Bulletin of the American Physical Society
2006 59th Annual Meeting of the APS Division of Fluid Dynamics
Sunday–Tuesday, November 19–21, 2006; Tampa Bay, Florida
Session AH: Granular Flows I: Rotating Flows* |
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Chair: Kimberley Hill, University of Minnesota Room: Tampa Marriott Waterside Hotel and Marina Florida Salon 6 |
Sunday, November 19, 2006 8:00AM - 8:13AM |
AH.00001: S shape of a granular pile in a rotating drum Nicolas Taberlet, Patrick Richard, John Hinch The shape of a granular pile in a rotating drum is investigated. Using Discrete Elements Method simulations we show that the ``S shape'' obtained for high rotation speed can be accounted for by the friction on the end plates. A theoretical model which accounts for the effect of the end plates is presented and the equation of the shape of the free surface is derived. The model reveals a dimensionless number which quantifies the influence of the end plates on the shape of the pile. Finally, the scaling laws of the system are discussed and numerical results support our conclusions. [Preview Abstract] |
Sunday, November 19, 2006 8:13AM - 8:26AM |
AH.00002: A mechanism for axial band formation in a rotating drum Wolfgang Losert, Michael Newey When granular particles, like sand or glass beads, of different sizes are mixed and rotated in a cylindrical drum they tend to segregate into alternating bands along the axis of the drum. We study the mechanism for the formation of these axial bands by studying the flowing surface of the material. The surface height profile is analyzed with a laser line, and the individual particle motions are analyzed by direct imaging with a high speed camera. We propose that the significant differences in surface flow speeds between large and small particles, and the degree of radial segregation are the key factors for the formation of axial band. Our model is consistent with both microscopy observation of individual particle dynamics, and how the banding phenomena scale with parameters. It is also used to analyze the fascinating oscillatory dynamics observed in mixtures of three particle sizes. [Preview Abstract] |
Sunday, November 19, 2006 8:26AM - 8:39AM |
AH.00003: Rapidly Rotated Granular Materials in a Cell with Fixed Walls Eric Corwin, Heinrich Jaeger, Sidney Nagel Sand in a spinning bucket takes a shape governed by the interplay of gravity, the sand's own yield stress, and centrifugal acceleration as the sand comes to rest with respect to the bucket.\footnote{M.E. Vavrek and G.W. Baxter, Phys. Rev. E 50, 3353 (1994)} However, if the walls of the bucket are fixed and only the bottom rotates it becomes impossible for the sand to be at rest with respect to all the boundaries of the bucket. Such a setup has been used for fluids at very high rotation rates in which strong shear forces break the axial symmetry of the fluid's surface and give rise to polygonal shapes rotating on the fluid's surface.\footnote{T.R.N. Jansson, et. al., Phys. Rev. Lett. 96, 174502 (2006)} A similar setup has been employed for granular materials at low rotation rates and negligible grain momentums and leads to the formation of very broad shear bands.\footnote{D. Fenistein and M. van Hecke, Nature 425, 256 (2003)} We report on an experimental study of granular materials in such a system in which we observe a series of changes in the shape of the material's surface as we move from a regime in which momentum is negligible to one in which it is important. At high shear rates we see the development of a void in the center of the cell. Similarly to the fluid case, we see instabilities developing on the surface of the granular material surrounding this void. [Preview Abstract] |
Sunday, November 19, 2006 8:39AM - 8:52AM |
AH.00004: Bulk Evolution During Axial Segregation and Coarsening In a Rotating Cylinder L. Sanfratello, E. Fukushima, S. Altobelli Axial segregation of granular material in a rotating drum is an incompletely understood phenomenon. Theories which cite only surface effects cannot account for the experimental observation that the radial core of the smaller particles may develop undulations which do not reach the surface of the system. These theories also fail to explain recent experimental results in which even large differences in the dynamic angle of repose between the constituents of a biparticulate system was insufficient to induce segregation. To help elucidate what is occurring in the bulk of the system during the formation of axial banding we used MRI to track core evolution at a temporal resolution of 2Hz. We tracked both the long-term development of the axial segregation and the later band coarsening within the bulk. Furthermore, we found differences in the velocity depth profiles along the length of the cylinder that depended on the axial composition profile. These differences may drive the segregation patterns we have observed in the bulk. Results for various rotation rates, cylinder lengths, particle concentrations, and initial conditions will be discussed. [Preview Abstract] |
