Bulletin of the American Physical Society
66th Annual Meeting of the APS Division of Fluid Dynamics
Volume 58, Number 18
Sunday–Tuesday, November 24–26, 2013; Pittsburgh, Pennsylvania
Session G32: Granular Flows I: Impact, Locomotion and Drag |
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Chair: Amos Winter, Massachusetts Institute of Technology Room: 403 |
Monday, November 25, 2013 8:00AM - 8:13AM |
G32.00001: Impact response of shear thickening suspensions Eric Brown, Oktar Ozgen, Marcelo Kallmann, Benjamin Allen Dense suspensions of hard particles such as cornstarch in water exhibit shear thickening, in which the energy dissipation rate under shear dramatically increases with increasing shear rate. Recent work has established that in steady-state shear this phenomena is a result of a dynamic jamming of the particles in suspension. Several dynamic phenomena observed in such suspensions have long been assumed to be a consequence of this shear thickening; strong impact resistance, the ability of a person to run on the fluid surface, fingering and hole instabilities under vibration, and oscillations in the speed of sinking of an object in the fluid. However, I will present results of experiments consisting of an indenter impacting a dense suspension which demonstrate that the strong impact resistance cannot be explained by existing models for steady-state shear thickening. I will show these dynamic phenomena can be reproduced by graphical simulations based on a minimal phenomenological model in which the fluid has a stiffness with a dependence on velocity history. These and other recent results suggest a need for new models to understand the dynamic phenomena associated with shear thickening fluids. [Preview Abstract] |
Monday, November 25, 2013 8:13AM - 8:26AM |
G32.00002: Impact in dense granular suspensions: crucial role of dilatancy and pore pressure feedback Yoel Forterre, J. John Soundar Jerome, Nicolas Vandenberghe, Laurent Duchemin We investigate the impact of a rigid sphere onto a granular paste made of non-buoyant glass beads mixed with a liquid under gravity. We show that the initial volume fraction of the granular packing has a critical influence on the impact behavior. For loose packing, the ball sinks in the granular medium as in a liquid, giving rise to a collapsing cavity and a central jet as observed with fine powders in air. By contrast, for dense packing, the ball stops as soon as it hits the surface and its kinetic energy is almost instantly dissipated. We interpret this ``liquid-solid'' transition as the volume fraction change by a coupling between dilatancy effects and the liquid pore pressure during the impact. Dynamic pore pressure measurements and a simple diphasic model taking into account dilatancy support this mechanism. Our results show that ``shear-thickening-like'' phenomena in granular suspensions can arise from transient diphasic coupling rather than from the intrinsic rheology of the material. [Preview Abstract] |
Monday, November 25, 2013 8:26AM - 8:39AM |
G32.00003: Dimensional analysis scaling of impact craters in unconsolidated granular materials David R. Dowling, Thomas R. Dowling Dimensional analysis is a general technique for determining how the independent parameters that describe physical phenomena must be arranged to produce dimensionally self-consistent results. This presentation describes how dimensional analysis may be successfully applied to the formation of impact craters produced by dropping spherical objects into a bed of unconsolidated granular material. The experiment is simple and safe, and laboratory results for different impact energies (0.001 to 1.6 J), seven different spheres (masses from 4 to 64 grams, diameters from 1.0 to 4.3 cm), and two different dry granular materials (granulated sugar, and playground sand) may be collapsed to a single power-law using parametric scaling determined from dimensional analysis. Thus, impact crater formation may provide a useful validation test for simulations of granular material dynamics. Interestingly, the scaling law shows that the impacting sphere's diameter is not a parameter. And, the resulting power law can be extrapolated, with some success, over more than 16 orders of magnitude to produce an independent estimate of the impact energy that formed the 1.2-km-diameter Barringer Meteor Crater in northern Arizona. [Preview Abstract] |
Monday, November 25, 2013 8:39AM - 8:52AM |
G32.00004: Drag reduction due to interstitial air in a granular medium Tess Homan, Devaraj van der Meer The force experienced by an object while it penetrates a pre-fluidized sand bed strongly depends on the ambient air pressure. In this work we experimentally investigate the influence of interstitial air by systematically varying the penetration velocity and the ambient air pressure and measuring the resulting force required to push the intruder into the sand bed. Counterintuitively, we find that for the intruder to move faster through the bed a {\em lower} force is required. We hypothesize that, while the object moves down, sand in front of the intruder is compacted and the air in this compactified region is trapped. At higher penetration velocities air has no time to move out of the way causing a pressure build-up in front of the ball which leads to drag reduction. To test this hypothesis, we perform experiments at reduced ambient air pressures and find that indeed the dependence on the intruder velocity disappears: The measured force is constant and equal to the value of the drag found in the quasi-static limit, which emphasizes the role of air. [Preview Abstract] |
