On dense granular flows

The European Physical Journal E - 2004

Tóm tắt

The behaviour of dense assemblies of dry grains submitted to continuous shear deformation has been the subject of many experiments and discrete particle simulations. This paper is a collective work carried out among the French research group Groupement de Recherche Milieux Divisés (GDR MiDi). It proceeds from the collection of results on steady uniform granular flows obtained by different groups in six different geometries both in experiments and numerical works. The goal is to achieve a coherent presentation of the relevant quantities to be measured i.e. flowing thresholds, kinematic profiles, effective friction, etc. First, a quantitative comparison between data coming from different experiments in the same geometry identifies the robust features in each case. Second, a transverse analysis of the data across the different configurations, allows us to identify the relevant dimensionless parameters, the different flow regimes and to propose simple interpretations. The present work, more than a simple juxtaposition of results, demonstrates the richness of granular flows and underlines the open problem of defining a single rheology.

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Tài liệu tham khảo

R.L. Brown, J.C. Richards, Principle of Powder Mechanics (Pergamon, New York, 1970).

J. Duran, Sand, Powders and Grains (Springer-Verlag, New York, 1999).

H.J. Herrmann, J.-P. Hovi, S. Luding (Editors), Physics of Dry Granular Media (Kluwer Academic Publishers, Dordrecht, 1998).

F. Chevoir, J.N. Roux (Editors), Colloque physique et mécanique des matériaux granulaires (Laboratoire Central des Ponts et Chaussées, Paris, 2000).

P.G. De Gennes, Physica A 261, 267 (1998).

U. Tüzün, G.T. Houlsby, R.M. Nedderman, S.B. Savage, Chem. Eng. Sci. 37, 1691 (1982).

S.B. Savage, Flow of granular materials, in Theoretical and Applied Mechanics, edited by P. Germain, M. Piau, D. Caillerie (Amsterdam, North Holland, 1989) pp. 241-266

K.R. Hutter, K.R. Rajagopal, Continuum Mech. Thermodyn. 6, 81 (1994).

J. Rajchenbach, Adv. Phys. 49, 229 (2000).

R.M. Nedderman, Statics and Kinematics of Granular Materials (Cambridge University Press, Cambridge, 1992).

A. Schofield, P. Wroth, Critical State Soil Mechanics (McGraw-Hill, London, 1968).

C.S. Campbell, Ann. Rev. Fluid Mech. 22, 57 (1990).

I. Goldhirsch, Chaos 9, 659 (1999).

O. Pouliquen, F. Chevoir, C. R. Phys. 3, 163 (2002).

S.B. Savage, M. Sayed, J. Fluid Mech. 142, 391 (1984).

D.M. Hanes, D.L. Inman, J. Fluid Mech. 150, 357 (1985).

M. Babic, H.H. Shen, H.T. Shen, J. Fluid Mech. 219, 81 (1990).

P.A. Thompson, G.S. Grest, Phys. Rev. Lett. 67, 1751 (1991).

Y. Zhang, C.S. Campbell, J. Fluid Mech. 237, 541 (1992).

O.J. Schwarz, Y. Horie, M. Shearer, Phys. Rev. E 57, 2053 (1998).

E. Aharonov, D. Sparks, Phys. Rev. E 65, 051302 (2002).

D. Volfson, L.S. Tsimring, I.S. Aranson, Phys. Rev. E 68, 021301 (2003).

I. Iordanoff, M.M. Khonsari, ASME J. Tribol. (2002).

F. da Cruz, F. Chevoir, J.-N. Roux, I. Iordanoff, Macroscopic friction of dry granular materials, in Transient Processes in Tribology, Proceedings of the 30th Leeds-Lyon Symposium on Tribology, edited by A Lubrecht, G. Dalmaz, Tribol. Interface Eng. Vol. 43 (Elsevier, Amsterdam, 2004).

F. Chevoir, F. da Cruz, M. Prochnow, P. Rognon, J.-N. Roux, Dense granular flows: friction and Jamming, in Proceedings of the 17th ASCE Engineering Mechanics Conference, June 13-16, 2004, University of Delaware, Newark, DE, USA.

F. da Cruz, Friction and jamming in granular flows, PhD Thesis, Ecole Nationale des Ponts et Chaussees, Marne la vallée, France, 2004.

J.N. Roux, G. Combe, C. R. Phys. 3, 131 (2002).

G.I. Tardos, M.I Khan, and D.G. Schaeffer, Phys. Fluids 10, 335 (1998).

