Continuum description of vibrated sand

Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

Volumn 59, Issue 4, 1999, Pages 4476-4483

  Eggers, Jens ^a   Riecke, Hermann ^b  

^a UNIVERSITY OF DUISBURG ESSEN   (Germany)

^b Northwestern University   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000488765     PISSN: 1063651X     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevE.59.4476     Document Type: Article

References (38)

1. H. Jaeger and S. Nagel, Science 255, 1523 (1992).
2. P. K. Haff, J. Fluid Mech. 134, 401 (1983).
3. J. T. Jenkins and S. B. Savage, J. Fluid Mech. 130, 187 (1983).
4. S. Savage, R. Neddermann, U. Tüzün, and G. Houlsby, Chem. Eng. Sci. 38, 189 (1983).
5. C. Lun, S. Savage, D. Jeffrey, and N. Chepurniy, J. Fluid Mech. 140, 223 (1984).
6. J. Jenkins and M. Richman, J. Fluid Mech. 171, 53 (1986).
7. C.-H. Wang, R. Jackson, and S. Sundaresan, J. Fluid Mech. 342, 179 (1997).
8. N. Sela and I. Goldhirsch, J. Fluid Mech. 361, 41 (1998).
9. S. Fauve, S. Douady, and C. Laroche, J. Phys. 50, Suppl. 3, 187 (1989).
10. S. Douady, S. Fauve, and C. Laroche, Europhys. Lett. 8, 621 (1989).
11. F. Melo, P. Umbanhowar, and H. Swinney, Phys. Rev. Lett. 72, 172 (1994).
12. F. Melo, P. Umbanhowar, and H. Swinney, Phys. Rev. Lett. 75, 3838 (1995).
13. S. Luding, E. Clément, J. Rajchenbach, and J. Duran, Europhys. Lett. 36, 247 (1996).
14. K. Aoki and T. Akiyama, Phys. Rev. Lett. 77, 4166 (1996).
15. E. Clément, L. Vanel, J. Rajchenbach, and J. Duran, Phys. Rev. E 53, 2972 (1996).
16. R. Metcalf, J. Knight, and H. Jaeger, Physica A 236, 202 (1997).
17. L. Labous and E. Clément, in Physics of Dry Granular Matter, edited by H. Herrmann, and S. Luding, J.-P. Hovi (Kluwer, Amsterdam, 1998), p. 619.
18. C. Bizon, M. D. Shattuck, J. B. Swift, W. D. McCormick, and H. L. Swinney, Phys. Rev. Lett. 80, 57 (1998).
19. J. deBruyn, C. Bizon, M. D. Shattuck, D. Goldman, J. B. Swift, and H. L. Swinney, Phys. Rev. Lett. 81, 1421 (1998).
20. M. Shattuck, C. Bizon, P. B. Umbanhowar, J. B. Swift, and H. L. Swinney, in Physics of Dry Granular Media, edited by H. Herrmann, and S. Luding, J.-P. Hovi (Kluwer, Amsterdam, 1998), pp. 613–618.
21. A. Kudrolli and J. Gollub, Physica D 97, 133 (1996).
22. T. Shinbrot, Nature (London) 389, 574 (1997).
23. D. Rothman, Phys. Rev. E 57, 1239 (1998).
24. E. Cerda, F. Melo, and S. Rica, Phys. Rev. Lett. 79, 4570 (1997).
25. L. Tsimring and I. Aranson, Phys. Rev. Lett. 79, 213 (1997).
26. S. Venkataramani and E. Ott, Phys. Rev. Lett. 80, 3495 (1998).
27. C. Crawford and H. Riecke, Physica D (to be published).
28. P. Umbanhowar, F. Melo, and H. Swinney, Nature (London) 382, 793 (1996).
29. H. Sakaguchi and H. Brand, Europhys. Lett. 38, 341 (1997).
30. J. Fineberg (private communication).
31. P. Umbanhowar, Ph.D. thesis, U. Texas, Austin, 1996.
32. M. Bourzutschky and J. Miller, Phys. Rev. Lett. 74, 2216 (1995).
33. S. Edwards and D. Wilkinson, Proc. R. Soc. London, Ser. A 381, 17 (1982).
34. To obtain (Formula presented) in Eq. (1b) from the material derivative (Formula presented) mass conservation, Eq. (1a) is used. However, the diffusion term (Formula presented) which would lead to an additional, nonlinear term in the momentum equation, comes from grains flying above the layer. This requires a much more sophisticated model to be treated consistently, and is therefore ignored in the following.
35. R. A. Bagnold, Proc. R. Soc. London Ser. A225, 49 (1954).
36. C. Bizon, M. D. Shattuck, J. R. deBruyn, J. B. Swift, W. D. McCormick, and H. L. Swinney, J. Stat. Phys.93, 449 (1998).
37. P. Umbanhowar (private communication).
38. O. Zik, J. Stavans, and Y. Rabin, Europhys. Lett. 17, 315 (1992).