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Competition between randomizing impacts and inelastic collisions in granular pattern formation

Nature volume 389, pages 574–576 (1997)Cite this article

Abstract

The flow and mixing of granular materials occur during handling of a wide variety of substances, from pharmaceuticals to cement to cereal grains1,2. The understanding of such flows is, however, considerably more limited than it is for fluids3; even basic processes such as tumbling4,5, simple shear6,7,8 and shaking9,10,11,12 give rise to unexpected results. A case in point is granular pattern formation. A rich variety of patterns, including stripes, squares, hexagons and solitary structures, has been observed in vertically shaken, shallow granular beds13,14. The vertical dynamics responsible for these patterns have been explored15,16,17,18,19, but the role of horizontal motions of the grains is less well understood. Here I present a model of these motions that identifies two aspects as central to pattern formation: the randomization of horizontal velocities20 by shaking, and the inelastic nature of grain collisions. These two elements alone, even without the influence of gravity, are sufficient to produce organized patterns in the horizontal plane — both those observed and others not yet seen experimentally.

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Figure 1: Evolution of particles subject to random expansion followed by inelastic collisions.
Figure 2: Patterned states as a function of the strength of the randomizing tap ( V) and the period between taps ( T).
Figure 3: Particle densities from mean-field simulation in square (left), and striped (right) patterns.

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Acknowledgements

I thank J. M. Ottino for thoughtful advice, J. J. McCarthy for valuable comments and assistance, and H. Jaeger, M. Mavrovouniotis, H. Swinney and P. Umbanhowar for crucial scientific discussions. This work was supported by the National Science Foundation (Division of Chemical and Transport Systems) and the American Chemical Society (Petroleum Research Fund).

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  1. Department of Chemical Engineering, Northwestern University, Evanston, 60208, Illinois, USA

    Troy Shinbrot

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Correspondence to Troy Shinbrot.

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Shinbrot, T. Competition between randomizing impacts and inelastic collisions in granular pattern formation. Nature 389, 574–576 (1997). https://doi.org/10.1038/39264

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