Bulletin of the American Physical Society
2005 APS March Meeting
Monday–Friday, March 21–25, 2005; Los Angeles, CA
Session L36: Focus Session: Granular Gases and Liquids I |
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Sponsoring Units: GSNP DFD Chair: Eli Ben-Naim, Los Alamos National Laboratory Room: LACC 510 |
Tuesday, March 22, 2005 2:30PM - 2:42PM |
L36.00001: Velocity statistics of a uniformly heated granular fluid Pedro M. Reis, Mark D. Shattuck We report results from an experimental investigation of a uniformly heated granular fluid. We vertically vibrate an ensemble of spheres (diameter $D$) confined by two horizontal glass plates. The top and bottom plates are separated by $1.6D$ which ensures a quasi-two dimensional configuration. We show that the use a rough, instead of flat, bottom plate has the considerable advantage of a more effective transfer of momentum from the vertical mode of the cell's vibration onto the motion of individual spheres in the horizontal plane. This allows a greater range of cell's filling fraction, $\phi$, to be explored. We study the single particle velocity distributions, $f(c)$, as a function of $\phi$ and vibration parameters; frequency and amplitude. In agreement with previous studies, we find a consistent overpopulation in the distribution's high energy tails, of the form $\log f \sim -c^{3/2}$. Moreover, we calculate the deviations from a Mawellian, $\Delta(c)=f(c)/f_{MB}(c)-1$, where $f_{MB}\sim\exp(-c^2)$. We find $\Delta(c)$ to be well described by a 4th-order polynomial which, however, is not the Sonine polynomial commonly used in the solution of the Enskog-Boltzmann equation for inelastic hard spheres driven by a stochastic thermostat. [Preview Abstract] |
Tuesday, March 22, 2005 2:42PM - 2:54PM |
L36.00002: Testing Kinetic Theory in a Driven Granular Gas Experiment for a Mechanically Fluidized Bed G. W. Baxter, J. S. Olafsen Robust Gaussian velocity statistics[*] and uncorrelated particle-particle velocities indicative of Molecular Chaos[**], are exhibited in a novel two-layer experiment in which a vertically shaken horizontal plate drives a layer of heavy coupled grains that, in turn, drive a layer of lighter monomer grains. While the experiment is clearly driven far from equilibrium, the dynamics are well-described by an analogy to equilibrium kinetic theory, providing a testbed for phenomena not easily observed in real molecular gases. Recent measurements have sought to test theoretical assertions concerning the relationship between pressure and temperature in granular gases as well as the conditions under which kinetic theory fails to describe inelastic hard sphere dynamics. The novel design also allows a variety of results from hard sphere molecular dynamics simulations to be tested in a real experiment including the relationships between temperature, pressure, and volume effects. [*] G. W. Baxter and J. S. Olafsen, Nature, 425, 680 (2003). [**] G. W. Baxter and J. S. Olafsen, submitted to Physical Review Letters. [Preview Abstract] |
Tuesday, March 22, 2005 2:54PM - 3:06PM |
L36.00003: Equipartition of energy for a gas-fluidized grain. A.R. Abate, D.J. Durian The dynamics of a sphere rolling in a nearly-levitating upflow of air are described perfectly by the Langevin equation [1]. Surprisingly, statistical mechanics is applicable and can be exploited to infer the nature of the forces at play in this driven mechanical system. To probe the flexibility of statistical mechanics we perturb the original experiment in three ways: first, we break the circular symmetry of the confining potential by using a stadium-shaped trap and observe if the velocity distributions remain circularly symmetric; second, we fluidize multiple grains of different density to check if each has the same effective temperature; and third, we fluidize two grains of different size and check to see whether statistical mechanics remains applicable. It is found that the velocity distributions are unresponsive to asymmetry in the trapping potential and that the effective temperature is independent of grain mass-density, so that statistical mechanics remains applicable. When grains differ in size beyond a critical ratio, however, statistical mechanics breaks down. [1] Ojha et. al., Nature 427, 521 (2004). [Preview Abstract] |
Tuesday, March 22, 2005 3:06PM - 3:42PM |
L36.00004: Experiments on long-time effective temperatures in granular fluids Invited Speaker: Studies of effective temperatures to describe the state of fluidization of a granular medium have emphasized kinetic granular temperatures determined from the instantaneous motions of grains. In this talk, I will focus on experiments that study effective temperatures derived from long-time grain dynamics. One formulation to extract long-time effective temperatures is via the fluctuation-dissipation relation, which is valid for linear response to small perturbations to near-equilibrium states; I will report briefly on experiments that study the applicability of this relation to vibrated and flowing granular media. I will then discuss in greater detail an effective temperature that emerges from consideration of the statistics of the power input to maintain the granular fluid in its nonequilibrium steady state. The analysis is done in the context of recent Fluctuation theorems\footnote{ G. Gallavotti, E.G.D. Cohen, Phys. Rev. Lett. \textbf{74}, 269 (1995).} that are proven for dynamical steady-states arbitrarily far from equilibrium. We have performed experiments\footnote{ K. Feitosa, N. Menon, Phys. Rev. Lett. \textbf{92}, 164301 (2004)} and simulations which show that power fluxes in our system satisfy the Fluctuation relation and that the pertinent effective temperature is an intensive variable. In the dilute, nearly-elastic regime, this effective temperature and the kinetic temperature follow each other as experimental parameters are varied. Beyond this regime, these temperature scales depart from each other. We speculate that the effective temperature remains a useful variable even in the regime where kinetic approaches to granular fluids no longer apply. [Preview Abstract] |
