Dense flows of dry granular material

Olivier Pouliquen; François Chevoir

doi:10.1016/S1631-0705(02)01309-9

Physique de la matière en grains/Physics of granular media

Dense flows of dry granular material
[Écoulements de milieux granulaires secs]

Olivier Pouliquen ¹ ; François Chevoir ²

¹ Institut universitaire des systèmes techniques industriels, Université de Provence, Technopôle de Château-Gombert, 5, rue Enrico Fermi, 13453 Marseille cedex 13, France
² Laboratoire des matériaux et des structures du génie civil, Unité mixte de recherche LCPC–ENPC–CNRS, 2, allée Kepler, 77420 Champs sur Marne, France

Comptes Rendus. Physique, Volume 3 (2002) no. 2, pp. 163-175.

Résumé
Abstract

Le comportement d'assemblées denses de grains secs soumises à un cisaillement rapide est encore mal compris, et a fait récemment l'objet de nombreuses études expérimentales et de simulations numériques discrètes. Nous présentons les caractéristiques générales de tels écoulements tant à surface libre que confinés, ainsi que les information obtenues à l'échelle du réseau de contact. Nous décrivons ensuite les principaux modèles rhéologiques, ainsi que leurs prédictions.

The behavior of dense assemblies of dry grains submitted to continuous shear deformation is still not well understood. Recently it has been the subject of several experiments and discrete particle simulations. For both confined and free surface geometries, we present the general features of such flows as well as grain-level information. We then describe the main rheological models and their predictions.

Reçu le : 2001-09-20
Accepté le : 2001-12-11
Publié le : 2002-01-01

DOI : 10.1016/S1631-0705(02)01309-9

Keywords: granular media, hydrodynamics, rheology
Mot clés : milieux granulaires, hydrodynamique, rhologie

Affiliations des auteurs :

Olivier Pouliquen ¹ ; François Chevoir ²

@article{CRPHYS_2002__3_2_163_0,
     author = {Olivier Pouliquen and Fran\c{c}ois Chevoir},
     title = {Dense flows of dry granular material},
     journal = {Comptes Rendus. Physique},
     pages = {163--175},
     publisher = {Elsevier},
     volume = {3},
     number = {2},
     year = {2002},
     doi = {10.1016/S1631-0705(02)01309-9},
     language = {en},
}

TY  - JOUR
AU  - Olivier Pouliquen
AU  - François Chevoir
TI  - Dense flows of dry granular material
JO  - Comptes Rendus. Physique
PY  - 2002
SP  - 163
EP  - 175
VL  - 3
IS  - 2
PB  - Elsevier
DO  - 10.1016/S1631-0705(02)01309-9
LA  - en
ID  - CRPHYS_2002__3_2_163_0
ER  -

%0 Journal Article
%A Olivier Pouliquen
%A François Chevoir
%T Dense flows of dry granular material
%J Comptes Rendus. Physique
%D 2002
%P 163-175
%V 3
%N 2
%I Elsevier
%R 10.1016/S1631-0705(02)01309-9
%G en
%F CRPHYS_2002__3_2_163_0

Olivier Pouliquen; François Chevoir. Dense flows of dry granular material. Comptes Rendus. Physique, Volume 3 (2002) no. 2, pp. 163-175. doi : 10.1016/S1631-0705(02)01309-9. https://comptes-rendus.academie-sciences.fr/physique/articles/10.1016/S1631-0705(02)01309-9/

Bibliographie
Cité par

[1] R.L. Brown; J.C. Richards Principles of Powder Mechanics, Pergamon Press, Oxford, 1970

[2] J. Duran Sands, Powders and Grains, Springer-Verlag, New-York, 1999

[3] Physics of Dry Granular Media (H.J. Hermann; J.P. Hovi; S. Luding, eds.), Balkema, Dordrecht, 1998

[4] Colloque physique et mécanique des matériaux granulaires (F. Chevoir; J.N. Roux, eds.), Laboratoire Central des Ponts et Chausses, Paris, 2000

[5] P.G. De Gennes Reflections on the mechanics of granular matter, Physica A, Volume 261 (1998), pp. 267-293

[6] U. Tüzün; G.T. Houlsby; R.M. Nedderman; S.B. Savage The flow of granular material—velocity distribution in slow flow, Chem. Eng. Sci., Volume 37 (1982), pp. 1691-1709

