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 EH: Granular Flows III: Packed Beds |
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Chair: Robert Behringer, Duke University Room: Tampa Marriott Waterside Hotel and Marina Florida Salon 6 |
Sunday, November 19, 2006 4:15PM - 4:28PM |
EH.00001: The self-ergodicity of granular contact forces Philip Metzger A formal mathematical proof of ergodicity has been accomplished for granular contact forces. It is a special type ergodicity having unique characteristics compared to thermal systems, because (for one thing) it operates across multiple spatial dimensions with orthogonal conservation laws, whereas in thermodynamics the ergodicity and the conservation laws all operate across one single dimension (namely, the time dimension). This higher-dimensional ergodicity causes the concept of temperature to become a rank-2 tensor instead of a scalar, with the dimensionality of the tensor equal to the number of ergodic dimensions (three for 3D packings). Furthermore, symmetries in the granular packing ensemble ensure that certain types of packings will always exist at maximum contact force entropy without first having to explore phase space. Thus, the ergodicity is an inherent ``self-ergodicity,'' which explains why the granular contact force distribution is so immediate and repeatable and why it has an exponential tail. The theory predicts the distribution of contact forces and other statistics of the stress state of the individual grains. These predictions have been tested via discrete element modeling and have been overwhelmingly validated. The theory has a number of practical ramifications that are important to developing a full theory of rheology. [Preview Abstract] |
Sunday, November 19, 2006 4:28PM - 4:41PM |
EH.00002: Minimum spanning tree analysis of force networks in granular media Jin Sun, Francine Battaglia, Shankar Subramaniam Force networks, formed by particles interacting with repulsive contact forces, are a salient feature of dense granular media, and play an important role in determining mechanical properties of granular media. We use a graph-theoretic approach based on the minimum spanning tree (MST) algorithm to analyze force networks in a dense granular bed under vibration and to provide structural information in a statistical sense. Using particle information from a molecular dynamics simulation, we show that the MST approach is able to capture the important structural information. We also developed a multi-pass MST algorithm, which is able to recover all the contacts within the force network and thus is able to recover the force distribution and force correlation. The results indicate that effect of wall friction transmits through the medium over several tens of particle diameters and affects the dynamical behavior of the system through local short-range interactions as indicated by the spatial force correlation. Therefore, the MST provides a possible route to constructing a continuum model with structural information supplied from this algorithm. [Preview Abstract] |
Sunday, November 19, 2006 4:41PM - 4:54PM |
EH.00003: Sliding Friction on a 2D Photoelastic Granular Bed Peidong Yu, Robert Behringer, Brian Utter We describe ongoing experiments to characterize the nature of granular friction. In the experiment, a slider is pulled by a spring moving at constant speed across the top of a 2D granular bed confined to a vertical channel. The pulling force is measured synchronously with image acquisition of the granular bed taken by a camera moving along with the slider. We use the pulling force and the slider position to find out the frictional force. We observed stick-slip motion by analyzing the slider position and the frictional force data and characterize the nature of friction as a function of the experimental parameters such as pulling speed and slider mass. Comparing those different features helps us undestrand the current friction models of granular materials. By observing images of the photoelastic grains, we also study the force networks of the granular bed under the moving slider. We tried to correlate the distribution, the formation and the annihilation of the force chains with the frictional force and the position of the slider. [Preview Abstract] |
Sunday, November 19, 2006 4:54PM - 5:07PM |
EH.00004: Jamming and Plasticity for Granular Materials Trush Majmudar, Matthias Sperl, Bob Behringer We describe experiments, using quasi-2D photoelastic particles, that characterize the jamming transition for isotropic compression and that explore the microscopic origins of plastic failure for shear deformation. The experiments were carried out in a biaxial tester that allowed us to generate precise states of deformation. We use photoelasticity to extract the vector forces at contacts and to reliably obtain contacts. Regarding jamming, we find that near the jamming point, there is a rapid increase in the contact number, Z. Above the transition, Z continues to increase as a power law in $\phi - \phi_c$, where $\phi$ is the packing fraction. The critical exponent is 0.55 within experimental error. Above jamming, the pressue, P, varies as a power law with exponent 1.1. In a different set of experiments, we applied pure shear to a sample with $\phi$ near the jamming value. We find a series of localized failure events, which lead to energy dissipation and decreases in the stress. Failure occurs in a shear band that is dominated by vortex-like flow. On cycling the shear deformation, there is a substantial change in the background structure of force chains. [Preview Abstract] |