Tuesday, March 22, 2005 3:42PM - 3:54PM |
L36.00005: Shear banding of slowly sheared granular packings in an annular geometry J.C. Tsai, J.P. Gollub We investigate experimentally a quasi-static flow of glass beads packed and sheared in an annular channel under a constant normal load. The experiments utilize techniques of refractive-index-matched fluorescent imaging to determine the motion of individual particles inside the sheared packing.[1] The measured steady-state velocity fields have a dynamical range of five decades; parameters such as packing size and particle size are varied systematically. We demonstrate that crystalline ordering has a significant impact on the spatial gradient of grain velocity. Changing particle size does not influence the gradient of particle velocity significantly; the characteristic length for velocity decay does not show a direct scaling with particle size. Instead, the characteristic length for velocity decay decreases as the channel width is narrowed. By analyzing the measurements in this and other experimental systems of granular shear flows, we argue that the spatial scale for the decay of grain velocity should be geometry-specific; a heuristic model is proposed to explain the shear banding in this geometry. Supported by NSF-DMR-0405187 [1] Phys.Rev.E 70, 031303 (2004) [Preview Abstract] |
Tuesday, March 22, 2005 3:54PM - 4:06PM |
L36.00006: MRI Study of Granular Flow in a Split-Bottomed Couette Cell Xiang Cheng, Antonio Barbero, Matthias Mobius, Heinrich Jaeger, Sidney Nagel Recent studies of dense granular flow in a split-bottomed Couette geometry have brought new insights into the concept of shear bands in granular systems [1]. However, to date experimental results have primarily focused on the flow at the top surface of the system. Here we present a study of the 3- dimensional structure of shear band formed in such a geometry using magnetic resonance imaging (MRI). We show that the angular velocity profiles in horizontal plane follow an error function as observed at the top surface. By measuring the center and the width of the shear band at the different heights in the bulk, we map out the 3-D shape of the shear band and investigate the behavior of the shear band as a function of the total filling height. We find that when the top of the shear band detaches from the surface of the bulk, its shape changes dramatically, similar to a first order transition as has been proposed by theory [2]. [1] D. Fenistein, J. W. van de Meent, and M. van Hecke, PRL 92, 094301 (2004). [2] T. Unger, J. Torok, J. Kertesz, D. E. Wolf, PRL 92, 214301 (2004). [Preview Abstract] |
Tuesday, March 22, 2005 4:06PM - 4:18PM |
L36.00007: Simultaion of Dense Granular Flows in a Modified Couette Cell Jeremy B. Lechman, Gary S. Grest Dense granular flows often exhibit thin, localized regions of particle motion, shear bands, separating largely solid-like regions. Recent experiments using a split-bottom Couette cell found that the width of the shear zone grew as the pack height increased and the azimuthal velocities when rescaled fall on a universal curve regardless of the particle properties. Here we present large-scale Discrete Element simulations of a similar system for packs of varying height up to 180,000 monodisperse spheres. We find a similar universal scaling relation for the azimuthal velocities both at the surface as well as in the bulk of the pack. However, we find the rescaled velocity profiles are asymmetric for smaller diameter systems. We observe a quasi-static inner core which changes shape with increasing pack height and undergoes a transition from a curved cylinder intersecting the surface of the pile to a closed surface within the bulk as predicted by theory. The mean-squared velocity fluctuations are found not to follow a simple scaling form with the shear rate as observed in traditional Couette cells and the velocity fluctuations in the cross-coordinate radial-azimuthal and azimuthal-vertical directions differ significantly from the other directions suggesting secondary flows. \\ \\ Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for the United States Department of Energy's NNSA under contract No. DE-AC04-94AL75000. [Preview Abstract] |
Tuesday, March 22, 2005 4:18PM - 4:30PM |