[7] S.B. Savage Flow of granular materials (P. Germain; M. Piau; D. Caillerie, eds.), Theoretical and Applied Mechanics, North-Holland, Amsterdam, 1989, pp. 241-266

[8] K. Hutter; K.R. Rajagopal On flows of granular materials, Continuum Mechanics and Thermodynamics, Volume 6 (1994), pp. 81-139

[9] J. Rajchenbach Granular flows, Advances in Physics, 49, 2000, pp. 229-256

[10] P.A. Vermeer Non-associated plasticity for soils, concrete and rock (H.J. Hermann; J.P. Hovi; S. Luding, eds.), Physics of Dry Granular Media, Balkema, Dordrecht, 1998

[11] R.M. Nedderman Statics and Kinematics of Granular Materials, Cambridge University Press, Cambridge, 1992

[12] J.N. Roux; G. Combe Quasi-static rheology and the origins of strain, C. R. Phys., Volume 3 (2002) (this volume)

[13] A. Schofield; P. Wroth Critical State Soil Mechanics, McGraw-Hill, London, 1968

[14] R. Jackson Some mathematical and physical aspects of continuum models for the motion of granular materials (R.E. Meyer, ed.), Theory of Dispersed Multiphase Flow, Academic Press, New York, 1983

[15] G.I. Tardos A fluid mechanistics approach to slow, frictional flow of powders, Powder Technol., Volume 92 (1997), pp. 61-74

[16] C.S. Campbell Rapid granular flows, Annu. Rev. Fluid Mech., Volume 22 (1990), pp. 57-92

[17] B. Miller; C. O'Hern; R.P. Behringer Stress fluctuations for continuously sheared granular materials, Phys. Rev. Lett., Volume 77 (1996), pp. 3110-3113

[18] D. Howell; R.P. Behringer; C.T. Veje Stress fluctuations in a 2D granular couette experiment a continuum transition, Phys. Rev. Lett., Volume 82 (1999), pp. 5241-5244

[19] C.T. Veje; D.W. Howell; R.P. Behringer Kinematics of a two-dimensional granular couette experiment at the transition to shearing, Phys. Rev. E, Volume 59 (1999), pp. 739-745

[20] W. Losert; L. Bocquet; T.C. Lubensky; J.P. Gollub Particle dynamics in sheared granular matter, Phys. Rev. Lett., Volume 85 (2000), pp. 1428-1431

[21] D.M. Mueth; G.F. Debregeas; G.S. Karczmar; P.J. Eng; S.R. Nagel; H.M. Jaeger Signatures of granular microstructure in dense shear flows, Nature, Volume 406 (2000), pp. 385-389

[22] D.M. Mueth Measurements of particle dynamics in slow, dense granular couette flow (2001) | arXiv

[23] M. Lätzel; S. Luding; H.J. Hermann Macroscopic material properties from quasi-static, microscopic simulations of a two-dimensional shear-cell, Granular Matter, Volume 2 (2000), pp. 123-135

[24] O.J. Schwarz; Y. Horie; M. Shearer Discrete element investigation of stress fluctuation in granular flow at high shear rates, Phys. Rev. E, Volume 57 (1998), pp. 2053-2061

[25] S. Schöllmann Simulation of a two-dimensional shear cell, Phys. Rev. E, Volume 59 (1999), pp. 889-899

[26] M. Babic; H.H. Shen; H.T. Shen The stress tensor in granular shear flows of uniform, deformable discs at high solid concentrations, J. Fluid Mech., Volume 219 (1990), pp. 81-118

[27] P.A. Thompson; G.S. Grest Granular flow and the dilatancy transition, Phys. Rev. Lett., Volume 67 (1991), pp. 1751-1754

[28] Y. Zhang; C.S. Campbell The interface between fluid-like and solid-like behaviour in two-dimensional granular flows, J. Fluid Mech., Volume 237 (1992), pp. 541-568

[29] E. Aharonov; D. Sparks On phase transition and self-organized critical state in granular packings, Phys. Rev. E, Volume 60 (1999), p. 6890

[30] R.M. Nedderman; C. Laohakul The thickness of the shear zone of flowing granular materials, Powder Technology, Volume 25 (1980), pp. 91-100

[31] V.V.R. Natarajan; M.L. Hunt; E.D. Taylor Local measurements of velocity fluctuations and diffusion coefficients for a granular material flow, J. Fluid Mech., Volume 304 (1995), pp. 1-25

