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Towards a theoretical picture of dense granular flows down inclines

Nature Materials volume 6, pages 99–108 (2007)Cite this article

Abstract

Unlike most fluids, granular materials include coexisting solid, liquid or gaseous regions, which produce a rich variety of complex flows. Dense flows down inclines preserve this complexity but remain simple enough for detailed analysis. In this review we survey recent advances in this rapidly evolving area of granular flow, with the aim of providing an organized, synthetic review of phenomena and a characterization of the state of understanding. The perspective that we adopt is influenced by the hope of obtaining a theory for dense, inclined flows that is based on assumptions that can be tested in physical experiments and numerical simulations, and that uses input parameters that can be independently measured. We focus on dense granular flows over three kinds of inclined surfaces: flat-frictional, bumpy-frictional and erodible. The wealth of information generated by experiments and numerical simulations for these flows has led to meaningful tests of relatively simple existing theories.

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Figure 1: A typical facility for producing dense granular flows down inclines.
Figure 2: Snapshots of periodic MD simulations of 10,000 grains in a domain bounded by frictionless sidewalls separated by W = 20d along z, streamwise length L = 25d, inclination α = 20°, a friction coefficient μ = 0.8 between grains, and other grain interaction parameters found in Bi et al.27.
Figure 3: Profiles along y in the simulations of Fig. 2 for a bumpy base (black lines) and a flat base (red lines)27.
Figure 4: Diagrams of dimensionless flow height against tanα, highlighting similarities between simulations and experiments.
Figure 5: Snapshot of MD simulations with frictional sidewalls (μ = 0.8), 60,000 grains and α = 40° (refs 8, 27).
Figure 6: Profiles along y highlighting similarities between SSH experiments and numerical simulations27.
Figure 7: Predictions of the kinetic theory for stresses on planes parallel to the flow compared with numerical simulations of a two-dimensional inclined flow of identical spheres34.
Figure 8: Ratio of shear and normal stress (effective friction) on a flat, frictional wall versus Froude number Fr based on mean velocity and weight6.

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Acknowledgements

We thank Daniel Bideau, Gérard Le Caër, Luc Oger, Nathalie Thomas, and our colleagues in the Groupement de Recherche Milieux Divises (GDR MiDi) for valuable discussions. We thank James T. Jenkins for contributing several paragraphs on merits of the kinetic theory, and Namiko Mitarai for providing data shown in Fig. 7. The preparation of this review was assisted by financial support from the GDR MiDi and US–France Cooperative Research grant INT-0233212. Our research in dense, inclined flows is sponsored by the French Ministry of Education and Research (ACI PCN (INSU): Écoulements gravitaires: modélisation des processus), the CNRS (PNRN: Programme National des Risques Naturels, écoulements gravitaires), and NASA grants NCC3-468, NAG3-2705, NCC3-797 and NAG3-2353.

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  1. Groupe Matière Condensée et Matériaux, UMR CNRS 6626, Université Rennes I, Campus de Beaulieu, Rennes, F-35042, France

    R. Delannay, P. Richard, N. Taberlet & A. Valance

  2. Sibley School of Mechanical and Aerospace Engineering, Cornell University, Ithaca, 14853, New York, USA

    M. Louge

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Delannay, R., Louge, M., Richard, P. et al. Towards a theoretical picture of dense granular flows down inclines. Nature Mater 6, 99–108 (2007). https://doi.org/10.1038/nmat1813

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