B. Miller, C. O’Hern, and R.P. Behringer, Phys. Rev. Lett. 77, 3110 (1996).

D. Howell, R.P. Behringer, C. Veje, Phys. Rev. Lett. 82, 5241 (1999).

C. Veje, D. Howell, R.P. Behringer, Phys. Rev. E 59, 739 (1999).

D.M. Mueth G.F. Debregeas, G.S. Karczmart, P.J. Eng, S.R. Nagel, H.M. Jaeger, Nature 406, 385 (2000).

L. Bocquet, W. Losert, D. Schalk, T.C. Lubensky, J.P. Gollub, Phys. Rev. E 65, 011307 (2002).

M. Lätzel, S. Luding, H.J.Hermann, Granular Matter 2, 123 (2000).

S. Schöllmann, Phys. Rev. E 59, 889 (1999).

F. da Cruz, F. Chevoir, D. Bonn, P. Coussot, Phys. Rev. E 66, 051305 (2002).

G. Chambon, J. Schmittbuhl, A. Corfdir, J.P. Vilotte, S. Roux, Phys. Rev. E 68, 011304 (2003).

S. Nasuno, A. Kudrolli, A. Bak, J.P. Gollub, Phys. Rev. E 58, 2161 (1998).

R.M. Nedderman, C. Laohakul, Powder Technol. 25, 91 (1980).

V.V.R. Natarajan, M.L. Hunt, E.D. Taylor, J. Fluid Mech. 304, 1 (1995).

O. Pouliquen, R. Gutfraind, Phys. Rev. E 53, 552 (1996).

N. Menon, D.J. Durian, Science 257, 1920 (1997).

F. Chevoir, M. Prochnow, P. Moucheront, F. da Cruz, F. Bertrand, JP. Guilbaud, Ph. Coussot, J.N. Roux, Dense granular flows in a vertical chute, in Powder and Grains 2001, edited by Y. Kishino (A.A. Balkema, Amsterdam, 2001) pp. 399-402.

M. Prochnow, Ecoulements denses de grains secs, PhD Thesis, Ecole Nationale des Ponts et Chaussées, Marne la vallée, France, 2002.

C. Denniston, H. Li, Phys. Rev. E 59, 3289 (1999).

G.W. Baxter, R.P. Behringer, T. Fagert, G.A Johnson, Phys. Rev. Lett. 62, 2825 (1989).

Y. Bertho, F. Giorgiutti, J.P. Hulin, Phys. Fluids 459, 3358 (2003).

Y. Bertho, F. Giorgiutti, T.E. Raafat, J. Hinch, H.J. Hermann, J.P. Hulin, J. Fluid Mech. 459, 317 (2002).

P.C. Johnson, P. Nott, R. Jackson, J. Fluid Mech. 210, 501 (1990).

C. Ancey, Phys. Rev. E 65, 011304 (2001).

E. Azanza, Ecoulements granulaires bidimensionnels sur un plan incliné, PhD Thesis, Ecole des Ponts et Chaussées, Marne la Vallée, France, 1997.

G. Berton, R. Delannay, P. Richard, N. Taberlet, A. Valance, Phys. Rev. E 68, 051303 (2003).

S. Dippel, Microscopic dynamics of granular materials, PhD Thesis, Höchstleistungsrechenzentrum Jül-3510 (1998).

O. Pouliquen, Phys. Fluids 11, 542 (1999).

C. Goujon, N. Thomas, B. Dalloz-Dubrujeaud, Eur. Phys. J. E 11, 147 (2003).

G. Félix and N. Thomas, Earth Planet. Sci. Lett. 221, 197 (2004).

P. Rognon, Ecoulements granulaires sur plan incliné: étude expérimentale de la transition vers l’arrêt. Internship report Maîtrise de sciences des matériaux, Université de Marne la Vallée, 2003.

A. Daerr, S. Douady, Nature 399, 241 (1999).

L. Quartier, B. Andreotti, GDR MiDi communication (2003).

L.E. Silbert, D. Ertas, G.S. Grest, T.C. Halsey, D. Levine, S.J. Plimpton, Phys. Rev. E 64, 051302 (2001).

L.E. Silbert, J.W. Landry, G.S. Grest, Phys. Fluids 15, 1 (2003).

F. Chevoir, M. Prochnow, J.T. Jenkins, P. Mills, Dense Granular Flows Down an Inclined Plane, in Powders and Grains, edited by Y. Kishino (Lisse, Swets and Zeitlinger, Tokyo, 2001) pp. 373-376,.

Y. Forterre, O. Pouliquen, J. Fluid Mech. 486, 21 (2003).

S. Douady, B. Andreotti, A. Daerr, P. Cladé, The Four Fronts and the Two Avalanches (Lisse, Swets and Zeitlinger, Tokyo, 2001) pp. 443-446.

