Bulletin of the American Physical Society
2009 APS March Meeting
Volume 54, Number 1
Monday–Friday, March 16–20, 2009; Pittsburgh, Pennsylvania
Session Q14: Granular Fluctuations |
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Sponsoring Units: DFD Chair: Wolfgang Losert, University of Maryland Room: 315 |
Wednesday, March 18, 2009 11:15AM - 11:27AM |
Q14.00001: Cooling and aggregation in wet granulates Annette Zippelius, Stephan Ulrich, Timo Aspelmeier, Klaus Roeller, Axel Fingerle, Stephan Herminghaus Wet granular materials are characterized by a defined bond energy in their particle interaction such that breaking a bond implies an irreversible loss of a fixed amount of energy. Associated with the bond energy is a nonequilibrium transition, setting in as the granular temperature falls below the bond energy. The subsequent aggregation of particles into clusters is shown to be a self-similar growth process with a cluster size distribution that obeys scaling. In the early phase of aggregation the clusters are fractals with $D_f=2$, for later times we observe gelation. We use simple scaling arguments to derive the temperature decay in the early and late stages of cooling and verify our results with event-driven simulations. [Preview Abstract] |
Wednesday, March 18, 2009 11:27AM - 11:39AM |
Q14.00002: Propagating Waves in a Monolayer of Self-Propelling Gas-Fluidized Rods Lynn J. Daniels, Douglas J. Durian We report on the existence of propagating compression waves in a quasi-two-dimensional monolayer of self-propelling rods fluidized by an upflow of air. This behavior is unique to rods; a comparable system of spheres exhibits no waves and displays `thermal' number fluctuations, proportional to N$^{1/2}$. The waves, however, give rise to anomalously large number fluctuations, having both magnitude and exponent greater than `thermal' fluctuations. This occurs as rarefaction zones relax after a compression front has traveled through a region. We characterize the waves by calculating a dynamic structure factor. The position of observed peaks, as a function of frequency $\omega$ and wavevector $k$, yield a linear dispersion relationship in the long-time, long-wavelength limit and a wavespeed $\omega/k$ = 20 cm/s. By contrast, spheres exhibit $1/\omega^{2}$ decay for all wavevectors in the hydrodynamic limit, consistent with the diffusive decay of density fluctuations. [Preview Abstract] |
Wednesday, March 18, 2009 11:39AM - 11:51AM |
Q14.00003: Phase diagram of wet granular matter under vertical vibrations Kai Huang, Klaus Roeller, Stephan Herminghaus The phase diagram of vertically vibrated wet granular matter is investigated by both experiments and simulations. We find a critical point where the coexistence (C) regime of the fluid (F) and gas (G) phases terminates. The energy driven F-C transition is found to scale with the rupture energy of a liquid bridge if the corresponding vibration amplitude(A) is less than particle diameter(d). This is in good agreement with our simulations. Close to the F-G transition line, the variation of the size of the gas bubble with vibration amplitude shows a hysteretic behavior. Within the hysteresis loop, we observe temporary gas bubbles with strong fluctuations in size. The F-G boundary is shown to have an interfacial tension and non-trivial wetting behavior at container walls. Focusing on the solid (S)- F transition line, we find that the fluidization is a surface melting process. This is demonstrated by detecting the mobility of ruby tracers utilizing ruby fluorescence. This as well agrees with our simulation results. [Preview Abstract] |
Wednesday, March 18, 2009 11:51AM - 12:03PM |
Q14.00004: Stress wave mitigation in granular media Chiara Daraio, F. Fernando, Mason Porter We study stress wave mitigation in one- and two-dimensional granular media employing evolutionary algorithms to investigate the optimal design of composite protectors using granular chains composed of beads of various sizes, masses, and stiffnesses. We define a fitness function using the maximum force transmitted from the protector to a ``wall'' that represents the body to be protected and accordingly optimize the topology (arrangement), size, and material of the chain. We obtain optimally randomized granular protectors characterized by high-energy equipartition and the transformation of incident waves into interacting solitary pulses. We provide a quantitative characterization of dissipative effects using the propagation of highly nonlinear solitary waves as a diagnostic tool and develop optimization schemes that allow one to compute the relevant exponents and prefactors of the dissipative terms in the equations of motion. We thus propose a quantitatively-accurate extension of the Hertzian model encompassing realistic material dissipative effects. Experiments and computations with steel, brass, and polytetrafluoroethylene reveal a common dissipation exponent (for a discrete Laplacian of the velocities) with a material-dependent prefactor. [Preview Abstract] |
Wednesday, March 18, 2009 12:03PM - 12:15PM |
