Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session AM: Granular Flows I |
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Chair: Michael Shearer, North Carolina State University Room: Salt Palace Convention Center 251 A |
Sunday, November 18, 2007 8:30AM - 8:43AM |
AM.00001: Optimal resistance in impact and penetration of parallel rods in a granular medium Yang Ding, Lionel London, Mateo Garcia, Daniel Goldman Inspired by foot and toe morphology in sand-running lizards, we study in laboratory experiment and experimentally validated Molecular Dynamics (MD) simulation the resistance force during penetration of parallel rods (diameter $1.27$ cm) into a granular medium of plastic spheres (diameter $d=0.6$ mm) as a function of rod separation $l$. We measure the normal force exerted on the rods by the medium both during normal penetration at constant velocity ($\approx 10$ cm/sec) and during normal impact after freefall (impact velocity $\approx 2.5$ m/sec). For constant velocity penetration, the resistance force increases linearly with increasing penetration depth. The slope of this curve (force/depth) displays a maximum as a function of $l$ at $l \approx 1.6d$. In the impact studies, we observe a maximum in the collision force at $l \approx 1.6d$ and a minimum in penetration depth at $l \approx 2d$. The extrema are correlated with an increase in lateral force between the rods indicating that jammed grains increase the effective surface area during penetration. [Preview Abstract] |
Sunday, November 18, 2007 8:43AM - 8:56AM |
AM.00002: Dynamics of the Jamming Transition. Mahesh Bandi, Andras Libal, Michael Rivera, Robert Ecke We experimentally study the force fluctuations felt by a disk as it is dragged through a two-dimensional bi-disperse system of randomly packed disks. The fluctuations are studied as a function of packing fraction where the system goes from an unjammed to a jammed state with increasing packing fraction. As the system approaches the Jamming Point, the fluctuations are expected to diverge and become increasingly intermittent. The primary interest of this experimental work is to characterize the nature of the Jamming transition by analyzing the force fluctuations felt by the disk as it approaches the jammed state. We present the probability distribution functions and other statistical measures of jamming for many different packing fractions. [Preview Abstract] |
Sunday, November 18, 2007 8:56AM - 9:09AM |
AM.00003: Jamming in Hopper Flow Sepehr Sadighpour, Paul Mort, R.P. Behringer It known that the flow rate, $\dot{m}$, of sand from a hopper is independent of the amount of material in the hopper due to stress screening. This is the basis for the Beverloo equation which relates $\dot{m}$ to an effective fluidized region near the outlet. We use the screening idea to characterize the probability of jamming for flow from a hopper. We focus on the probability $P_s(t) = 1 - P_j(t)$ that flow has continued without a jam, a `survival' probability. Screening suggests that in time $dt$, the jamming probability is $dP_j = dt/T$, where $T$ is a constant characteristic time. Simple analysis gives $P_s(t) = \exp (-t/T)$ where $t$ is the time since the start of flow. We can also write $P_s(M) = \exp [-M/(\dot{m}T)]$, where $M$ is the mass that has flowed out. We have carried out experiments in a quasi-2D hopper to test this idea. Our sand grains are photoelastic disks confined between two Plexiglas sheets. We obtain two types of data, first, data for $s_(t)$ and second, photoelastic images showing the force structures within the hopper during flow. We find that $P_s$ is well described by an exponential. Ongoing work seeks to relate $T$ to the properties of the material near the outlet. [Preview Abstract] |
Sunday, November 18, 2007 9:09AM - 9:22AM |
AM.00004: Studies in a 2D granular pure shear experiment Jie Zhang, Peidong Yu, Trush Majmudar, Robert Behringer We have performed two dimensional granular experiments under pure shear using bidisperse photo-elastic disks. Starting from a stress free state, a squre box filled with granular particles is subject to shear. The forward shear involved thirty steps, leading to maximum strain of 0.1. The network of force chains gradually built up as the strain increased, leading to increased pressure and shear stress. Backward shear was then applied to return the system to zero strain in the next thirty steps. Following each change of the system, contact forces of individual disks were measured by applying an inverse algorithm. We also kept track of the displacement and angle of rotation of every particle from frame to frame. We present the results for the contact forces, particle displacement, particle rotations, fabric, etc. Work supported by NSF grant DMR0555431. [Preview Abstract] |
Sunday, November 18, 2007 9:22AM - 9:35AM |
AM.00005: Sliding Friction on a 2D Photoelastic Granular Bed Peidong Yu, Robert Behringer We describe experiments to characterize the stick-slip nature of granular friction. In the experiment, a slider is pulled by a spring moving at constant speed across the top of a 2D granular bed of photoelastic particles confined to a vertical channel. The pulling force is measured synchronously with image acquisition of the granular bed taken by a camera moving along with the slider. Typical stick regimes yield a characteristic elasticity for the combined material and spring. From the known spring constant, we deduce the granular elasticity. Slip occurs when one or more force chains fail. On the basis of these observations, we develop a multi-spring model for the data. [Preview Abstract] |
Sunday, November 18, 2007 9:35AM - 9:48AM |
AM.00006: Particle-size segregation in granular flow: a conservation law in two space dimensions. Michael Shearer Kinetic sieving is the process by which large particles rise in granular avalanches, while smaller particles fall. Recent models of this effect reduce to a scalar conservation law in two dimensions and time, but with non-constant coefficients, reflecting the shear needed to induce segregation. Various topics of significance to applications are considered using the theory and constructions of scalar hyperbolic equations: steady solutions in which the direction of flow is time-like, leading to a sharp estimate of how long a chute should be to guarantee full segregation; breaking of interfaces, forming an evolving lens-shaped mixture zone; and the connection to recent experiments of Daniels on shear flow, for which the model is adjusted to account for nonuniform shear, with the consequent loss of constant solutions. [Preview Abstract] |
Sunday, November 18, 2007 9:48AM - 10:01AM |
AM.00007: 2D Granular Collapse: Experiments and Discrete Element Modelling Laurent Lacaze, Jeremy Phillips, Richard Kerswell We will discuss the 2D finite-time collapse under gravity of a monodisperse granular column which is one particle deep. Both laboratory experiments and discrete element modelling of such a configuration have been carried out. The final shape of the granular pile -- in particular the final height and the typical runout in the spreading direction - is investigated as a function of the initial aspect ratio a = H/W of the granular column (H being the initial height and W the initial length of the column in the spreading direction). Very good agreement is found between the numerical simulations and experimental data opening up the possibility of examining the dynamics of this fascinating transient flow in detail. [Preview Abstract] |
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