Hostname: page-component-745bb68f8f-cphqk Total loading time: 0 Render date: 2025-02-04T13:42:35.340Z Has data issue: false hasContentIssue false
  • English
  • Français

A Simple Description of Thick Avalanches at the Surface of a Granular Material

Published online by Cambridge University Press:  01 February 2011

Achod Aradian ,
Elie Raphaël  and
Pierre-Gilles de Gennes
Achod Aradian
Affiliation:
Laboratoire de Physique de la Matière Condensée, URA n°792 du C.N.R.S., Collège de France, 11 place Marcelin Berthelot, 75231 Paris Cedex 05, Francee-mail: Achod.Aradian@college-de-france.fr, Elie.Raphael@college-de-france.fr, Pierre-Gilles.deGennes@espci.fr
Elie Raphaël
Affiliation:
Laboratoire de Physique de la Matière Condensée, URA n°792 du C.N.R.S., Collège de France, 11 place Marcelin Berthelot, 75231 Paris Cedex 05, Francee-mail: Achod.Aradian@college-de-france.fr, Elie.Raphael@college-de-france.fr, Pierre-Gilles.deGennes@espci.fr
Pierre-Gilles de Gennes
Affiliation:
Laboratoire de Physique de la Matière Condensée, URA n°792 du C.N.R.S., Collège de France, 11 place Marcelin Berthelot, 75231 Paris Cedex 05, Francee-mail: Achod.Aradian@college-de-france.fr, Elie.Raphael@college-de-france.fr, Pierre-Gilles.deGennes@espci.fr
Get access

Abstract

Some years ago, Bouchaud et al. introduced a phenomenological model to describe surface flows of granular materials [J. Phys. Fr. I 4, 1383 (1994)]. According to this model, one can distinguish between a static phase and a rolling phase that are able to exchange grains through an erosion/accretion mechanism. Later, Boutreux et al. [Phys. Rev. E 58, 4692 (1998)] proposed a modification of the exchange term in order to describe thicker flows where saturation effects are present. However, these two approaches assumed that the downhill convection velocity of the grains is constant inside the rolling phase, a hypothesis that is not verified experimentally. We have recently modified the above models by introducing a velocity profile in the flow, and analyzed the physical consequences of this modification in the simple situation of an avalanche in an open cell. We here emphasize the physical predictions of our model, and show, in particular, that the thickness of the avalanche depends strongly on the velocity profile.

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 627: Symposium BB – The Granular State , 2000 , BB2.7
Copyright
Copyright © Materials Research Society 2000

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1] For a detailed description of the Coulomb approach and its extensions, see Nedderman, R.M., Statics and Kinematics of Granular Materials (Cambridge University Press, Cambridge, 1992).Google Scholar
[2] Rajchenbach, J., in Physics of Dry Granular Media, Hermann, H.J., Hovi, J.P., and Luding, S., eds. (Kluwer Academic Publishers, Dordrecht, 1998), p. 421.Google Scholar
[3] de Gennes, P.-G., in From Rice to Snow, Lecture at the Nishina Memorial Foundation, Publication Nr 38 (Nishina Memorial Foundation, April 1998). See also Ref. [8].Google Scholar
[4] Radjai, F., Wolf, D., and Roux, S., Phys. Rev. Lett., 77, 274 (1996);Google Scholar
Liu, C.H., Nagel, S., Shechter, D., Coppersmith, S., Majumdar, S., Narayan, O., and Witten, T., Science, 269, 513 (1995);Google Scholar
Radjai, F., Wolf, D.E., Roux, S., Jean, M., and Moreau, J.-J., in Powders and Grains 97, Behringer, R. and Jenkins, J., eds., Balkema Publishers, Rotterdam, 1997), p. 211.Google Scholar
[5] Bouchaud, J.-P., Cates, M.E., Ravi Prakash, J., and Edwards, S.F., J. Phys. France I, 4, 1383 (1994);Google Scholar
Bouchaud, J.-P., Cates, M.E., Ravi Prakash, J., and Edwards, S.F., Phys. Rev. Lett., 74, 1982 (1995).Google Scholar
See also Mehta, A., in Granular Matter, Mehta, A., ed. (Springer Verlag, Heidelberg, 1994).Google Scholar
[6] de Gennes, P.-G., C. R. Acad. Sci. Paris, Ser. IIb, 321, 501 (1995).Google Scholar
[7] de Gennes, P.-G., Cours du Collège de France, unpublished (Collège de France, Paris, 1997).Google Scholar
[8] Boutreux, T., Raphaël, E. and de Gennes, P.-G., Phys. Rev. E, 58, 4692 (1998).Google Scholar
[9] Boutreux, T. and Raphaël, E., Phys. Rev. E, 58, 7645 (1998).Google Scholar
[10] Bouchaud, J.-P. and Cates, M.E., in Physics of Dry Granular Media, Hermann, H.J., Hovi, J.P., and Luding, S. eds., (Kluwer Academic Publishers, Dordrecht, 1998), p. 465.Google Scholar
[11] Samson, L., Ippolito, I., Dippel, S., Batrouni, G.G., in Powders and Grains 97, Behringer, R. and Jenkins, J., eds. (Balkema Publishers, Rotterdam, 1997), p. 503.Google Scholar
[12] Dippel, S., Batrouni, G.G., Wolf, D.E., in Powders and Grains 97, Behringer, R. and Jenkins, J., eds. (Balkema Publishers, Rotterdam, 1997), p. 559.Google Scholar
[13] Douady, S., Andreotti, B., and Daerr, A., Eur. Phys. J. B, 11, 131 (1999).Google Scholar
[14] Rajchenbach, J., Clément, E. and Duran, J., in Fractal Aspects of Materials, Family, F., Meakin, P., Sapoval, B. and Wool, R., eds., M.R.S. Symposia Proceedings No. 367 (Materials Research Society, Pittsburgh, 1995), p. 525.Google Scholar
[15] Azanza, E., Chevoir, P. and Moucheron, P., in Powders and Grains 97, Behringer, R. and Jenkins, J., eds. (Balkema Publishers, Rotterdam, 1997), p. 455.Google Scholar
[16] Pouliquen, O., Phys. Fluid, 11, 542 (1999).Google Scholar
[17] Aradian, A., Raphaël, E., de Gennes, P.-G., Phys. Rev. E, 60, 2009 (1999).Google Scholar
[18] Boutreux, T. and de Gennes, P.-G., J. Phys. France I, 6, 1295 (1996).Google Scholar
[19] Makse, H.A., Phys. Rev. E, 56, 7008 (1998);Google Scholar
Makse, H.A., Cizeau, P. and Stanley, H.E., Phys. Rev. Lett., 78, 3298 (1997).Google Scholar
[20] Savage, S.B. and Hutter, K., J. Fluid Mech., 199, 177 (1989).Google Scholar
[21] Dorogovtsev, S.N. and Mendes, J.F.F., Phys. Rev. Lett., 83, 2946 (1999).Google Scholar
[22] Mahadevan, L. and Pomeau, Y., Europhys. Lett., 46, 595 (1999).Google Scholar
[23] Emig, T., Claudin, P. and Bouchaud, J.-P., Europhys. Lett., 50, 594 (2000).Google Scholar