Monday, November 25, 2013 8:52AM - 9:05AM |
G32.00005: The Mechanics of Localized Fluidization Burrowing Amos Winter This presentation will focus on the granular mechanics and critical timescales related to localized fluidization burrowing, a digging method inspired by the Atlantic razor clam (\textit{Ensis directus}). The animal uses motions of its valves to locally fail and then fluidize surrounding soil to reduce burrowing energy and drag. The characteristic contraction time to achieve fluidization can be determined from substrate properties. The geometry of the fluidized zone is dictated by the coefficient of lateral earth pressure and friction angle of the soil. Calculations using full ranges for these parameters indicate that the fluidized zone is a local effect, occurring between 1--5 body radii away from the animal. The energy associated with motion through fluidized substrate -- characterized by a depth-independent density and viscosity -- scales linearly with depth. In contrast, moving through static soil requires energy that scales with depth squared. For engineers, localized fluidization offers a mechanically simple and purely kinematic method to dramatically reduce energy costs associated with digging. This concept is demonstrated with RoboClam, an \textit{E. directus}-inspired robot. Using a genetic algorithm to find optimal digging kinematics, RoboClam has achieved localized fluidization burrowing performance comparable to that of the animal, with a linear energy-depth relationship, in both idealized granular glass beads and \textit{E. directus}' native cohesive mudflat habitat. [Preview Abstract] |
Monday, November 25, 2013 9:05AM - 9:18AM |
G32.00006: Reversibility in locomotion in granular media William Savoie, Daniel Goldman A recent study of a self-deforming robot [Hatton et al, PRL, 2013] demonstrated that slow movement in dry granular media resembles locomotion in low Re fluids, in part because inertia is dominated by friction. The study indicated that granular swimming was kinematically reversible, a surprise because yielding in granular flow is irreversible. To investigate if reciprocal motions lead to net displacements in granular swimmers, in laboratory experiments, we study the locomotion of a robotic ``scallop'' consisting of a square body with two flipper-like limbs controlled to flap forward and backward symmetrically (a flap cycle). The body is constrained by linear bearings to allow motion in only one dimension. We vary the the flapping frequency $f$, the body/flipper burial depth $d$, and the number of flaps $N$ in a deep bed of 6 mm diameter plastic spheres. Over a range of $f$ and $d$, the $N=1$ cycle produces net translation of the body; however for large $N$, a cycle produces no net translation. We conclude that symmetric strokes in granular swimming are irreversible at the onset of self-deformation, but become asymptotically reversible. [Preview Abstract] |
Monday, November 25, 2013 9:18AM - 9:31AM |
G32.00007: Sidewinding as a control template for climbing on sand Hamidreza Marvi, Chaohui Gong, Nick Gravish, Joseph Mendeslon, Ross Hatton, Howie Choset, Daniel Goldman, David Hu Sidewinding, translation of a limbless system through lifting of body segments while others remain in static contact with the ground, is used by desert-dwelling snakes like sidewinder rattlesnakes {\em Crotalus cerastes} to locomote effectively on hard ground, rocky terrain, and loose sand. Biologically inspired snake robots using a sidewinding gait perform well on hard ground but suffer significant slip when ascending granular inclines. To understand the biological organisms and give robots new capabilities, we perform the first study of sidewinding on granular media. We vary the incline angle ($0<\theta<20^\circ$) of a trackway composed of desert sand. Surface plate drag measurements reveal that as incline angle increases, downhill yield stresses decrease by 50\%. Our biological measurements reveal that the animals double the length of the contact region as $\theta$ increases; we hypothesize that the snakes control this contact to reduce ground shear stress and avoid slipping. Implementing the anti-slip motion in a snake robot using contact patch modulation enables the robot to ascend granular inclines. [Preview Abstract] |
Monday, November 25, 2013 9:31AM - 9:44AM |
G32.00008: A predictive, nonlocal rheology for granular flows Ken Kamrin, David Henann We propose a continuum model for flowing granular matter and demonstrate that it quantitatively predicts flow and stress fields in many different geometries. The model is constructed in a step-by-step fashion. First we compose a relation based on existing granular rheological approaches (notably the ``inertial'' granular flow rheology) and point out where the resulting model succeeds and where it does not. The clearest missing ingredient is shown to be the lack of an intrinsic length-scale. To tie flow features more carefully to the characteristic grain size, we compose a nonlocal model that includes a new size-dependent term (with only one new material parameter). This new nonlocal model resolves some outstanding questions in the granular flow literature --- of note, it is the first model to predict all features of flows in split-bottom cell geometries, a decade-long open question in the field. In total, we will show that this new model, using three material parameters, quantitatively matches the flow and stress data from over 160 experiments in several different geometries. [Preview Abstract] |
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