Q14.00005: Anisotropies in granular temperature in a dense sheared granular flow Chris Rycroft, Ashish Orpe, Arshad Kudrolli We investigate a three-dimensional, slow, gravity-driven, sheared granular flow, making use of both simulation (carried out using the Discrete-Element Method) and experiment (using glass beads, imaged via an index-matched fluid). We begin by performing a quantitative comparison between the two procedures, concentrating on the level of agreement at the microscopic scale. After establishing how well the simulation can reproduce the microscopic fluctuations in particle velocities seen in experiment, we proceed to carry out a tensorial analysis of granular temperature. Our results show different types of behavior near the boundary and in the bulk of a granular flow, due to differences in the particle packing structure, and highlight anisotropies that may have implications for granular continuum modeling. [Preview Abstract] |
Wednesday, March 18, 2009 12:15PM - 12:27PM |
Q14.00006: Correlation Functions of a Homogeneously Driven Granular Fluid in Steady State Katharina Vollmayr-Lee, Timo Aspelmeier, Annette Zippelius We study a homogeneously driven granular fluid of hard spheres at intermediate volume fractions and focus on time-delayed correlation functions in the stationary state. The results of computer simulations using an event driven algorithm are compared to the predictions of generalized fluctuating hydrodynamics. The incoherent scattering function ($F_{\rm incoh}(q,t)$) follows time-superposition and is well approximated by a Gaussian $F_{\rm incoh}=\exp \left ( - \frac{q^2}{6} \langle \Delta r^2(t) \rangle \right )$. For sufficiently small wavenumber $q$ we observe sound waves in the intermediate scattering function $F(q,t)$ and in the longitudinal current correlation function $C_l(q,t)$. We determine their dispersion and damping. Temperature fluctuations are predicted to be either diffusive or nonhydrodynamic, depending on wavenumber and inelasticity as characterized by incomplete normal restitution. [Preview Abstract] |
Wednesday, March 18, 2009 12:27PM - 12:39PM |
Q14.00007: Interparticle friction between gently contacting spheres Greg Farrell, Narayanan Menon In previous experimental work we have found that the packing fraction of gently-sedimented monodisperse spheres is affected by particle roughness as well as the viscosity and buoyancy provided by the surrounding fluid. In order to provide a macroscopic quantification of the microscopic effects of particle surface and of the fluid, we have developed a new technique to measure the coefficients of static and kinetic friction between two spheres in a fluid. We find that even in fluid environments, there are static and kinetic coefficients of friction characteristic of solid-on-solid contact. Surprisingly, even for a given pair of spheres, we measure a broad range of friction coefficients corresponding to contacts made at different locations on the surface. Thus, even for lubricated surfaces, surface heterogeneity is more apparent for small normal forces than at familiar force-scales. [Preview Abstract] |
Wednesday, March 18, 2009 12:39PM - 12:51PM |
Q14.00008: Spatial Force Correlations in 3D Granular Flow . Nalini Easwar, Kelsey Hattam, Efrosyni Seitaridou, Alisa Stratulat, Narayanan Menon We measure the force delivered at four locations on the boundary of a 3D flow of mono-disperse glass spheres in a vertical, cylindrical chute. A variable opening at the bottom is used to change the flow velocity v$_{f}$ from 3 to 30cm/s. The force is measured at 80KHz, allowing us to resolve individual collisions. We measure two-point spatial correlations in the flow direction and normal to it. The equal-time correlation between forces that are higher than a threshold shows a weak but measurable spatial correlation. This correlation shows no spatial directionality or dependence on flow rate. The time correlations are synchronous between diametrically opposed locations, and shifted in time between locations along the flow. From the time-lag we determine that the correlations are carried up the flow at speeds $\sim $ 1000 v$_{f}$ . This speed increases as the flow approaches jamming. [Preview Abstract] |
Wednesday, March 18, 2009 12:51PM - 1:03PM |
Q14.00009: Impact phenomena in fluidized granular matter Patrick Mayor, Hiroaki Katsuragi, Douglas Durian Projectiles dropped into granular media form a crater and come to rest in a particular way that has been actively investigated in numerous studies. These impact phenomena illustrate how particulate materials respond to externally applied forces. Several recent experiments have focused on the penetration of projectiles impacting granular materials at relatively low speeds, and measured the dynamics of the impact process, yielding force laws accounting for the observations. We present results showing how granular impacts are affected when the load on the grains is modified using a vertical gas flow. Balls or cylinders are dropped into a dry, noncohesive granular medium and we measure the penetration depth when gas is flown upward (thus unloading the contacts) or downward (loading the contacts). We observe that the frictional drag decreases linearly with the flow rate, and vanishes completely once the system is fluidized. Different projectile geometries allow us to separate the effect of normal and tangential frictional forces. We also consider the case of objects that are lowered quasistatically into the granular medium and measure the net vertical force exerted by the granular system on the objects at each immersion depth. We then discuss how this resistance force compares with the forces observed in actual impacts experiments. [Preview Abstract] |
