Granular Fingering in a Hele-Shaw Cell

The finger-like branching pattern that occurs when a less viscous fluid displaces a more viscous one confined between two parallel plates, the so-called Hele-Shaw geometry, has been studied widely and with various normal fluids. We have investigated the granular analogue of such Hele–Shaw cell, where air (the low-viscosity fluid) displaces glass beads (the high viscosity granular "fluid"). Because granular fluids composed of dry, non-cohesive grains exhibit negligible surface tension, this allows us to explore a regime not accessible with ordinary fluids. We demonstrate that the grain–gas interface exhibits a fractal structure and sharp cusps, which are associated with the hitherto-unrealizable singular hydrodynamics predicted for the zero-surface-tension limit of normal fluid fingering. The scaling for the finger width is distinct from that for ordinary fluids, reflecting unique granular properties such as friction-induced dissipation as opposed to viscous damping. However, the fractal dimension of the fingering pattern and the shape of the singular cusps on the interface agree with the theories based on simple Laplacian growth of conventional fluid fingering in the zero-surface-tension limit. Read more at Nature News.

• Xiang Cheng, Lei Xu, Aaron Patterson, Heinrich M. Jaeger and Sidney Nagel, "Towards the zero-surface-tension limit in granular fingering instability", Nature Physics 4, 234 (2008)

Impact of a Granular Jet: Emergence of a Liquid with Zero Surface Tension

When one or two particles strike a smooth wall at normal incidence, they rebound in the direction whence they came. Yet, as we show here, a dense stream of non-cohesive particles hitting a target retains its integrity and deforms into a thin sheet with a shape resembling the structures created by an impinging liquid jet. However, with the granular materials, this “liquid” has special property of zero surface-tension. Furthermore, by decreasing the number of particles inside a jet, we can turn the behavior of the granular jet from the liquid-like behavior back to the normal particle-like behavior. We believed that this experiment is the classical analog of the much more microscopic and exotic experiment done at the Brookhaven National Laboratory, where the quark-gluon plasma produced by the high-energy collisions of gold ions also shows the liquid-like scattering pattern, similar to what we observed with granular materials. Read more in the press: UofC Chronicle, AIP Physics News, RHIC News

• Xiang Cheng, German Varas, Daniel Citron, Heinrich M. Jaeger and Sidney R. Nagel, “Collective Behavior in a Granular Jet: Emergence of a Liquid with Zero Surface Tension”, Phys. Rev. Lett. 99, 188001 (2007).

Fast X-ray Imaging of Impact Dynamics in a Granular Bed

The impact of solid objects into a granular bed has been studied since the 1800’s, yet many fundamental questions remain unresolved.  The complex response of the bed to sudden impact differs substantially from impact in ordinary solids and liquids.  We investigate how this response is mediated by the presence of interstitial gas between the grains.  Using high-speed x-ray radiography we track the motion of a steel sphere through the interior of a bed of fine, loose granular material.  We find a crossover from nearly incompressible, fluid-like behavior at atmospheric pressure to a highly compressible, dissipative response once most of the gas is evacuated.  Read more and see movies

• John R. Royer, Eric I. Corwin, Peter J. Eng, Heinrich M. Jaeger, “Gas-Mediated Impact Dynamics in Fine-Grained Granular Materials”, Phys. Rev. Lett. 99, 038003 (2007).
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Tracking the Flow Field Inside a Sheared Granular System

Shear bands in dense granular materials are localized regions of large velocity gradients; they are the antithesis of the broad uniform flows seen in slowly sheared Newtonian fluids. Until recently it was generally assumed that all granular shear bands were narrow. However, in 2003 Fenistein et al. discovered that in modified Couette cells granular shear bands can be made arbitrarily broad. In collaboration with Gary Grest's group at Sandia, we have investigated the evolution of granular shear flow as a function of height in a split-bottom Couette cell. Using particle tracking, magnetic-resonance imaging, and large-scale simulations, we find a transition in the nature of the shear as a characteristic height H* is exceeded. Below H* there is a central stationary core; above H* we observe the onset of additional axial shear associated with torsional failure. Radial and axial shear profiles are qualitatively different: the radial extent is wide and increases with height, while the axial width remains narrow and fixed.

