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 GJ: Granular Media: Clusters and Shocks |
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Chair: Heinrich Jaeger, University of Chicago Room: Hilton Chicago Williford C |
Monday, November 21, 2005 10:34AM - 10:47AM |
GJ.00001: Granular drops Matthias Mobius, Sidney Nagel, Heinrich Jaeger In fluid dynamics the instability that leads to the breakup of a fluid column into droplets is well known. This so-called Rayleigh-Taylor instability is driven by the competition between gravity and surface tension. We report that a similar phenomenon can be observed for a column of small granules in free fall. The flow out of a circular nozzle starts out uniform and then, further downstream, starts to break up into well defined clusters. This is surprising since granular media do not possess any surface tension. The ambient gas enhances the formation of the drops, but we find clustering at pressures down to 1/2000$^{th}$ of an atmosphere. We investigate the drop formation as a function of pressure and nozzle diameter and discuss the origin of this phenomenon. [Preview Abstract] |
Monday, November 21, 2005 10:47AM - 11:00AM |
GJ.00002: Formation of Granular Jets Observed by High-Speed X-ray Radiography John Royer, Eric Corwin, Bryan Conyers, Andrew Flior, Maria-Luisa Cordero, Mark Rivers, Peter Eng, Heinrich Jaeger When a heavy sphere is dropped onto a bed of loose, fine sand, a large, focused jet of sand shoots upward.\footnote{Thoroddsen, S. T. and Shen, A. Q. Phys. Fluids {\bf13}, 4-6 (2001).} \footnote{Lohse, D. et al. Phys. Rev. Lett. {\bf93} (2004).} While similar looking jets are observed upon impact in fluid systems, their formations relies on surface tension. Surprisingly, the granular jet exists in the absence of both surface tension and cohesion. Previous work proposed that the jet is created solely by the gravity-driven collapse of a void left by the sphere’s descent through the pack. Here we present experimental evidence that granular jets are instead driven by a more complex process involving the interaction between the sand and interstitial air. Using high-speed x-ray radiography, and high-speed digital video, we observe the formation of the jet both inside and above the bed. We find that what previously was thought of as a single jet in fact consists of two components: a wispy, thin jet that varies little with pressure followed by a thick air-pressure-driven jet. The x-ray movies reveal that gravity-driven collapse produces the initial, thin jet, while the compression of an air pocket trapped below the surface drives up the thick jet. [Preview Abstract] |
Monday, November 21, 2005 11:00AM - 11:13AM |
GJ.00003: The granular Leidenfrost effect: Experiment and theory of floating particle clusters Peter Eshuis, Ko van der Weele, Devaraj van der Meer, Detlef Lohse Granular material is vertically vibrated in a 2-D container: Above a critical shaking strength, and for a sufficient number of beads, a crystalline cluster is elevated and supported by a dilute gaseous layer of fast beads underneath. We call this phenomenon the \emph{granular Leidenfrost effect}. The experimental observations are explained by a hydrodynamic model featuring three dimensionless control parameters: The energy input $S$, the number of particle layers $F$, and the inelasticity of the particle collisions $\varepsilon$. The $(S,F)$ phase diagram, in which the Leidenfrost state lies between the purely solid and gas phases, shows accurate agreement between experiment and theory. [Preview Abstract] |
Monday, November 21, 2005 11:13AM - 11:26AM |
GJ.00004: Raining into shallow water as a description of the collapse of a column of grains John Hinch, Emeline Larrieu, Lydie Staron A modified shallow-water model is presented for the collapse of tall columns of grains. The flow is divided in two parts. Depth-averaged shallow-water equations are applied to a thin horizontally spreading layer which is subjected to Coulombic friction. The falling mass of grains is gradually added in the zone of the initial column during the free-fall time of the column. This `rain' is assumed to have no horizontal momentum. The results obtained here are in agreement with both planar and axisymmetric experiments over a range of aspect-ratio $a$. In particular, the runout distance is found to vary as $a^{0.65}$ (planar) and $a^{0.52}$ (axisymmetric). The flow dynamics compares well with discrete simulations which have been successfully compared with experiments. [Preview Abstract] |
Monday, November 21, 2005 11:26AM - 11:39AM |
GJ.00005: Impact of a Binary Size Distribution on the Clustering Instability R. Brent Rice, Christine M. Hrenya The impact of a binary size distribution on clusters formed during rapid, granular, simple shear flow is investigated via discrete-particle simulations. Two novel characterization methods are used to provide physically meaningful insight into the behavior of the clusters. First, an analysis of the concentration distribution in the system provides insight into the average volume and concentration associated with clustered and non-clustered regions, as well as size segregation. Second, a new feature of the radial distribution function is identified for dissipative granular systems, namely a long-scale minimum. This technique substantiates a subset of the results obtained using the former technique, and also provides information on the length scale between clusters. The characterization results suggest that the prevalence of clusters decreases with an increase in size disparity, and that large particles preferentially segregate within the clustered region. [Preview Abstract] |
Monday, November 21, 2005 11:39AM - 11:52AM |
GJ.00006: Normal shock propagation in a granular funnel Erin Rericha, Jonathen Bougie, Jack Swift, Harry Swinney We examined the propagation of a normal shock formed in a quasi-two dimensional funnel. We compare results from experiment and MD simulations to a Hugoniot-Rankine type approximation of the inelastic continuum equations. Both MD and experimental results show behavior similar to the simplified equations, but inelastic collisions cause evolution of the shock unaccounted for in this simple approximation. We find the flow parameters behind the shock and the shock speed as a function of inelasticity compare well with an asymptotic solution of a set of inelastic equations proposed by Goldshtein, et al [1-2].\newline \newline [1] A. Goldshtein et al. \textit{JFM} \textbf{287}, 349 (1995). \newline [2] V. Kamenetsky et al$.$ \textit{Phys of Fluids} \textbf{12}, 3036 (2000): [Preview Abstract] |
Monday, November 21, 2005 11:52AM - 12:05PM |
GJ.00007: The Internal Structure and Velocity Distribution of a Granular Shock John Perez, Greg Voth Shock wave formation and propagation in granular materials is a complex phenomenon that is only partially understood. For the most part, the \textit{internal }structure of a granular shock is unknown. This talk explores this issue in the context of an experimental vertically driven quasi-2-D granular gas for which we have measured the single particle velocity distribution as a function of space and time to a very high resolution. Average density, momentum and temperature fields as functions of space and time are an immediate by-product of our methodology. Our statistics are robust. These experimentally determined fields reveal that under steady sinusoidal driving the formation and propagation of shocks in this simple system is surprisingly complex. The data clearly shows a striated substructure in the shocks on the scale of a particle diameter. This substructure is the result of an intriguing interaction between collisional and ballistic momentum transport which registers in the mean fields as a punctuated deviation from a continuum shock profile on the scale of a particle diameter. We discuss whether shock propagation speed and other aspects of these shocks are similar to weak shocks in molecular gasses or whether they depend essentially on the mesoscopic and dissipative nature of granular gasses. [Preview Abstract] |
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