Sunday, November 19, 2006 8:52AM - 9:05AM |
AH.00005: Free surface deformation of dry sand in hollow spinning cones Rocio Chicharro, Cesar Trevi\~no, Abraham Medina, Francisco J. Higuera In this work we have studied the free surface deformation of dry sand in hollow inverted conical cylinders which rotate axisymmetrically respect to the vertical axis. In these systems we show theoretically and experimentally that, for dimensionless angular velocities slightly above a critical Froude number, \textit{Fr}, (\textit{Fr=w}$^{2}L/g$>$f$ where $w$ is the angular velocity, $L$ is a length measured from the apex, $g$ is the gravity acceleration and $f$ is the friction coefficient), the rotation deforms the free granular surface but at higher rates the grains themselves are expelled outside the cones as spiral jets. Conditions for the occurrence of the ejection of a single grain also will be discussed. [Preview Abstract] |
Sunday, November 19, 2006 9:05AM - 9:18AM |
AH.00006: Power dissipation and fluidization in a vibrated/stirred granular flow James Gilchrist, Kenneth Ford, Hugo Caram We investigate flow of powders within a model high shear granulation process. High shear granulators typically produce flow by sweeping a pitched bladed under a granular bed at high rotation rates, providing both fluidization from upward lift from fast moving blades and flow in a circular motion. In our experimental setup, we partially decouple the fluidization and circulation by independently vibrating and stirring a deep granular bed. Without stirring, vibration begins to fluidize the bed when the Froude number, Fr $>$ 1. By attaching an accelerometer to the vessel, we measure the resulting time of flight. The deep granular bed primarily behaves as a solid mass at moderate Fr, and we compare the accelerometer data to a simple model of a bouncing mass on a spring. The stirring mechanism allows measurement of the power required to maintain a constant rotation rate. Without vibration, the power draw is linearly related to the rotation rate. At high Fr, the power requirements for stirring the fluidized bed decrease dramatically. At intermediate Fr, we observe a transition between dense granular flow and fluidized granular behavior with increased vibration and stirring by monitoring the power requirements for stirring. This transition marks the boundary between dense granular flow and fluidized granular flow, and suggests the degree to which stirring influences bulk fluidization. [Preview Abstract] |
Sunday, November 19, 2006 9:18AM - 9:31AM |
AH.00007: Subharmonic Square Waves for a Vibrated Powder Jean-Philippe Matas, Jun Uehara, Bob Behringer We describe experiments on vibrated powders in a gas environment. Because the powders are fine, typically about 60 $\mu m$ in diameter, the system is inherently two-phase in nature. In the experiments, we control the amplitude and frequency of shaking and the ambient pressure, P. At high enough accelerations, subharmonic waves appear. We focus on a novel wave form that consists of unusual and striking square waves. These waves appear in a narrow frequency window that depends on P. We analyze a simple model for Darcian flow in a porous medium to obtain a qualitative understanding of some of the wave properties. We find that the wave amplitude depends on the shaking amplitude and P. However, the wavelength appears to depend on the penetration depth for gas in the porous medium consisting of the grains. In particular, this leads to a qualitatively different form for the dispersion relation for the waves that has been seen in experiments, such as those by Melo et al. for granular subharmonic waves in vacuum. [Preview Abstract] |
Sunday, November 19, 2006 9:31AM - 9:44AM |
AH.00008: Comparison of granular and viscous swimmers Benjamin Robertson, Stephan Koehler, Raenell Soller Inspired by Purcell's fundamental investigations of swimming in viscous fluids, we built a robotic granular swimmer with two rotating paddles. We investigate two types of swimming strategies, which have either one or two degrees of freedom. The strategy with one degree of freedom consists of two steps and mimics the opening and closing of Purcell's scallop. We observe that the robot using the two- step scallop strategy can propel itself, which shows that unlike viscous fluids, quasi-static flows in granular media are not time reversible. The strategy with two degrees of freedom has four steps, where the rotation alternates between each paddle. The displacements using Purcell's four-step strategy are remarkably similar for granular and viscous swimming. Moreover, the four-step strategy is far more effective than the two-step strategy. [Preview Abstract] |