Wednesday, March 18, 2009 1:03PM - 1:15PM |
Q14.00010: A Statistical Approach to the Filtration of Rods Scott Franklin We investigate the efficacy of a square-grid mesh at filtering rods from solution. The volume fraction $\phi$ is kept low, reducing the chance of rods cooperatively jamming at the mesh. For round particles, filtering at low $\phi$ is trivially determined by the ratio of particle diameter to mesh size. Because rods have two length scales, filtering is non-trivial for meshes larger than the rod width but smaller than the length, a potentially very large range. We have measured experimentally the probability for a rod to be filtered as a function of mesh size, particle length, and aspect ratio. Results are compared with a theoretical extension of the Buffon-Laplace Needle problem that accounts for finite rod width and an isotropic distribution in the zenith angle. The solution is the probability that a sphero-cylinder in three dimensions makes contact with a 2D sieve-like mesh, a necessary but not sufficient condition for filtration. Comparison of experiment and theory is then suggestive of what conditions are both necessary and sufficient. [Preview Abstract] |
Wednesday, March 18, 2009 1:15PM - 1:27PM |
Q14.00011: Granular Breathing Surajit Sen, Robert Simion, Adam Sokolow We study the dynamics of monodispersed and tapered granular alignments held within a fixed boundary and a moving boundary. The system is assumed to be driven at one end by imparting a constant or time dependent acceleration to the edge grain. Analytical and simulational studies show that such a driven system can eventually get ``over-compressed" and begin to dilate due to repulsive grain-grain interactions. Continuous driving results in the phenomenon of granular breathing. The talk shall discuss the dynamical processes associated with granular breathing for time-independent and time-dependent driving. The phenomenon of nonlinear resonance and related processes that arise in these systems will be discussed. [Preview Abstract] |
Wednesday, March 18, 2009 1:27PM - 1:39PM |
Q14.00012: Combustion of Micropowdered Biomass Ethan Geil, Robert Thorne Combustion of finely powdered biomass has the potential to replace heating oil, which accounts for a significant fraction of US oil consumption, in heating, cooling and local power generation applications. When ground to 30-150 micron powders and dispersed in air, wood and other biomass can undergo deflagrating combustion, as occurs with gaseous and dispersed liquid fuels. Combustion is very nearly complete, and in contrast to sugar/starch or cellulose-derived ethanol, nearly all of the available plant mass is converted to usable energy so the economics are much more promising. We are exploring the fundamental combustion science of biomass powders in this size range. In particular, we are examining how powder size, powder composition (including the fraction of volatile organics) and other parameters affect the combustion regime and the combustion products. [Preview Abstract] |
Wednesday, March 18, 2009 1:39PM - 1:51PM |
Q14.00013: On the nonlocality of the fractional Schr\"{o}dinger equation Shiliyang Xu, Monwhea Jeng, Eli Hawkins, J.M. Schwarz A wide variety of stochastic processes are more general than the familiar Brownian motion, but presumably can still be described by modifying the diffusion equation using a fractional Laplacian operator. In analogy with fractional diffusion, the fractional Schr\"{o}dinger equation is the ordinary Schr\"{o}dinger equation with the fractional Laplacian operator replacing the ordinary one. Over the past eight years, a number of papers have claimed to solve the fractional Schr\"{o}dinger equation for systems ranging from the one-dimensional infinite square well to the Coulomb potential to one-dimensional scattering with a rectangular barrier. However, some of the claimed solutions ignore the fact that the fractional diffusion operator is inherently nonlocal, preventing the fractional Schr\"{o}dinger equation from being solved in the usual piecewise fashion. We focus on the one-dimensional infinite square well and show that the purported groundstate, which is based on a piecewise approach, is definitely not a solution of the fractional Schr\"{o}dinger equation for general fractional parameters $\alpha$. On a more positive note, we present a solution to the fractional Schr\"{o}dinger equation for the one-dimensional harmonic oscillator with $\alpha=1$. Potential physical applications will also be discussed. [Preview Abstract] |
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