[32] O. Pouliquen; R. Gutfraind Stress fluctuations and shear zones in quasi-static granular chutes flows, Phys. Rev. E, Volume 53 (1996), pp. 552-561

[33] N. Menon; D.J. Durian Diffusing wave spectroscopy of dynamics in a three dimensional granular flow, Science, Volume 275 (1997), pp. 1920-1922

[34] F.F. Chevoir; M. Prochnow; P. Moucheront; F. da Cruz; F. Bertrand; J.P. Guilbaud; P. Coussot; J.N. Roux Dense granular flows in a vertical chute (Y. Kishino, ed.), Powders and Grains, Lisse, Swets and Zeitlinger, 2001, pp. 399-402

[35] C. Denniston; H. Li Dynamics and stress in gravity driven granular flow, Phys. Rev. E, Volume 59 (1999), pp. 3289-3292

[36] M.Y. Louge; S.C. Keast On dense granular flows down flat frictional inclines, Phys. Fluids, Volume 13 (2001), pp. 1213-1233

[37] T.G. Drake Structural features in granular flows, J. Geophys. Res., Volume 95 (1990), pp. 8681-8696

[38] C. Ancey; P. Coussot; P. Evesque Examination of the possibility of a fluid-mechanics treatment of dense granular flows, Mech. Coh. Frict. Mater., Volume 1 (1996), pp. 385-403

[39] O. Pouliquen; N. Renaut Onset of granular flows on an inclined rough surface: dilatancy effects, J. Phys. II, Volume 6 (1996), pp. 923-935

[40] E. Azanza, Ecoulements granulaires bidimensionnels sur un plan inclin, PhD thesis, École Nationale des Ponts et Chausses, Paris, 1998

[41] O. Pouliquen Scaling laws in granular flows down rough inclined planes, Phys. Fluids, Volume 11 (1999), pp. 542-548

[42] A. Daerr; S. Douady Two types of avalanches behaviour in granular media, Nature, Volume 399 (1999), pp. 241-243

[43] P.A. Lemieux; D.J. Durian From avalanches to fluid flow: a continuum picture of grain dynamics down a heap, Phys. Rev. Lett., Volume 85 (2000), pp. 4273-4276

[44] D.M. Hanes; O.R. Walton Simulations and physical measurements of glass spheres flowing down a bumpy incline, Powder Technol., Volume 109 (2000), pp. 133-144

[45] S. Dippel; D. Wolf Rapid granular flow on a rough inclined plane, Comput. Commun., Volume 121 (1999), pp. 284-289

[46] F. Chevoir; M. Prochnow; J.T. Jenkins; P. Mills Dense granular flows down an inclined plane (Y. Kishino, ed.), Powders and Grains, Lisse, Swets and Zeitlinger, 2001, pp. 373-376

[47] S.L. Silbert; D. Ertas; G.S. Grest; T.C. Halsey; D. Levine; S.J. Plimpton Granular flow down an inclined plane, Phys. Rev. E, Volume 64 (2001), p. 051302

[48] D.V. Khakhar; A.V. Orpe; P. Andersen; J.M. Ottino Surface flow of granular materials: model and experiments in heap formation, J. Fluid Mech., Volume 441 (2001), pp. 255-264

[49] B. Andreotti; S.S. Douady Selection of velocity profile and flow depth in granular flow, Phys. Rev. E, Volume 63 (2001) no. 1–8, p. 031305

[50] T.S. Komatsu; S. Inagaki; M. Nakagawa; S. Nasuno Creep motion in a granular pile exhibiting steady surface flow, Phys. Rev. Lett., Volume 86 (2001), pp. 1757-1760

[51] D. Bonamy; F. Daviaud; L. Laurent Experimental study of granular flows via high speed camera: a continuous description | arXiv

[52] M. Nakagawa; S.A. Altobelli; A. Caprihan; E. Fukushima; E.K. Jeong Non-invasive measurements of granular flow by magnetic resonance imaging, Exp. Fluids, Volume 16 (1993), pp. 54-60

[53] S. Nasuno; A. Kudrolli; A. Bak; J.P. Gollub Time-resolved studies of stick-slip friction in sheared granular layers, Phys. Rev. E, Volume 58 (1998), pp. 2161-2171

[54] G.I. Tardos; M.I. Khan; D.G. Schaeffer Forces on a slowly rotating, rough cylinder in a Couette device containing a dry, frictional powder, Phys. Fluids, Volume 10 (1998), pp. 335-341