• Xiang Cheng, Jeremy B. Lechman, Antonio F. Barbero, Gary S. Grest, Heinrich M. Jaeger, Greg S. Karczmar, Matthias E. Möbius, and Sidney R. Nagel, “Onset of three-dimensional shear in granular flow”, Phys. Rev. Lett. 96, 038001 (2006).

Granular Jets

When a heavy sphere is dropped onto a bed of loose, fine sand, a remarkable phenomenon occurs: a large, focused jet of sand shoots upwards. Although similar looking jets are observed on impact in fluid systems, they are held together by surface tension. Surprisingly, the granular jet exists in the absence of both surface tension and cohesion, thus fluid jet models are of limited use. Previous work by Shen and Thoroddson (UIUC) and by Detlef Lohse's group at Twente (The Netherlands) proposed that the jet is created solely by the gravity-driven collapse of a void left by the sphere’s descent through the pack. We have found experimental evidence that granular jets are instead driven by a more complex process involving the interaction between the sand and interstitial air. Using high-speed X-ray radiography, and high-speed digital video, we observe the formation of the jet both inside and above the bed.We find that what previously was thought of as a single jet in fact consists of two components: a wispy, thin jet that varies little with pressure followed by a thick air-pressure-driven jet. This is further evidence that qualitatively new phenomena in granular systems can emerge as a function of air pressure. Our results highlight the importance of the dynamic coupling between gas and granule motion............More on granular jets including movies and a demonstration on how to produce a jet in your kitchen (with a glass jar, a ball bearing and a package of baking soda). Also....What ended up in the press: UofC Chronicle, NSF press release, AIP Physics News

• John R. Royer, Eric I. Corwin, Andrew Flior, Maria-Luisa Cordero, Mark Rivers, Peter Eng, and Heinrich M. Jaeger, “Formation of Granular Jets Observed by High-Speed X-ray Radiography”, Nature Physics 1, 164-167 (2005).

How do forces propagate through a granular medium?

A "nugget" on force propagation through a granular sphere pack

• D. M. Mueth, H. M. Jaeger, and S. R. Nagel, “Force Distribution in a Granular Medium,” Physical Review E 57, 3164 (1998)
• Daniel L. Blair, Nathan W. Mueggenburg, Adam H. Marshall, Heinrich M. Jaeger, and Sidney R. Nagel, “Force distributions in 3D granular assemblies: Effects of packing order and inter-particle friction”, Phys. Rev. E 63, 041304 (2001)
• Nathan W. Mueggenburg, Heinrich M. Jaeger, Sidney R. Nagel, “Stress transmission through three-dimensional ordered granular arrays”, Phys. Rev. E 66, 031304 (2002)
• J. Michael Erikson, Nathan W. Mueggenburg, Heinrich M. Jaeger, Sidney R. Nagel, “Force Distributions in Three-Dimensional Compressible Granular Packs”, Phys. Rev. E 66, 040301 (2002).

Using force measurements as a "microscope" to detect the onset of jamming

Glasses are rigid, but flow when the temperature is increased. Similarly, granular materials are rigid, but become unjammed and flow if sufficient shear stress is applied. The rigid and flowing phases are strikingly different, yet measurements reveal that the structures of glass and liquid are virtually indistinguishable. It is therefore natural to ask whether there is a structural signature of the jammed granular state that distinguishes it from its flowing counterpart. Here we find evidence for such a signature, by measuring the contact-force distribution between particles during shearing. Because the forces are sensitive to minute variations in particle position, the distribution of forces can serve as a microscope with which to observe correlations in the positions of nearest neighbours. We find a qualitative change in the force distribution at the onset of jamming. If, as has been proposed, the jamming and glass transitions are related, our observation of a structural signature associated with jamming hints at the existence of a similar structural difference at the glass transition — presumably too subtle for conventional scattering techniques to uncover. Our measurements also provide a determination of a granular temperature that is the counterpart in granular systems to the glass-transition temperature in liquids.Read more... ..NSF Press Release on this work and closely related research by Bob Behringer's group at Duke. Plus: a write-up in the UofC Chronicle.