Sunday, November 19, 2006 9:44AM - 9:57AM |
AH.00009: Granular lubrication by adding small beads to sheared monodisperse granular beds Jessica Cook, Stephan Koehler, Raenell Soller We investigate the change in torque of a vane slowly rotating in a monodisperse granular bed when small beads are added. We find that torque decreases and slowly increases with time. Depending on the amount of lubricating beads that have been added, the torque can drop to a level comparable to the torque for a monodisperse bed of small beads. Moreover, the random fluctuations in the torque also decrease and approach those for a monodisperse bed of small beads and slowly increase with time. [Preview Abstract] |
Sunday, November 19, 2006 9:57AM - 10:10AM |
AH.00010: Density and Size Dependence of Dense Granular Flow K. Hill, J. Zhang We experimentally investigate the kinematics of dense granular mixtures in rotating drums to ascertain how the properties of the mixture components affect the kinematic details of the flow. Then, we discuss how differences in the kinematic details of the flow may in turn be responsible for observed differences in segregation behaviors for the different mixtures. In contrast with more energetic and sparse granular systems, in these dense flows, the velocity fluctuations - often associated with a granular temperature - scale inversely to the size of the beads and are independent of particle density. We show this supports the premise that the structure of the flow determines the size of the velocity fluctuations in these systems. For mixtures with higher concentrations of small particles, the reduction in velocity fluctuation appears related to a measurable increase in the mixture velocity. We show through a simple model how this may be responsible for certain segregation behaviors only seen in particle mixtures where the components differ in size. [Preview Abstract] |
Sunday, November 19, 2006 10:10AM - 10:23AM |
AH.00011: Kinematics of granular slurry Jiafeng Zhang, Kimberly Hill When mixtures of particles are rotated in a cylindrical drum, they first radially segregate and then axially segregate. Radial segregation has been shown to precede axial segregation and has been suggested as integrally tied to axial banding and pattern evolution. Recently, it has been shown that the rate of axial segregation increases dramatically when the interstitial fluid of air is replaced by water. Surprisingly, we have found the rate of radial segregation to decrease dramatically under the same conditions. To determine how the properties of the interstitial fluid affect the particle flow and also the segregation properties, we measure the kinematics of the particles with different interstitial fluids. We find that the flowing layer becomes thicker and the velocity and velocity fluctuations decrease dramatically when the interstitial fluid's viscosity increases. The difference in settling rate appears to affect radial segregation adversely, while the difference in velocity fluctuations appears to affect axial segregation positively. [Preview Abstract] |
Sunday, November 19, 2006 10:23AM - 10:36AM |
AH.00012: Relating Segregation Patterns and Symmetries in Chaotic Granular Flow Stephen Cisar, Steven Meier, Richard Lueptow, Julio Ottino Segregation patterns formed by time-periodic flow of polydisperse granular material (varying in particle size) in quasi-two-dimensional (quasi-2D) tumblers capture the symmetries of Poincar\'{e} sections, stroboscopic maps of the underlying flow, derived from a continuum model. The similarities are striking despite the fact that the model contains no information about particle properties. We study this phenomenon experimentally by using mixtures of bidisperse granular material in which the concentration of small particles is varied in quasi-2D tumblers with square and pentagonal cross-sections. Experimental segregation patterns can be connected to the dynamics of the underlying flow by an analysis of periodic points. Patterns vary with small particle concentration based on the location of both elliptic points that characterize islands of regular flow and hyperbolic points that characterize regions of chaotic flow seen in Poincar\'{e} sections. The calculation of the eigenvectors and unstable manifolds of hyperbolic points shows that lobes of segregated small particles stretch from hyperbolic points toward corners of the tumbler, demonstrating the connection between regions of chaotic flow and the shape of the segregation patterns. Furthermore, unstable manifolds map the shape of lobes of segregated particles. Funded by DOE, Office of Basic Energy Sciences and NSF. [Preview Abstract] |
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