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 FJ: Granular Media: Patterning & Mixing |
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Chair: Kimberly Hill, University of Minnesota Room: Hilton Chicago Williford C |
Monday, November 21, 2005 8:00AM - 8:13AM |
FJ.00001: Noise strength in shaken granular media near onset Jennifer Kreft, Jack B. Swift, Harry L. Swinney The effects of fluctuations in Rayleigh-Benard (RB) convection near the onset of long range order have been found to be described well by the stochastic Swift-Hohenberg (SH) equation with a noise strength proportional to $kT$ [J. Oh and G. Ahlers, Phys. Rev. Lett. \textbf{91}, 094501, (2003)]. Similar behavior has been found in vertically oscillated granular material where the thermal fluctuations are negligible [D. I. Goldman, \emph{et al}., Phys. Rev. Lett.\textbf{92}, 174302, (2004)]. We conjecture that fluctuations in the granular system arise from the small number of particles per wavelength, typically of order $10$, in contrast to the $~10^6$ particles per wavelength in RB convection. Here, we investigate the onset of patterns in an event-driven molecular dynamics simulation of vertically oscillated frictional hard spheres, and we use the SH equation to quantify the strength of the noise for different wavelengths. We show that the noise decreases as the wavelength increases, but is independent of layer depth, suggesting that only the fluidized grains on the surface of the bulk contribute. [Preview Abstract] |
Monday, November 21, 2005 8:13AM - 8:26AM |
FJ.00002: Spontaneous Patterning of Confined Granular Rods Jennifer Galanis, Daniel Harries, Dan Sackett, Wolfgang Losert, Ralph Nossal Vertically vibrated rod-shaped granular materials confined to quasi-2D containers self organize into distinct patterns. We find, consistent with theory and simulation, a density dependent isotropic-nematic transition. Along the walls, rods interact sterically to form a wetting layer. For high rod densities, complex patterns emerge as a result of competition between bulk and boundary alignment. A continuum elastic energy accounting for nematic distortion and local wall anchoring reproduces the structures seen experimentally. [Preview Abstract] |
Monday, November 21, 2005 8:26AM - 8:39AM |
FJ.00003: Granular Segregation with Anisotropic Particles Tim Sykes, Tom Mullin The results from experimental investigations of horizontally vibrated mixtures of anisotropic poppy seeds and long chains of linked spheres will be presented. A critical packing fraction was observed to be required to initiate a transition to segregation. The average size of the resulting patterns was measured and the concentration ratio of the mixtures was varied by changing the number of chains present in the mixtures. A change in the order of the transition, from second to first order with associated hysteresis, was observed as the chain number was reduced. This gave rise to three distinct regions of behaviour: segregated, mixed and a bi-stable state. [Preview Abstract] |
Monday, November 21, 2005 8:39AM - 8:52AM |
FJ.00004: Analysis of microstructures in a Brazil Nut Problem Jin Sun, Francine Battaglia, Shankar Subramaniam It is challenging to describe dense granular flow at a macroscopic level using continuum models. In an attempt to fulfill this goal, current research has been focused on revealing microscopic structural information on prevailing many-body collisions and force chain formations, which are important aspects of the microscopic behavior of dense granular flows and can be used to improve continuum models. Molecular dynamics for granular flow (also referred to as discrete element method) is used to simulate segregation of a large particle in a partially fluidized dry granular bed consisting of smaller particles with an imposed low frequency vibration, known as the Brazil nut effect. It will be shown that the force chains formed by wall friction play an important role in ascending the large particle. Cluster information including cluster number evolution and size distribution, coordination number and spatial distribution will be analyzed, which could be used as additional parameters in continuum models. [Preview Abstract] |
Monday, November 21, 2005 8:52AM - 9:05AM |
FJ.00005: Radial striping in granular mixtures: a positive feedback mechanism Z. Huang, J. Zhang, V. Mittal, K.M. Hill When mixtures of particles differing only in size (S-systems) or only in density (D-systems) are rotated in a circular drum, the components quickly un-mix, and a simple cylindrically symmetric segregation pattern forms. In D-systems the circularly symmetric segregation (`moon') pattern is stable for all drum fill levels. In contrast, in S-systems this simple segregation pattern will further evolve into a dramatic radial striping (`sun') pattern for drum fill levels near 50 percent. While the simple radial segregation pattern is considered well-understood, the mechanism driving the striped segregation pattern is not. In this talk we present experimental evidence that the growth of the stripes is driven by a positive feedback mechanism based on a concentration dependence of the velocity of the particles. This model is tested and supported using computational experiments using a continuum model based on these experimental observations. [Preview Abstract] |
Monday, November 21, 2005 9:05AM - 9:18AM |
