Bulletin of the American Physical Society
67th Annual Meeting of the APS Division of Fluid Dynamics
Volume 59, Number 20
Sunday–Tuesday, November 23–25, 2014; San Francisco, California
Session G24: Granular Flows: Mixing, Segregation and Separation |
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Chair: Sylvain Joubaud, Ecole Normale Superieure de Lyon Room: 2003 |
Monday, November 24, 2014 8:00AM - 8:13AM |
G24.00001: Continuum modeling of diffusion and dispersion in dense granular flows Ivan C. Christov, Howard A. Stone Continuum modeling of granular flows remains a challenge of modern statistical physics. Granular materials do not perform Brownian motion, yet diffusion and shear dispersion can be observed in such systems when agitation causes inelastic collisions between particles. In a number of canonical flow regimes (e.g., in a rotating container or down an incline), granular materials can behave like fluids. We formulate and solve the granular counterparts to two basic fluid mechanics problems: diffusion of a pulse and shear dispersion of a pulse for dense granular materials in rapid flow. We provide a theory to account for the concentration-dependent diffusivity of bidisperse granular 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. For shear dispersion, we show that the effective dispersivity of the depth-averaged concentration of the dispersing powder varies as the P\'eclet number squared, as in classical Taylor--Aris dispersion of molecular solutes. The calculation is extended to generic shear profiles, showing a significant enhancement for convex profiles due to the shear-rate dependence of the diffusivity of granular materials. [Preview Abstract] |
Monday, November 24, 2014 8:13AM - 8:26AM |
G24.00002: Multiscale modelling of multi-component granular mixtures Deepak Tunuguntla, Anthony Thornton, Stefan Luding, Thomas Weinhart Efforts to extract, or ``coarse grain,'' continuum fields (macroscopic dynamics) from microscopic data have existed for decades. We present novel coarse graining expressions for the stress fields for discrete mechanical systems and illustrate their application to segregating granular chute flow. These expressions are applicable near boundaries/interfaces and also to multi-component granular mixtures. Boundary interaction forces are taken into account in a self-consistent way and thus allow for construction of a continuous stress and interaction force field, avoiding problems many other methods have near boundaries. Similarly, stress and drag forces can be determined for individual constituents/components of a mixture. The resolution and shape of the coarse-graining function used in the formulation can be chosen freely, such that both microscopic and macroscopic effects can be studied. The method does not require temporal averaging and thus can be used to investigate time-dependent flows as well as static and steady situations. Furthermore, discrete element simulations of granular mixtures are presented to illustrate the strength of the new boundary/mixture treatment and show that the coarse graining scale (i.e. resolution) is independent of the size of the components (for spheres). [Preview Abstract] |
Monday, November 24, 2014 8:26AM - 8:39AM |
G24.00003: Modeling Size Polydisperse Granular Flows Richard M. Lueptow, Conor P. Schlick, Austin B. Isner, Paul B. Umbanhowar, Julio M. Ottino Modeling size segregation of granular materials has important applications in many industrial processes and geophysical phenomena. We have developed a continuum model for granular multi- and polydisperse size segregation based on flow kinematics, which we obtain from discrete element method (DEM) simulations.~The segregation depends on dimensionless control parameters that are functions of flow rate, particle sizes, collisional diffusion coefficient, shear rate, and flowing layer depth. To test the theoretical approach, we model segregation in tri-disperse quasi-2D heap flow and log-normally distributed polydisperse quasi-2D chute flow. In both cases, the segregated particle size distributions match results from full-scale DEM simulations and experiments.~ While the theory was applied to size segregation in steady quasi-2D flows here, the approach can be readily generalized to include additional drivers of segregation such as density and shape as well as other geometries where the flow field can be characterized including rotating tumbler flow and three-dimensional bounded heap flow. [Preview Abstract] |
Monday, November 24, 2014 8:39AM - 8:52AM |
G24.00004: Asymmetric flux models for particle-size segregation in granular avalanches Parmesh Gajjar, Nico Gray Particle-size segregation commonly occurs in dense shallow flows of grains down an incline, through the combined processes of \textit{kinetic sieving} and \textit{squeeze expulsion}. Recent experimental observations suggest that a single small particle can percolate downwards through a matrix of large particles faster, than a single large particle can be levered upwards through a matrix of fines. In this work, this asymmetry is modelled using a segregation flux that is dependent only on the small particle concentration. The flux function is asymmetric about its maximum point, differing from the symmetric quadratic form used in recent models of particle size-segregation, and a cubic flux function is used in this work for illustration. Exact solutions are presented for steady non-diffuse flow in two dimensions with both a homogeneously mixed and normally graded inflow, as well as for a steady-state breaking wave. The new asymmetric flux results in a concentration dependence on both the distance to fully segregate, and the length of the breaking wave. [Preview Abstract] |