L36.00008: Secondary Granular Flow a Split-Bottomed Couette Cell Antonio Fernandez-Barbero, Heinrich Jaeger, Sidney Nagel Granular materials and ordinary fluids react differently to shear stresses. The former develop shear bands rather than deform uniformly. Thus, shear regions of large particle motion are present in the surrounding of the essentially rigid adjacent zones. The extent of these shear bands may be increased when the system is sheared from the bottom of the container, thus taking advantage of the gravity [1]. In this talk, a new effect appearing in slit-bottom geometry is shown. A secondary flow in the vertical and radial directions becomes apparent and strongly depends on the height of grains in the system. Video tracking from the top free surface and MRI videos from the bulk of the system show this effect. [1] D. Fenistein, J. W. van de Meent, and M. van Hecke, PRL 92, 094301 (2004) [Preview Abstract] |
Tuesday, March 22, 2005 4:30PM - 4:42PM |
L36.00009: Axial transport of bidisperse granular mixtures in a rotating drum Zeina Khan, Stephen Morris Bidisperse granular mixtures rapidly size segregate when tumbled in a partially filled, horizontal drum. The smaller component moves radially toward the axis of rotation and forms a buried core. On a longer time scale, axial modulations of the core may develop and grow into a series of bands along the drum, which become visible upon breaking the surface. Using a narrow pulse of the smaller component as the intitial condition, we observe that the axial transport of the radial core is a subdiffusive front advancement process. The front motion is subdiffusive in the sense that the radially integrated concentration forms a self-similar, compact axial pulse whose width grows as $t^{\alpha}$, with $\alpha \sim 1/3 < 1/2$, and hence it spreads much more slowly than by diffusion in a mixture which does not exhibit axial banding. By coloring some of the larger grains, we find that the mixing and axial transport of the larger grains is similarly subdiffusive. We report on the effects of changing relative grain size and drum diameter on the axial transport of grains. We find that mixing occurs in the radial core, and axial band formation is enhaced in these cases. [Preview Abstract] |
Tuesday, March 22, 2005 4:42PM - 4:54PM |
L36.00010: Simulating and Shaking a Rotating Drum of Beads Michael Newey, Andrew Porter, Nicolas Taberlet, Wolfgang Losert It is well known that different sized particles will segregate when rotated in a horizontal cylinder, but the mechanism--for axial segregation in particular--is not well understood. We use a combination of high-speed imaging and perturbation experiments to elucidate flow properties during axial segregation in bi- and tri- disperse mixtures in a rotating drum. In addition, we use molecular dynamics (MD) simulations to investigate the motion of particles in the bulk and to measure internal stresses and dissipation. Experimental results indicate slow convective flow on timescales comparable to the band formation time. We use MD simulation to thoroughly investigate this possibility in three dimensions. The MD simulations also highlight the crucial role of sidewalls in the segregation phenomena. To further investigate the stability properties of the flowing layer, we shake the rotating drum horizontally--perpendicular to the surface flow direction. This allows us to estimate a `viscosity' of the flowing layer based on amplitude and phase lag of the oscillation at the surface of the flow. [Preview Abstract] |
Tuesday, March 22, 2005 4:54PM - 5:06PM |
L36.00011: Numerical Tests of Kinetic Theory for Sheared Granular Flows Gregg Lois, Anael Lemaitre, Jean Carlson The Revised Enskog Theory generalizes the kinetic theory of dense gases to include granular materials by incorporating inelasticity. It still relies, however, on the assumption that grains interact only through binary collisions. We explore the validity and breakdown of kinetic theory for granular materials utilizing Contact Dynamics simulations of two-dimensional sheared granular materials. Using an analytical expression for the contribution of binary collisions to the stress tensor, we directly measure the ``collisional'' stress and the total (Kirkwood) stress for a wide range of densities and restitution coefficients. Our measurements demonstrate that the ``collisional'' stress becomes negligible at high densities and low restitution coefficients. This suggests that the whole structure of kinetic theory breaks down in these regimes and emphasizes that jamming results from variations of the frictional stress, but not from a crossover between a collision-dominated and friction-dominated regime. [Preview Abstract] |
Tuesday, March 22, 2005 5:06PM - 5:18PM |
L36.00012: Friction coefficients in 2D granular Couette flow Matthias Sperl, Kenneth McKenzie, Robert P. Behringer Within geologic fault zones the internal friction in a material is expected to produce a large amount of heat. However, far less heat than expected is generated, giving rise to what is known as the heat flow paradox in geophysics. One possible explanation is that a fraction of the stress is not released by sliding friction but rolling of particles. We address this issue by studying a dense two-dimensional granular system under shear. In a Couette cell the overall torque is measured on the inner wheel for various packing fractions. This is compared to stress measured within the system using photoelastic particles. The relation between torque and mean shear force is interpreted as an effective friction coefficient $\mu$. The goal of this work is to determine $\mu$ as a function of the mean applied load. [Preview Abstract] |
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