FJ.00006: Microscopic properties and initial transients of the banded state in a rotated drum of granular material Michael Newey, Wolfgang Losert We study the microscopic properties of the banded state of steel and glass beads in a rotated cylindrical drum. Imaging the top surface of the flow we can extract average velocity, drift, and diffusion. We study these properties from the start of rotation and throughout the band formation. We find that large particles begin to flow significantly faster at the region where a small particle band will form even before visible band formation. Contrary to what is expected by most modeling of the problem, we do not find any overall surface drift of small particles into like bands. We do find, however, an interesting pattern of particle drift as the particles flow down the surface. The velocity increase and the drift results show the critical importance of subsurface dynamics in driving the band formation. [Preview Abstract] |
Monday, November 21, 2005 9:18AM - 9:31AM |
FJ.00007: Dynamics of Axial Segregation in Granular Slurries: Influence of Viscosity, Aspect Ratio and Periodic Tilting explored via Parallel Experiments Stanley Fiedor, Paul Umbanhowar, Julio Ottino Flowing granular matter tends to segregate when particle properties such as size or density vary. In partially filled rotating tumblers, particles segregate perpendicular to the axis of rotation (radial segregation). In longer tumblers, binary particle mixtures may also form bands which are alternately rich and lean in one component (axial segregation). This process is accelerated in wet granular systems. Performing experiments in parallel, we investigate the influence of the interstitial fluid viscosity, cylinder length at fixed radius, and periodic tilting on the formation and long term dynamics of the bands. Changing the viscosity produces the most dramatic results: band formation time decreases with increasing viscosity and asymptotes for viscosities greater than about 4 cS, but the number of bands is maximized for a viscosity of approximately 3 cS. Surprisingly, periodic rocking of the cylinder at the rotation frequency does not influence band formation or long term dynamics even with maximum displacements of twice the tumbler radius. [Preview Abstract] |
Monday, November 21, 2005 9:31AM - 9:44AM |
FJ.00008: Particle-size segregation in granular avalanches Michael Shearer Particle size segregation in avalanches occurs through shearing within the granular flow. In such a flow, large particles migrate upwards, their vacated spaces being filled by smaller particles. Gray and Thornton recently proposed a simple model to capture this segregation, based on conservation of mass for two-phase flow, and basic mixture theory. The equation is a scalar conservation law in two space variables and time, but with variable coefficients corresponding to the spatially dependent velocity in shear flow. In this talk, I describe initial boundary value problems for this equation, and show numerical simulations. In simple circumstances, the problem can be solved explicitly, by combining basic multidimensional solutions to understand the overall flow and segregation. Interfaces with large particles below small are physically unstable, and this property can be explained mathematically. Indeed, unstable interfaces provide the richest multidimensional structures, one of which is analyzed in this talk. [Preview Abstract] |
Monday, November 21, 2005 9:44AM - 9:57AM |
FJ.00009: Discrete Models for Mixing in 2D Granular Tumblers Stephen E. Cisar, Richard M. Lueptow, Julio M. Ottino An effective method to study mixing of granular materials in a variety of cases is through the use of discrete models. We study the mixing of granular materials in 2D tumblers rotating in the avalanching regime using two different discrete models. First, since mixing in the avalanching regime is well suited for a geometric interpretation, we use a model based on mapping of wedge avalanches along with random mixing within the wedge. Second, we develop a cellular automata (CA) model based on comparing the heights of columns of particles in the CA grid that results in irregular avalanching and mixing of particles. We compare mixing of like particles in tumblers of various shapes and fill levels using both models. Mixing rates for half-full tumblers demonstrate a strong dependence on the symmetries of the tumbler shape. More than half-full tumblers contain a core of unmixed particles with a shape that changes with fill level. Together with the overlapping of wedges, this results in multiple extrema when the mixing rate is plotted as function of fill level. While the two models produce qualitatively similar results, the cellular automata model is substantially more flexible and typically runs in about 1/10$^{th}$ of the time. [Preview Abstract] |
Monday, November 21, 2005 9:57AM - 10:10AM |
FJ.00010: Surface wave assisted assembly of multi-segment magnetic structures Alexey Snezhko, Igor Aranson, Wai-Kwong Kwok A new type of multi-segment magnetic self-assembled structures induced in a magnetic granular media at the surface of water by an alternating magnetic field is reported. We demonstrate that these structures are directly related to surface waves in the liquid generated by the collective response of magnetic microparticles to the alternating magnetic field. A large-scale vortex flows are generated in the vicinity of the generated structure.The flow can be as fast as $2$cm/sec and depends on the magnetic field parameters. In addittion, the segments of magnetic ``snake'' exhibit long-range antiferromagnetic ordering mediated by the surface waves, while each segment is composed of ferromagnetically aligned chains of microparticles. [Preview Abstract] |
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