Sunday, November 19, 2006 5:07PM - 5:20PM |
EH.00005: Spatial Distribution of Forces within Granular Materials John Wambaugh, Robert Behringer Granular materials display surprisingly inhomogeneous distributions of forces. Some chains of inter-grain contacts carry forces much greater than the mean while other contacts with adjacent particles carry almost no force at all, resulting in the phenomenon of force chains. Recently, a theoretical framework for understanding the spatial distribution of these networks of force chains was proposed by analogy to bond percolation theory [Ostojic, S., Somfai, E. and Nienhuis, B. Nature \textbf{439}, 828—830 (2006)]. In this experimental work, we test these predictions on static, isotropic force networks in two-dimensions using photo-elastic techniques. We observe the distribution of clusters of grains connected by contacts with forces in excess of a threshold of the mean force. We find that these distributions can be scaled to a function that is independent of overall isotropic pressure. We then use a numerical model to predict similar scale-independence for anisotropic pressures. We believe our results provide evidence for a mechanism for comparing the spatial fluctuations on the laboratory-scale with other systems. [Preview Abstract] |
Sunday, November 19, 2006 5:20PM - 5:33PM |
EH.00006: Random twists of vanes in granular beds Stephan Koehler, Raenell Soller We observe that vanes immersed into and withdrawn from granular beds undergo small rotations. For granular beds that are uniformly prepared these rotations are random and scale with the bead size and geometry's dimensions. Preshearing the granular media creates a bias of the random rotations, which is in the opposite direction of the preshear. We propose a simple model based upon releasing residual strains to capture this new phenomenon. [Preview Abstract] |
Sunday, November 19, 2006 5:33PM - 5:46PM |
EH.00007: Washboard Road Jim McElwaine, Stuart Dalziel, Nicolas Taberlet, Stephen Morris The tendency of unpaved road surfaces to develop lateral ripples (``washboard'' or ``corrugated'' road) is annoyingly familiar to drivers on dry gravel roads. Similar ripples are well known on railroad tracks and many other rolling or sliding, load bearing surfaces. Our approach combined laboratory experiments, soft-particle direct numerical simulations and simple nonlinear dynamics models. The experiment consisted of a rotating table 60 cm in radius with a thick layer of sand forming a roadbed around the circumference. A 6 cm radius hard rubber wheel, with a support stationary in the lab frame, rolled on the sand layer. We varied the speed of the table and the details of the suspension of the wheel. The onset of the ripple pattern exhibits a sharp threshold and was strongly subcritical with a large hysteresis as a function of the speed of the table. The ripple pattern appears as small patches of travelling waves which eventually spread to the entire circumference. The ripples move slowly in the driving direction. Interesting secondary dynamics of the saturated ripples were observed. All of these effects are captured qualitatively by a 2D soft particle simulations. The simulations clearly indicate that neither compaction nor particle size segregation are crucial for the appearance of the ripples, and we present a simple model to describe the wavelength and amplitude of the ripples. [Preview Abstract] |
Sunday, November 19, 2006 5:46PM - 5:59PM |
EH.00008: Slow relaxation and compaction dynamics of granular piles Nicolas Vandewalle, Geoffroy Lumay, Francois Ludewig We present the results of an experimental study of compaction dynamics at three different scales. The density of the packing is measured during compaction. Extremely slow dynamics towards an asymptotic density has been evidenced. The motion of every grain in a pile is also tracked. The mobility of the grains is found to vanish when the packing approaches its asymptotic density. The mobility of the grains is related to the increasing density of the packing. The domains of grains ideally ordered, i.e. hexagonal structures, are tracked. The growth of these domains obeys a crystalization kinetics, described by the Avrami theory. This allows us to propose a new law for the compaction dynamics. The application of those results to 3d sphere packings, as well as anisotropic grains, is also discussed. [Preview Abstract] |
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