Bulletin of the American Physical Society
60th Annual Meeting of the Divison of Fluid Dynamics
Volume 52, Number 12
Sunday–Tuesday, November 18–20, 2007; Salt Lake City, Utah
Session GM: Granular Flows IV |
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Chair: Kimberly Hill, University of Minnesota Room: Salt Palace Convention Center 251 A |
Monday, November 19, 2007 10:30AM - 10:43AM |
GM.00001: Application of dynamical systems tools to mixing in quasi-2d and 3d tumblers Steven W. Meier, Rob Sturman, Richard M. Lueptow, Stephen Wiggins, Julio M. Ottino Granular mixing in rotating tumblers is countered by the tendency of the flow to induce segregation by particle size or density. The study of the competing underlying dynamics becomes complicated. However, all of the nontrivial dynamics takes place in a thin flowing surface layer. This observation, coupled with experimental measurements of the variation of the flow with depth in the surface layer and with tumbler geometry, leads to a continuum-based dynamical systems framework applicable to time-periodic flow in quasi-2d and 3d tumblers rotated about one or more axes of rotation. The case of time-periodic systems, in its simplest version, can be viewed as a mapping of a domain into itself. The placement of periodic points is investigated using symmetry concepts; the character of the periodic points and associated manifolds provide a skeleton for the flow and a template for segregation processes. Experiments validate the theoretical construction of time-periodic flows as maps. [Preview Abstract] |
Monday, November 19, 2007 10:43AM - 10:56AM |
GM.00002: The Linked Twist Map Approach to Granular Tumbler Mixers Rob Sturman, Steven Meier, Stephen Wiggins, Julio Ottino The simplest type of time-periodic granular tumbler mixer can be cast in the form of a linked twist map (LTM). These are examples of dynamical systems for which, under the correct conditions, the strongest mixing properties can be rigorously proved. Despite the fact that tumblers do not satisfy these conditions, the LTM approach allows the prediction of the location and size of prominent islands in a two-dimensional tumbler, and in three dimensions a similar approach reveals interesting dynamical structures which in turn yield information about islands. The dynamics of a hitherto abstract dynamical system - a piecewise isometry - further suggests that complicated dynamics are not solely the result of dynamics in the flowing layer. [Preview Abstract] |
Monday, November 19, 2007 10:56AM - 11:09AM |
GM.00003: The Onset of Axial Segregation in Rotating Tumblers Pengfei Chen, Julio M. Ottino, Richard M. Lueptow The onset of axial segregation of binary mixtures having different size particles in rotating tumblers is numerically investigated using the discrete element method. Results confirm the existence of axial flows between bands, which is the basis for most theoretical models of the phenomenon. We consider the distribution of axial fluxes of the two types of particles in transverse planes and their variance along the length of the tumbler. The onset of axial segregation occurs when the ratio of the axial flux of the two kinds of particles differs in the upstream and downstream part of the flowing layer. This difference is likely to be generated from the transverse segregation occurring in the flowing layer. Based on this, a phenomenological model with a negative diffusion coefficient can account for the onset of axial segregation qualitatively. The criterion for the onset of axial segregation and the roles of endwalls and tumbler parameters are also discussed. [Preview Abstract] |
Monday, November 19, 2007 11:09AM - 11:22AM |
GM.00004: Axial Band Dependence on Relative Particle Concentration in Bidisperse Mixtures Gabriel Juarez, Julio M. Ottino, Richard M. Lueptow Although axial band formation in long rotating tumblers has been long-studied, the dependence of band formation on the relative concentration of the bidisperse particles has not been addressed. We examine axial band formation for dry and liquid granular systems of bidisperse mixtures of particles with the volume composition of small particles ranging from 10{\%} to 90{\%} in a half filled tumbler for various rotation rates. Experiments were conducted in a tumbler of length 75 cm and diameter of 6.35 cm, with mixtures of 0.6 and 2 mm, and 1 and 2 mm particles. Single bands form for small particle concentrations as low as 10{\%} and as high as 90{\%}, usually near the end walls, although band formation along the entire tumbler is less likely for very low or very high concentrations. Bands then merge, or coarsen, and for small particle concentrations of 50{\%} and greater, the coarsening is logarithmic. For very low or very high particle concentrations, the rate of coarsening is not logarithmic or coarsening does not occur within the duration of the experiment (600 revolutions). The band width of small and large particles scales with the tumbler diameter. [Preview Abstract] |
Monday, November 19, 2007 11:22AM - 11:35AM |
GM.00005: Coarsening of segregation patterns in quasi-two-dimensional granular tumblers Diego A. Melani, Steven W. Meier, Julio M. Ottino, Richard M. Lueptow A fundamental characteristic of granular flows is segregation based on particle size or density. In previous studies, a segregation pattern of several radial streaks occurs within $O (10)$ revolutions in quasi-two-dimensional rotating tumblers with fill fractions between 50\% and 70\%. By extending the duration of the experiments, we observe coarsening of the radial streak pattern to as few as one streak over $O(10^2$-- $10^3)$ tumbler revolutions for a wide range of conditions. We observe coarsening in 55\%-full circular and square tumblers containing bidisperse size varying mixtures of glass particles of varying concentrations ($20$--$75$\% by volume small particles) for a range of rotation rates. Bidisperse size and density varying mixtures of small steel and large glass particles also exhibit coarsening. The coarsening mechanism appears to occur by transport from one streak to another via the radial core. [Preview Abstract] |
