Size and Density Separation in Granular Materials
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SIZE AND DENSITY SEPARATION IN GRANULAR MATERIALS MATTHIAS MÖBIUS, SIDNEY R. NAGEL, HEINRICH M. JAEGER James Franck Institute and Department of Physics, The University of Chicago, Chicago, IL 60637 ABSTRACT We review mechanisms leading to the separation of granular mixtures according to the size or density of the constituent particles. Besides a general overview, the focus of this article is on separation induced by vertical vibrations of the vessel holding the granular material, and specifically on recent results showing a density-dependence to the separation process. A convenient measure of the separation speed is the rise time of a larger “intruder particle” from some fixed initial depth to the free surface, where it will remain. Recent experiments have shown that for large intruder sizes the rise time depends on the density of the intruder particle. Furthermore, in three-dimensional systems we found that this density dependence is highly nonmonotonic. While there is no detailed theoretical understanding available yet, our experiments demonstrate that this surprising behavior is produced by interactions not only between the large intruder particle and the smaller particles of the surrounding granular bed, but also between the particles and the interstitial air. BACKGROUND AND INTRODUCTION One of the key characteristics of dry granular materials is their propensity to size separate. Stirring, jostling or shaking a container filled with a mixture of different particle sizes will produce a final state in which, typically, the larger particles aggregate on top of the smaller ones. This phenomenon immediately sets mechanically agitated granular materials apart from ordinary fluids, even though both exhibit many flow properties that appear similar. As it turns out, the important difference is the strongly non-equilibrium character of granular matter and, consequently, purely thermodynamic considerations, such as the use of entropy arguments, fail. Instead, the response of granular matter to external driving is dominated by the dynamics of the system [1].
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The first reports of granular size separation date back to the 1930’s, and a number of reviews exist in both the engineering and physics literature (see, e.g.,[2-6]). By now several independent mechanisms have been identified. Besides the obvious “sifting”-type mechanism in which very small particles can simply fall through the gaps between larger grains already if the material is at rest, this includes mechanisms based on surface avalanching, arching or ratcheting inside the bulk of the material, and convection. Avalanche-based mechanisms have been shown to drive size separation in flows down inclined chutes or in debris flows down the slope of hills [4, 7, 8]. Typically, the main ingredients here are shear-induced dilation in the flowing zone of the material, followed by percolation of the smaller particles through voids that have opened up. Avalanche-based mechanisms also play a key role in producing segregated regions in rotating drum mixers [6,
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