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Clusters in dense-inertial granular flows

Published online by Cambridge University Press:  13 October 2011

Charles S. Campbell*
Affiliation:
Department of Aerospace and Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1453, USA
*
Email address for correspondence: campbell@usc.edu

Abstract

In the dense-inertial regime of granular flow, the stresses scale inertially, but the flow is dominated by clusters of particles. This paper describes observations of cluster development in this regime. Clusters were seen to form for both elastic and inelastic reasons: elastic when the shear rate pushes the particles together faster than the contacts can elastically disperse them, and inelastic as large energy dissipation leads to cluster formation. Furthermore, large particle surface friction leads to cluster formation both for structural reasons, because it generates stronger clusters, and for energetic reasons, as friction dissipates energy. However, the most intriguing result of this work is that clusters appear to have little effect on the rheology of the dense inertial regime, which suggests that one can model the dense inertial regime with entirely collisional hard sphere models, and not have to worry about the complexities of modelling clusters. But at the same time it presents a physical puzzle, as one would normally expect the rheology to be strongly dependent on microstructural features such as clusters, particularly as they present an elastic pathway for internal momentum transport. There is no completely satisfying explanation for why the clusters can be ignored, but two possibilities suggest themselves. Because the clusters are short-lived, it is possible that they do not survive long enough to make a significant contribution to the momentum transport. And it is also possible for the granular temperature that governs transport between clusters to act as a rate-limiting bottleneck that is in overall control of the momentum transport rate.

Type
Papers
Copyright
Copyright © Cambridge University Press 2011

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References

1. Bagnold, R. A. 1954 Experiments on a gravity-free dispersion of large solid particles in a Newtonian fluid under shear. Proc. R. Soc. Lond. A 225, 4963.Google Scholar
2. Campbell, C. S. 1989 The stress tensor for simple shear flows of a granular material. J. Fluid Mech. 203, 449473.CrossRefGoogle Scholar
3. Campbell, C. S. 2002 Granular shear flows at the elastic limit. J. Fluid Mech. 465, 261291.Google Scholar
4. Campbell, C. S. 2003 A problem related to the stability of force chains. Granular Matt. 5, 129134.Google Scholar
5. Campbell, C. S. 2005 Stress-controlled elastic granular shear flows. J. Fluid Mech. 539, 273297.CrossRefGoogle Scholar
6. Campbell, C. S 2006a Granular flows: an overview. Powder Technol. 162, 208229.Google Scholar
7. Campbell, C. S. 2006b Computer simulation of powder flows. In Powder Technology Handbook (ed. Gotoh, K., Masuda, H. & Higashitani, K. ). 3rd edn. pp. 737748. Taylor and Francis.Google Scholar
8. Cundall, P. A. & Strack, O. D. L. 1979 A discrete numerical model for granular assemblies. Geotechnique 29, 4765.CrossRefGoogle Scholar
9. da Cruz, F., Emam, S., Prochnow, M., Roux, J. N. & Chevoir, F. 2005 Rheophysics of dense granular materials: discrete simulation of plane shear flows. Phys. Rev. E 72, 021309.Google Scholar
10. Forterre, Y. & Pouliquen, O. 2006 Flows of dense granular media. Annu. Rev. Fluid Mech. 40, 124.CrossRefGoogle Scholar
11. Midi, G. D. R. 2004 On dense granular flows. Eur. Phys. J. E 14, 341365.Google Scholar
12. Hopkins, M. A. & Louge, M. Y. 1991 Inelastic microstructure in rapid granular flows of smooth disks. Phys. Fluids A 3, 4757.Google Scholar
13. Janssen, H. A. 1895 Versuche über Getreidedruck in Silozellen. Zeitschrift des Vereines deutscher Ingenieure 39, 10451049.Google Scholar
14. Jop, P., Forterre, Y. & Pouliquen, O. 2006 A constitutive law for dense granular flows. Nature 441, 727730.Google Scholar
15. Lees, A. W. & Edwards, S. F. 1972 The computer study of transport processes under extreme conditions. J. Phys. C: Solid State Phys. 5, 19211929.Google Scholar
16. Lois, G., Lemaitre, A. & Carlson, J. M. 2007a Spatial force correlations in granular shear flow. Part I. Numerical evidence. Phys. Rev. E 76, 021302.CrossRefGoogle Scholar
17. Lois, G., Lemaitre, A. & Carlson, J. M. 2007b Spatial force correlations in granular shear flow. Part II. Theoretical implications. Phys. Rev. E 76, 021303.Google Scholar
18. Nakagawa, M., Altobelli, S. A., Caprihan, A., Fukushima, E. & Jeong, E.-K. 1993 Noninvasive measurement of granular flows by magnetic-resonance imaging. Exp. Fluids 16, 5460.Google Scholar
19. Pouliquen, O., Cassar, C., Jop, P., Forterre, Y. & Nicolas, M. 2006 Flow of dense granular material: towards simple constitutive laws. J. Statist. Mech.: Theory and Experiment P07020, 114.Google Scholar
20. Wassgren, C. & Sarkar, A. 2007 Visualization of particle-based computer data, http://pharmahub.org/resources/4.Google Scholar

Campbell supplementary movie

A series of animations of individual clusters in in a shear flow

Download Campbell supplementary movie(Video)
Video 11.7 MB

Campbell supplementary movie

A series of animations of individual clusters in in a shear flow

Download Campbell supplementary movie(Video)
Video 9.6 MB
Supplementary material: PDF

Campbell supplementary material

Supplementary data

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Supplementary material: PDF

Campbell supplementary material

Supplementary data 2

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