Monday, November 19, 2007 11:35AM - 11:48AM |
GM.00006: Subsurface Flow Structure in Rotating Tumblers Richard M. Lueptow, Pengfei Chen, Julio M. Ottino Granular flow in a rotating tumbler is altered near the endwalls, which is thought to be closely related to mixing and axial segregation near endwalls. Using the discrete element method, we compare the flowing layer for half-full 3D and quasi-2D tumblers containing particles with a monodisperse distribution. Results indicate that the flowing layer structure and velocity field at the center of a long tumbler differ from those near the endwalls. Furthermore, the flow is faster in a quasi-2D tumbler, but the flowing layer is not as deep. In 3D tumblers, endwalls introduce higher streamwise and transverse velocity fluctuations near the endwalls, but limit axial fluctuations. The axial flow near the endwalls is localized and independent with the length of the tumbler for long tumblers, but the axial flow regions associated with the endwalls interact with each other in short tumblers. [Preview Abstract] |
Monday, November 19, 2007 11:48AM - 12:01PM |
GM.00007: Sorting out segregation mechanisms in densely flowing granular mixtures Kimberly Hill, Yi Fan, Jiafeng Zhang Densely flowing granular mixtures segregate due to differences in the size, material density, and other particle properties. In some situations the segregation is simple: smaller particles tend to sink compared to their larger equal-density counterparts; denser particles tend to sink compared with their equal-sized lighter counterparts. These are often attributed to kinetic sieving and buoyancy, respectively. However, in some situations the segregation is more complex: particles poured into a pile may segregate into stratified layers, and in drums some mixtures will segregate into radial stripes and axial bands. It is difficult to determine the dominant segregation mechanism(s) in each case. In most experimental segregation studies of densely sheared granular mixtures, velocity gradients, volume fraction gradients and gravity simultaneously act on the granular mixture. We compare segregation in three different systems to isolate each mechanism. While gravity is important, eliminating the volume fraction gradient significantly reduces size segregation. Shear-induced segregation is also important, but appears the weakest of the three mechanisms in dense granular flow. [Preview Abstract] |
Monday, November 19, 2007 12:01PM - 12:14PM |
GM.00008: Segregation in a split-bottom cell Fan Yi, Kimberly Hill, Zoubair Entezari In most devices, it is difficult to isolate granular segregation driven by a velocity gradient and associated Reynolds stresses from the effects of gravity and a volume fraction gradient. We use a split-bottom cell [1] to isolate the effect of a velocity gradient and associated Reynolds stresses on segregation associated with differences in particle size and density. In this geometry, a wide shear band is formed away from side walls, and only shear (perpendicular to gravity and the free surface) drives the preferential particle movement in the horizontal direction. Horizontal segregation was observed for both differences in the particle size and particle density. Different particle size ratios can influence the segregation speed: the smaller the particle size ratio, the faster the segregation. The segregation speed is also influenced by the width of shear band: a wider shear band will leads to faster segregation. We will discuss these differences in the context horizontal diffusion, Reynolds stresses, and velocity differences. \newline \newline [1] D. Fenistein and M. van Hecke, Nature (London) \textbf{425}, 256 (2003) [Preview Abstract] |
Monday, November 19, 2007 12:14PM - 12:27PM |
GM.00009: Velocity fluctuations in granular mixtures in a rotating drum Jiafeng Zhang, Kimberly Hill Dense free surface granular flow often has two regimes. In the lower region, particles slide over one another in dense, low-energy laminar-like flow. In the upper region, particles bounce and ``saltate'' over one another in an energetic, low-density cloud. We numerically study the magnitude of velocity fluctuations -- often associated with a granular temperature -- for mixtures of particles differing in size and density in these two regimes coexisting in a rotating drum. We found that differences in the velocity fluctuation between the different mixture components depend on the regime of the flowing layer. In the low-density energetic regime, the velocity fluctuations of a component relative to the mixture vary with mass: heavier particles have smaller velocity fluctuations than lighter particles in the same mixture, regardless of size difference. In the high-density, low-energy regime, the smaller particles always have larger velocity fluctuations than the larger particles. We show this difference is attributable to the regime of flow: where the volume fraction is relatively low near surface, collisions dominates the interactions between particles; below the low volume region, geometric constraints dominate the interactions between particles. [Preview Abstract] |
Monday, November 19, 2007 12:27PM - 12:40PM |
GM.00010: Dune formation in pipe flow Malika Ouriemi, pascale Aussillous, Elisabeth Guazzelli We present a phase diagram of the different dune patterns observed when a bed composed of spherical particles is submitted to a shearing flow in a pipe. A stability analysis is performed to predict the threshold for dune formation. The control parameter of the instability is the Reynolds number and the predicted wavelength at onset is of the order of the fluid thickness. This analysis accounts reasonably well for the experimental observations. [Preview Abstract] |
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