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ScienceWeek
2004 2 July A5 MATERIALS SCIENCE: ON GRANULAR SEGREGATION
The following points are made by Troy Shinbrot (Nature 2004 429:352):
1) Every farmer can attest to the curious fact that the largest crop each spring is the boulders that appear, untended, on open fields. Common wisdom holds that this crop is loosened from the soil by frost heave, and rises because small pebbles can slip beneath large boulders, but not vice versa(1). This is the "brazil nut effect" -- named for the fact that in a container of mixed nuts the brazil nuts always seem to rise to the top. Because similar processes and effects occur in pharmaceutical, chemical and food processing, the problem of granular segregation has earned serious attention(2,3).
2) The first complication to the simple picture of pebbles slipping beneath boulders (termed "percolation") was the demonstration that a tapped bed of grains "convects" in a regular pattern: a wide swath of grains rises in the center of a container, and thin margins correspondingly sink(4). According to the convection picture, large "intruder" particles rise with the surrounding bed, and then find themselves simply unable to fit into narrow downwelling margins. This mechanism was confirmed by a clever experiment in which the convection rolls were reversed and, as predicted, large particles migrated to the bottom of vibrated beds(4). Later confirmations came from magnetic-resonance-imaging experiments that conclusively demonstrated the presence of segregating convection rolls(5), and from meticulous computational comparisons that revealed that convection dominates over percolation in producing segregation in deep beds.
3) Over the past decade, however, our understanding of the segregation of large particles in vibrated beds has been challenged by experiments revealing that although large heavy "intruder" particles can indeed rise in vibrated beds of finer grains, equally large light intruders can sink, contrary to expectation and common experience. Now termed the "reverse brazil nut effect", this observation is explained by neither the convection nor the percolation description. It is so counterintuitive that a reviewer of the original manuscript reporting the effect insisted that it could not be correct; and the manuscript editor at Physical Review Letters conscientiously (if skeptically) tested the effect in his office using a jar of sand, a large plastic pin (a light intruder) and a steel nut (a heavy intruder). Since this impromptu confirmation, particle-dynamics simulations (subsequently validated experimentally) have verified that the reverse brazil nut (RBN) effect appears under ideal in silico conditions, and that multiple intruders also separate in the curious RBN manner.
4) In fact the RBN effect turned out to be even more complex than realized at first. Subsequent experiments demonstrated that there are actually separate size and density influences at work in a tapped bed. On the one hand, for intruders of a fixed density there is a distinct size threshold above which intruders rise, and below which they sink. On the other hand, intruders of a fixed size rise with a speed that grows and then diminishes non-monotonically as the intruder density is increased. To complicate matters still further, there have been numerous commentaries on the RBN effect, some of which question whether the effect even exists, or whether it is actually a computational artefact.
References (abridged):
1. Walker, J. The Flying Circus of Physics 72 (Wiley, New York, 1975)
2. Muzzio, F. J., Glasser, B. J. & Shinbrot, T. Powder Technol. 124, 1-7 (2002)
3. Huerta, D. A. & Ruiz-Suarez, J. C. Phys. Rev. Lett. 92, 114301 (2004)
4. Knight, J. B., Jaeger, H. M. & Nagel, S. R. Phys. Rev. Lett. 70, 3728-3731 (1993)
5. Ehrichs, E. E. et al. Science 267, 1632-1634 (1995)
Nature http://www.nature.com/nature
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Related Material:
SAND AS A GRANULAR FLUID
The following points are made by Paul Umbanhowar (Nature 2003 424:886):
1) By measuring both the free and forced oscillations of a rigid pendulum immersed in an ordinary liquid, the temperature and viscosity of the liquid can be determined. This is due, in part, to a relation from equilibrium statistical mechanics known as the "fluctuation-dissipation theorem", which, in a precursor to its modern form, was devised by Einstein to explain the diffusive Brownian motion of small particles suspended in liquids. Driven granular materials, such as shaken sand, are systems far from equilibrium -- they have strong spatial and temporal variations in quantities such as density and local particle velocity, and would consequently not be expected to obey the fluctuation-dissipation theorem.
2) However, in many instances, the macroscopic behavior of granular materials seems, at least superficially, liquid-like. One might then wonder whether an experiment using a rigid pendulum would reveal a similar fluctuation-dissipation relation in driven granular materials, despite their dissipative nature. D'Anna et al (Nature 2003 424:909) have taken up this question and find, surprisingly, that the answer seems to be yes. In particular, their experiments show that the free and forced motions of the probe are related by a fluctuation-dissipation-like relation, and that an effective viscosity and temperature can be defined.
3) Granular materials -- such as peas, coal, pills, breakfast cereal and, not least of all, sand -- are usually defined to be discrete solid bits that interact with each other through energy-dissipating contact forces (although the definition is sometimes stretched to include wetted grains and powders for which attractive surface forces are also important). Many industrial practices require the efficient handling and mixing of granular materials: food and agricultural processing, sorting and assembly of parts, cement manufacturing, mining, radiation shielding and, of ever increasing scope, pharmaceutical production. Despite their somewhat humble nature, granular materials behave unusually because they combine properties of both liquids and solids. Examples of such behavior include the ability to de-mix when poured, to form waves or ripples when shaken or blown, and to expand when squeezed (as anyone can attest who has walked on wet sand and observed a dry halo around their foot).
4) Many of the unique properties of granular materials arise because, unlike an ordinary fluid, the kinetic energy associated with the relative motion of macroscopic particles (called "granular temperature") is not constant. Instead, it is continually and irrevocably transferred by collisions to internal (thermal or non-kinetic) degrees of freedom. Although individual grains possess a well-defined thermodynamic temperature, the associated thermal energy (equal to the product kT, where k is Boltzmann's constant and T is the temperature in kelvin) is too small to allow relative particle motion, as it does in ordinary liquids. So dynamic collections of grains require a continuous external source of energy to prevent them from getting stuck in a particular configuration.
Nature http://www.nature.com/nature
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Related Material:
SHOCKS IN GRANULAR SYSTEMS
The following points are made by E.C. Rericha et al (Phys. Rev. Lett. 2002 88:014302):
1) Shocks form around an object such as a bullet or an aircraft when the speed of the object relative to the incident flow exceeds the speed of sound in the fluid. Shocks analogous to those that form in fluid flows also occur in flows of macroscopic particles such as sand grains. The usual theoretical approach to understanding granular flows is dense-gas kinetic theory, treating the constituent grains as colliding and inelastic hard spheres. As in standard dense-gas kinetic theory, flows of particles that are described by Newton's laws are modeled with a Boltzmann equation, which in turn leads to Navier-Stokes-like continuum equations. For granular media, these continuum equations contain a term that describes the overall energy loss due to inelastic collisions.
2) The inelastic collisions in a granular flow reduce the relative velocities of the grains. Consequently, the local granular temperature, defined as the variance of the local velocity distribution, decreases. Whether the fluid is composed of grains or molecules, the speed of sound depends on the speed of the component particles and therefore on the temperature. (For a granular fluid, the speed of sound in the interstitial air is irrelevant: a granular fluid has the same sound speed even if the interstices are a vacuum.) Since inelastic conditions dissipate temperature, the speed of sound in a granular flow decreases. In the absence of further heating, a granular flow becomes supersonic as it progresses, i.e., the mean particle velocity surpasses the speed of sound. Thus, shocks form in granular systems for common rather than for extreme conditions whenever the flow encounters an obstacle.
Phys. Rev. Lett. http://prl.aps.org
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