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.
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For a detailed description of the Coulomb approach and its extensions, see R.M. Nedderman, Statics and Kinematics of Granular Materials (Cambridge University Press, Cambridge, 1992).
J. Rajchenbach, in Physics of Dry Granular Media, H.J. Hermann, J.P. Hovi, and S. Luding, eds. (Kluwer Academic Publishers, Dordrecht, 1998), p. 421.
P.-G. de Gennes, in From Rice to Snow, Lecture at the Nishina Memorial Foundation, Publication Nr 38 (Nishina Memorial Foundation, April 1998). See also Ref. .
F. Radjai, D. Wolf, and S. Roux, Phys. Rev. Lett., 77, 274 (1996)
C.H. Liu, S. Nagel, D. Shechter, S. Coppersmith, S. Majumdar, O. Narayan, and T. Witten, Science, 269, 513 (1995)
F. Radjai, D.E. Wolf, S. Roux, M. Jean, and J.-J. Moreau, in Powders and Grains 97, R. Behringer and J. Jenkins, eds., Balkema Publishers, Rotterdam, 1997), p. 211.
J.-P. Bouchaud, M.E. Cates, J. Ravi Prakash, and S.F. Edwards, J. Phys. France I, 4, 1383 (1994)
J.-P. Bouchaud, M.E. Cates, J. Ravi Prakash, and S.F. Edwards, Phys. Rev. Lett., 74, 1982 (1995). See also
A. Mehta, in Granular Matter, A. Mehta, ed. (Springer Verlag, Heidelberg, 1994).
P.-G. de Gennes, C. R. Acad. Sci. Paris, Ser. IIb, 321, 501 (1995).
P.-G. de Gennes, Cours du Collège de France, unpublished (Collège de France, Paris, 1997).
T. Boutreux, E. Raphaël and P.-G. de Gennes, Phys. Rev. E, 58, 4692 (1998).
T. Boutreux and E. Raphaël, Phys. Rev. E, 58, 7645 (1998).
J.-P. Bouchaud and M.E. Cates, in Physics of Dry Granular Media, H.J. Hermann, J.P. Hovi, and S. Luding eds., (Kluwer Academic Publishers, Dordrecht, 1998), p. 465.
L. Samson, I. Ippolito, S. Dippel, G.G. Batrouni, in Powders and Grains 97, R. Behringer and J. Jenkins, eds. (Balkema Publishers, Rotterdam, 1997), p. 503.
S. Dippel, G.G. Batrouni, D.E. Wolf, in Powders and Grains 97, R. Behringer and J. Jenkins, eds. (Balkema Publishers, Rotterdam, 1997), p. 559.
S. Douady, B. Andreotti, and A. Daerr, Eur. Phys. J. B, 11, 131 (1999).
J. Rajchenbach, E. Clément and J. Duran, in Fractal Aspects of Materials, F. Family, P. Meakin, B. Sapoval and R. Wool, eds., M.R.S. Symposia Proceedings No. 367 (Materials Research Society, Pittsburgh, 1995), p. 525.
E. Azanza, P. Chevoir and P. Moucheron, in Powders and Grains 97, R. Behringer and J. Jenkins, eds. (Balkema Publishers, Rotterdam, 1997), p. 455.
O. Pouliquen, Phys. Fluid, 11, 542 (1999).
A. Aradian, E. Raphaël, P.-G. de Gennes, Phys. Rev. E, 60, 2009 (1999).
T. Boutreux and P.-G. de Gennes, J. Phys. France I, 6, 1295 (1996).
H.A. Makse, Phys. Rev. E, 56, 7008 (1998)
S.B. Savage and K. Hutter, J. Fluid Mech., 199, 177 (1989).
S.N. Dorogovtsev and J.F.F. Mendes, Phys. Rev. Lett., 83, 2946 (1999).
L. Mahadevan and Y. Pomeau, Europhys. Lett., 46, 595 (1999).
T. Emig, P. Claudin and J.-P. Bouchaud, Europhys. Lett., 50, 594 (2000).
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Aradian, A., Raphaël, E. & de Gennes, PG. A Simple Description of Thick Avalanches at the Surface of a Granular Material. MRS Online Proceedings Library 627, 27 (2000). https://doi.org/10.1557/PROC-627-BB2.7