J. Rajchenbach, Phys. Rev. Lett. 65, 2221 (1990).

C.H. Liu, H.M. Jaeger, S.R. Nagel, Phys. Rev. A 43, 7091 (1991).

Y. Grasselli, H.J. Herrmann, Physica A 246, 301 (1997).

Y.C. Zhou, B.H. Xu, A.B. Yu, Phys. Rev. E 64, 021301 (2001).

Y.C. Zhou, B.H. Xu, A.B. Yu, P. Zulli, Powder Technol. 125, 45 (2002).

P. Evesque, J. Rajchenbach, C. R. Phys. Acad. Sci. (Paris) 307, 223 (1988).

M. Nakagawa, S.A. Altobelli, A. Caprihan, E. Fukushima, E. Jeong, Exp. Fluids 16, 54 (1993).

M. Caponeri, S. Douady, S. Fauve, C. Laroche, Dynamics of Avalanches in a Rotating Cylinder, in Mobile particulate systems, edited by E. Guazzelli & L. Oger (Kluwer Academic Publisher, Dordrecht, 1995) pp. 331-366.

D.V. Khakhar, J.J. McCarthy, T. Shinbrot, J.M. Ottino, Phys. Fluids 9, 31 (1997).

T. Elperin, A. Vikhanski, Europhys. Lett. 42, 619 (1998).

C.M. Dury, G.H. Ristow, J.L. Moss, M. Nakagawa, Phys. Rev. E 57, 4491 (1998).

K. Yamane, M. Nakagawa, S.A. Altobelli, T. Tanaka, Y. Tsuji, Phys. Fluids 10, 1419 (1998).

T.S. Komatsu, S. Inagasaki, N. Nakagawa, S. Nasuno, Phys. Rev. Lett. 86, 1757 (2001).

D.V. Khakhar, A.V. Orpe, P. Andresén, and J.M. Ottino, J. Fluid Mech. 9, 195 (2001).

A.V. Orpe, D.V. Khakhar, Phys. Rev E 64, 031302 (2001).

D. Bonamy, F. Daviaud, L. Laurent, Phys. Fluids 14, 1666 (2002).

D. Bonamy, F. Daviaud, L. Laurent, M. Bonetti, J.P. Bouchaud, Phys. Rev. Lett. 89, 034301 (2002).

G. Félix, PhD Thesis, Institut National Polytechnique de Lorraine, Nancy, France, 2002.

S. Courrech du Pont, Avalanches granulaires en milieu fluide, PhD Thesis, Université Paris XI, Orsay, France, 2003.

M. Renouf, GDR MiDi communication (2003).

N. Taberlet, P. Richard, A. Valance, W. Losert, J.M. Pasini, J.T. Jenkins, R. Delannay, Phys. Rev. Lett. 91, 264301 (2003).

S. Courrech du Pont, P. Gondret, B. Perrin, M. Rabaud, Phys. Rev. Lett. 90, 044301 (2003).

P. Boltenhagen, Eur. Phys. J. B 12, 75 (1999).

S. Courrech du Pont, P. Gondret, B. Perrin, M. Rabaud, Europhys. Lett. 61, 492 (2003).

O. Pouliquen, GDR MiDi communication (2003).

B. Andreotti, GDR MiDi communication (2003).

D. Bonamy, Phénoménes collectifs dans les matériaux granulaires, PhD Thesis, Université Paris XI, Orsay, France, 2001.

L. Vanel, D.W. Howell, D. Clark, R.P. Behringer, E. Clément, Phys. Rev. E 60, R5040 (1999).

D. Fenistein, M. van Hecke, Nature 425, 256 (2003).

D. Weaire, S. Hutzler, The Physics of Foam (Clarendon Press, Oxford, 1999).

A. Kabla, G. Debregeas, Phys. Rev. Lett. 90, 258303 (2003).

M.L. Falk, J.S. Langer, Phys. Rev. E 57, 7192 (1998).

J. Rajchenbach, Phys. Rev. Lett. 90, 144302 (2003).

D. Ertas, T.C. Halsey, Europhys. Lett. 60, 931 (2002).

M.R. Kuhn, Mech. Mater. 31, 407 (1999).

G. Debregeas, H. Tabuteau, J.M. di Miglio, Phys. Rev. Lett. 90, 258303 (2002).

F. Radjai, S. Roux, Phys. Rev. Lett. 89, 064302 (2003).

B. Andreotti, S. Douady, Phys. Rev. E 63, 0311305 (2001).

P. Mills, D. Loggia, M. Texier, Europhys. Lett. 45, 733 (1999).

O. Pouliquen, Y. Forterre, S. Ledizes, Adv. Complex Syst. 4, 441 (2001).

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The European Physical Journal E

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