Monday, November 24, 2014 8:52AM - 9:05AM |
G24.00005: A mixture theory for size and density segregation in granular free-surface flows Anthony Thornton, Deepak Tunuguntla In the past years much work has been undertaken on developing mixture theory continuum models to describe kinetic-sieving driven size-segregation [1-3]. We propose an extension to these models that allows their application to bidisperse flows over inclined channels, with particles varying in density and size [4]. Our model incorporates both a recently proposed explicit formula, for how the total pressure is distributed among different species of particles, of Marks et al. [2], which is one of the key elements of mixture theory-based kinetic sieving models and a shear rate-dependent drag. The resulting model is used to predict the range of particle sizes and densities for which the mixture segregates. The prediction of no segregation in the model is benchmarked by using discrete particle simulations, and good agreement is found when a single fitting parameter is used which determines whether the pressure scales with the diameter, surface area or volume of the particle. \\[4pt] [1] Gray and Thornton. Proc. Royal Soc. A, 461:1447-1473, 2005.\\[0pt] [2] Marks, Rognon, and Einav. JFM, 690:499-511, 2012.\\[0pt] [3] Fan and Hill.NJP, 13(9):095009, 2011.\\[0pt] [4] Tunuguntla, Bokhove and Thornton. JFM, 749:99-112, 2014. [Preview Abstract] |
Monday, November 24, 2014 9:05AM - 9:18AM |
G24.00006: Evolution of a dynamic suspension created by the invasion of an air flow in a granular bed Tess Homan, Valerie Vidal, Sylvain Joubaud We experimentally investigate the behavior of an immersed granular bed when perturbed by an air inflow from a single inlet at the bottom of a 2D cell. In particular, we focus on quasi-suspensions, meaning that the grains are slightly heavier than the fluid. We observe the creation of a dynamic suspension. We characterize the evolution of the local packing fraction, the percentage of particles mixed in the dynamic suspension and the shape of the ``dead zone,'' {\em i.e.} a region where the grains remain motionless. In particular, we study the influence of the air flow-rate or injection pressure. We complement the study by considering the effect of the density difference between the grains and the fluid, the initial height of the fluid or the height of the bed. [Preview Abstract] |
Monday, November 24, 2014 9:18AM - 9:31AM |
G24.00007: ABSTRACT WITHDRAWN |
Monday, November 24, 2014 9:31AM - 9:44AM |
G24.00008: Dynamics of density-inverted/Leidenfrost state in a vibrofluidized bed Istafaul Ansari, Meheboob Alam Akin to the original Leidenfrost state, a dense, compact layer of particles can be supported by a dilute gaseous region of fast moving particles underneath it in vertically shaken granular materials-- this is dubbed granular Leidenfrost state (gLS). Previous experiments and simulations have noted that the gLS is a stationary state that bifurcates from a time-periodic bouncing bed state with increasing shaking intensity. Here we report a novel unsteady behavior of the gLS in experiments on vertically shaken vibrofluidized bed of a monolayer of spherical balls. With the help of high speed imaging, we track the height of the interface (that separates the dense cloud of particles from the dilute gaseous region) as well as the top surface of the bed at various time instants of the oscillation cycle. Both these quantities are found to vary sinusoidally with time but with different amplitudes and a phase-lag and their oscillation frequencies closely match the frequency of the shaker. The amplitude difference and the phase-lag between the top-surface and interface motions are two distinguishing features of the ``oscillatory'' gLS. The transition from synchronized oscillatory motion to a probable ``steady'' gLS with increasing shaking intensity seems to be subtle. [Preview Abstract] |
Monday, November 24, 2014 9:44AM - 9:57AM |
G24.00009: Component morphology, size, and compositional impact on pharmaceutical powder blend flowability David Goldfarb, Hirotaka Nakagawa, Stephen Conway Through analysis of particle morphology, particle size, and compositional influences, we present experimental case studies revealing unexpected transitions in flowability and cohesion of pharmaceutical powder blends. We explore interactions between the needle-like API (Active Pharmaceutical Ingredient) and the more spherical remaining components (excipients) in the blend to explain these transitions, and optimal concentrations are identified. A range of particle sizes, aspect ratios (for API), and compositions were examined. Surprisingly, under certain conditions, a blend with a low API concentration exhibits less cohesive flowability properties than a placebo blend containing no API. Effective volume and coordination number models are tested by investigation of particle geometry, particle contact, and Van der Waals force factors. These results should translate both to the improved understanding of mixed component morphology systems and to a novel approach towards pharmaceutical product formulation optimization. [Preview Abstract] |
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