Bulletin of the American Physical Society
65th Annual Meeting of the APS Division of Fluid Dynamics
Volume 57, Number 17
Sunday–Tuesday, November 18–20, 2012; San Diego, California
Session G32: Granular Flows I |
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Chair: Yi Fan, Northwestern University Room: 33C |
Monday, November 19, 2012 8:00AM - 8:13AM |
G32.00001: A modified kinetic theory for frictional granular flows in dense and dilute regimes Sebastian Chialvo, Sankaran Sundaresan We investigate the rheology of granular materials in both the dense and dilute inertial regimes via molecular dynamics simulations of homogeneous, simple shear flows of soft, frictional spheres. Though traditional kinetic theories are often used for continuum modeling of such materials, they fail to describe flow behavior in dense systems near the jamming transition and do not account explicitly for interparticle friction. On the basis of our simulations, we propose a new model for the radial distribution function at contact as well as modifications to the shear stress and energy dissipation equations of one commonly used theory [1]. These changes account for stress and temperature scalings observed in our steady shear simulations while preserving the dynamic nature of the kinetic theory model. \\[4pt] [1] V.~Garz\'{o} and J.W.~Dufty, Phys.~Rev.~E 59, 5895 (1999). [Preview Abstract] |
Monday, November 19, 2012 8:13AM - 8:26AM |
G32.00002: Homogeneous Cooling Granular Gases of Cohesive Particles Eric Murphy, Shankar Subramaniam We consider the case of a homogeneously cooling gas of dissipative granular particles with the addition of short-range attractive potentials. An analytic solution is found using the pseudo-Liouville formalism in terms of a nondimensional ratio of interparticle potential energy to internal energy of the system. The solution reveals that the granular temperature evolution is indistinguishable from Haff's law until a critical temperature region is approached. In this critical region, an abrupt increase in cooling and aggregation are predicted. Lastly, the solution is compared against soft-sphere DEM data. The abrupt increase in cooling sheds light on the expected rheological behavior and jamming transitions in flows of such particles. [Preview Abstract] |
Monday, November 19, 2012 8:26AM - 8:39AM |
G32.00003: Axisymmetric Column Collapse in a Rotating System Jay Warnett, Peter Thomas, Petr Dennisenko We discuss experimental and computational results of a study investigating the collapse of an initially axisymmetric cylindrical column of granular material within a rotating environment of air or liquids. In industry this type of granular column collapse that is subject to background rotation is encountered, for instance, in the context of the spreading of powders and fertilizers. In comparison to its non-rotating counterpart the physical characteristics of the column collapse in a rotating system are expected to be modified by effects arising from centrifugal forces and Coriolis forces. We compare our new results for the rotating flow to data available in the literature for the collapse of granular columns in non-rotating systems to highlight the differences observed. [Preview Abstract] |
Monday, November 19, 2012 8:39AM - 8:52AM |
G32.00004: On the Collapse of Granular Columns in Different Gravities Horacio Tapia-McClung, Roberto Zenit By performing numerical simulations of the collapses of granular columns we find that the scaling of the final height of the emplacements ($\sim a^{\beta}$) is preserved when the inter-granular friction coefficient and the initial aspect ratio of the columns is varied under different gravitational accelerations. The top of the column initially evolves closely to the free falling law for large aspect ratios and gravities. For high aspect ratio columns in low gravities, an initial fluidization of the grains is observed. We present energy balances during the emplacement and measurements of a quantity equivalent to the inertial number, to understand the influence of varying the gravitational acceleration on the properties of the column collapses. [Preview Abstract] |
Monday, November 19, 2012 8:52AM - 9:05AM |
G32.00005: Collapse of a granular column: discrete element simulations and continuum modelling Laurent Lacaze, Edouard Izard, Rich Kerswell The unsteady dynamics of the collapse of a granular column onto a horizontal plane exhibits a wealth of interesting behaviour typical of granular flows. This canonical flow situation has therefore received attention for the last decade through different experimental and numerical studies. Using 3-dimensional soft particles simulations, the observed behaviour can be faithfully reproduced and the observed scaling laws for the final deposit captured. A coarse-graining procedure is then used to extract models for both the apparent rheology and slip velocity at the base. These are incorporated into a ``Saint-Venant''-type code to model unsteady granular collapse in the limit of small aspect ratio. [Preview Abstract] |
Monday, November 19, 2012 9:05AM - 9:18AM |
G32.00006: The hour-glass: comparisons of discrete granular flow and continuum plastic flow. Pierre-Yves Lagree, Lydie Staron, Aurelien Grabsh, Stephane Popinet A hour-glass is a fascinating way to measure time, surprisingly the flow is not function of the filling height as in a clepsydra. The discharge of a granular silo implies a constant rate, dictated by the size of the aperture, but independent of the height of material stored (the Berveloo law). This observation is often understood as resulting from the friction forces mobilized at the walls of the silo, which decrease the apparent weight of the material, and screen the bottom area from the pressure, (Janssen effect). This explanation fails however in the case of wide systems for which walls are distant from several times the height of material stored. In this contribution, we simulate the continuum counterpart of the granular silo by implementing the plastic (I)-rheology in a 2D Navier-Stokes solver (Gerris) and compare with Contact Dynamics simulations. Velocity field and the pressure field are compared and discussed in the light of the two simulation methods. We recover the Berverloo scaling relating discharge rate and aperture size. This result points at the existence of a yield stress, rather than at the mobilization of friction forces at walls, as controlling the discharge of the granular silo. [Preview Abstract] |
