is comparable to the size of Roboclam. [Preview Abstract] |
Tuesday, March 4, 2014 5:18PM - 5:30PM |
J17.00015: Shear alignment and orientational order of shape-anisotropic grains Ralf Stannarius, Sandra Wegner, Bal\'azs Szab\'o, Tam\'as B\"orzs\"onyi Granular matter research was focused for a long time mainly on ensembles of spherical or irregularly shaped grains. In recent years, interest has grown in the study of anisometric, i.e. elongated or flattened particles [see e. g. B\"{o}rzs\"{o}nyi, Soft Matter 9, 7401 (2013)]. However, many related phenomena are still only little understood, quantitative experiments are scarce. We investigate shear induced order and alignment of macroscopic shape-anisotropic particles by means of X-ray computed tomography. Packing and orientation of individual grains in sheared ensembles of prolate and oblate objects (ellipsoids, cylinders and similar) are resolved non-invasively [T. B\"{o}rzs\"{o}nyi PRL 108, 228302 (2012)]. The experiments show that many observations are qualitatively and even quantitatively comparable to the behavior of well-understood molecular liquid crystals. We establish quantitative relations between aspect ratios and shear alignment. The induced orientational order influences local packing as well as macroscopic friction properties. [Preview Abstract] |
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