• Eric Corwin, Heinrich Jaeger, Sidney Nagel, “Structural signature of jamming in granular media”, Nature 435, 1075-1078 (2005).

How the interstitial gas affects size separation in vibrated granular media

Vibrated granular materials can appear very much like a fluid. Yet there are important differences. A completely counter-intuitive property is that if a sufficiently heavy large object is placed inside a vibrated container filled with granular particles, it will rise to the top. Even more confounding is that a very light intruder can either rise or sink. Using magnetic resonance imaging and high-speed video techniques, we have demonstrated that both the rising and the sinking behavior is determined by the interaction of the granular medium with the air in its interstices: when the system is evacuated, the intruder follows the motion of the background particles. These results suggest a new model for understanding the role of the interstitial air on the so-called "Brazil Nut Effect", by which larger objects typically rise to the top of a shaken granular medium.......Here's more, including. movies demonstrating the effect of interstitial gas (air) on the rising or sinking of large granular particles in a vibrated bed of smaller particles

• Matthias E. Möbius, Benjamin E. Lauderdale, Sidney R. Nagel and Heinrich M. Jaeger, “Size Separation of Granular Particles”, Nature 414, 270 (2001)
• Matthias E. Möbius, Xiang Cheng, Peter G. Eshuis, Gregory Karczmar, Sidney R. Nagel, and Heinrich Jaeger, “The Effect of Air on Granular Size Separation in a Vibrated Granular Bed”, Phys. Rev. E 72, 011304 (2005)
• Matthias E. Möbius, Xiang Cheng, Peter G. Eshuis, Gregory Karczmar, Sidney R. Nagel, and Heinrich Jaeger, “The Effect of Air on Granular Size Separation in a Vibrated Granular Bed”, Phys. Rev. E 72, 011304 (2005).

Discovery Channel Canada's Interview
with Heinrich Jaeger on the Brazil Nut Effect
(requires QuickTime Player)

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What the Telegraph.co.uk had to say. Or the BBC.

Reviews of granular matter physics

• Heinrich M. Jaeger, “Sand, Jams and Jets”, Physics World 18, 34-39 (2005)
• Heinrich M. Jaeger, “Chicago Experiments on Convection, Compaction, and Compression,” in Physics of Dry Granular Media, NATO ASI Series Vol. E 350, ed. H. J. Herrmann, J.-P. Hovi and S. Luding (Kluwer Academic Publishers, Dordrecht, The Netherlands, 1998) p. 553..
• Heinrich M. Jaeger, Sidney R. Nagel, and Robert P. Behringer, "Granular Solids, Liquids and Gases", Rev. Mod. Phys. 68, 1259 (1996).
• Heinrich M. Jaeger, Sidney R. Nagel, and Robert P. Behringer, "The Physics of Granular Materials", Physics Today 49, 32 (1996).
• H. M. Jaeger, J. B. Knight, C.-h. Liu, and S. R. Nagel, "What is shaking in the sand box?", Mat. Res. Soc. Bull. 19 (5), 25 (1994).
• Heinrich M. Jaeger and Sidney R. Nagel, "La Fisica del Estado Granular", Mundo Cientifico 132, 108 (1993).
• Heinrich M. Jaeger and Sidney R. Nagel, "La Physique de l'Etat Granulaire", La Recherche 249, 1380 (1992).
• H.M. Jaeger and Sidney R. Nagel, "Physics of the Granular State", Science 255, 1523 (1992).
  

Avalanches

• Chu-heng Liu, H.M. Jaeger and Sidney R. Nagel, "Finite Size Effects in a Sandpile", Phys. Rev. A 43, 7091 (1991).
• H.M. Jaeger, Chu-heng Liu, Sidney R. Nagel and T.A. Witten, "Friction in Granular Flows", Europhysics Lett. 11, 619 (1990).
• H. M. Jaeger, Chu-heng Liu and Sidney R. Nagel, "Relaxation at the Angle of Repose", Phys. Rev. Lett. 62, 40 (1989).