Monday, November 19, 2012 9:18AM - 9:31AM |
G32.00007: A study of Force chain statistics in quasi-2D granular systems Jie Zhang, Ling Zhang, Yujie Wang, Robert Ecke, Robert Behringer Force chains play a key role in the understanding of mechanical properties of granular materials. In this study, we have examined several statistical properties of force chains in a number of different granular systems using bi-disperse photo-elastic disks. These systems include vertical slabs of granular materials under the gravitational field, horizontal layers of granular materials under isotropic compression and under pure shear. Despite of drastically different protocols and processes used to generate these systems, we have found that there is a universal distribution of force chain length: they all obey exponential --like distributions. The exponential distributions can be explained using a diffusion-like argument. Despite the success of this argument, a fundamental question remains: how can force chains, which are ``believed'' to be \textit{hyperbolic} in nature, have their lengths obey exponential distributions, which are intrinsically diffusion-like? [Preview Abstract] |
Monday, November 19, 2012 9:31AM - 9:44AM |
G32.00008: Kinematics of segregating granular mixtures in quasi-2D heaps Yi Fan, Paul Umbanhowar, Julio Ottino, Richard Lueptow Segregation of granular mixtures of different sized particles in heap flow appears in a variety of contexts. Our recent experiments showed that when bi-disperse mixtures of different sized spherical particles fill a quasi-two dimensional (2D) silo, three different final heap configurations -- stratified, segregated, and mixed -- occur, depending on either 2D flow rate or heap rise velocity. However, since it is difficult to measure the kinematic details of the segregating granular mixtures in heap flow experimentally, the underlying mechanisms for how 2D flow rate or heap rise velocity influences final particle configurations have not been well understood. In this work, we use the discrete element method (DEM) to simulate heap flow of bi-disperse mixtures in experimental scale quasi-2D heaps. The final particle distributions in the simulations agree quantitatively with experiments. We measure several key kinematic properties of the segregating granular mixtures including the local flow rate, velocity, and flowing layer thickness. We correlate the characteristics of these kinematic properties with the local particle distributions of the mixtures. This provides new insights for understanding the mechanisms of segregation and stratification in heap flow including the linear decrease in flow rate and maximum velocity down the heap as well as the relatively constant flowing layer thickness along the length of the heap. [Preview Abstract] |
Monday, November 19, 2012 9:44AM - 9:57AM |
G32.00009: Stratification, segregation and mixing of bi-disperse granular materials in quasi-2D heaps Richard Lueptow, Yi Fan, Paul Umbanhowar, Julio Ottino Segregation and mixing of granular mixtures during heap formation have important consequences across a range of contexts, from chemical processing to construction to agriculture. This research investigates three different final particle configurations of bi-disperse granular mixtures of spherical particles - stratified, segregated and mixed - during filling of quasi-two dimensional silos. We considered a larger number and relatively wider range of control parameters than previous studies, including particle size ratio, flow rate, system size, and heap rise velocity. The boundary between the stratified and unstratified states is primarily controlled by the two-dimensional flow rate, with the critical flow rate for the transition depending weakly on particle size ratio and flowing layer length. In contrast, the transition from segregated to mixed states is controlled by the rise velocity of the heap, a control parameter not previously considered. The critical rise velocity for the transition from a segregated state to a mixed state depends strongly on the particle size ratio. [Preview Abstract] |
Monday, November 19, 2012 9:57AM - 10:10AM |
G32.00010: Resolving a paradox of anomalous scalings in the diffusion of granular materials Ivan C. Christov, Howard A. Stone Granular materials do not perform Brownian motion, yet diffusion can be observed in such systems when agitation causes inelastic collisions between particles. It has been suggested that axial diffusion of granular matter in a rotating drum might be ``anomalous'' in the sense that the mean squared displacement of particles follows a power law in time with exponent less than unity. Further numerical and experimental studies have been unable to definitively confirm or disprove this observation. We show two possible resolutions to this apparent paradox without the need to appeal to anomalous diffusion. First, we consider the evolution of arbitrary (non-point-source) initial data towards the self-similar intermediate asymptotics of diffusion by deriving an analytical expression for the instantaneous collapse exponent of the macroscopic concentration profiles. Second, we account for the concentration-dependent diffusivity in bidisperse mixtures, and we give an asymptotic argument for the self-similar behavior of such a diffusion process, for which an exact self-similar analytical solution does not exist. The theoretical arguments are verified through numerical solutions of the governing partial differential equations. [Preview Abstract] |
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