[55] S.B. Savage; M. Sayed Stress developed by dry cohesionless granular materials sheared in an annular cell, J. Fluid Mech., Volume 142 (1984), pp. 391-430

[56] D.M. Hanes; D.L. Inman Observations of rapidly flowing granular fluid flow, J. Fluid Mech., Volume 150 (1985), pp. 357-380

[57] G.W. Baxter; R.P. Behringer; T. Fagert; G.A. Johnson Pattern formation in flowing sand, Phys. Rev. Lett., Volume 62 (1989), pp. 2825-2828

[58] L. Quartier; B. Andreotti; S. Douady; A. Daerr Dynamics of a grain on a sandpile model, Phys. Rev. E, Volume 62 (2000), pp. 8299-8307

[59] H.M. Jaeger; C.H. Liu; S.R. Nagel; T.A. Witten Friction in granular flows, Europhys. Lett., Volume 11 (1990), pp. 619-624

[60] H.M. Jaeger; C.H. Liu; S.R. Nagel Relaxation a the angle of repose, Phys. Rev. Lett., Volume 62 (1989), pp. 40-43

[61] G. Debregeas; H. Tabuteau; J.M. di Meglio Deformation and flow of a two-dimensional foam under continuous shear, Phys. Rev. Lett., Volume 87 (2001), p. 178305

[62] F. Radjai; S. Roux Features of the granular texture (Y. Kishino, ed.), Powders and Grains, Lisse, Swets and Zeitlinger, 2001, pp. 21-24

[63] F. Radjai Features of force transmission in granular media (Y. Kishino, ed.), Powders and Grains, Lisse, Swets and Zeitlinger, 2001, pp. 157-160

[64] L. Staron; J.P. Vilotte; F. Radjai Friction and mobilization of contacts in granular material avalanches (Y. Kishino, ed.), Powders and Grains, Lisse, Swets and Zeitlinger, 2001, pp. 451-454

[65] M.E. Cates; J.P. Wittmer; J.P. Bouchaud; P. Claudin Jamming, force chains and fragile matter, Phys. Rev. Lett., Volume 281 (1998), pp. 1841-1844

[66] J. Duran Static and dynamic arching effect in granular materials (H.J. Hermann; J.P. Hovi; S. Luding, eds.), Physics of Dry Granular Media, Balkema, Dordrecht, 1998

[67] C.K.K. Lun; A.A. Bent Numerical simulation of inelastic frictional spheres in simple shear flow, J. Fluid Mech., Volume 258 (1994), pp. 335-353

[68] C.S. O'Hern; S.A. Langer; A.J. Liu; S.R. Nagel Force distribution near jamming and glass transition, Phys. Rev. Lett., Volume 86 (2001), pp. 111-114

[69] F. Radjai; L. Brendel; S. Roux Nonsmoothness, indeterminacy, and friction in two-dimensional arrays of rigid particles, Phys. Rev. E, Volume 54 (1996), pp. 861-873

[70] D.E. Wolf Friction in granular media (H.J. Hermann; J.P. Hovi; S. Luding, eds.), Physics of Dry Granular Media, Balkema, Dordrecht, 1998

[71] P. Evesque Analysis of the statistics of sandpile avalanches using soil-mechanics results and concepts, Phys. Rev. A, Volume 43 (1991), pp. 2720-2740

[72] L.S. Mohan; P.R. Nott; K.K. Rao A frictional Cosserat model for the flow of granular materials trough a vertical channel, Acta Mech., Volume 138 (1999), pp. 75-96

[73] L.S. Mohan; K.K. Rao; P.R. Nott Frictional Cosserat model for slow granular flows (2001) | arXiv

[74] S.B. Savage Granular flows down rough inclines-review and extension (J.T. Jenkins; M. Satake, eds.), Mechanics of Granular Materials: New Models and Constitutive Relations, Elsevier, Amsterdam, 1983

[75] P.C. Johnson; R. Jacskson Frictional–collisional constitutive relations for granular materials, with application to plane shearing, J. Fluid Mech., Volume 176 (1987), pp. 67-93

[76] P.C. Johnson; P. Nott; R. Jackson Frictional–collisional equations of motion for particulate flows and their application to chutes, J. Fluid Mech., Volume 210 (1990), pp. 501-535

[77] L.S. Mohan; P.R. Nott; K.K. Rao Fully developed flow of coarse granular materials through a vertical channel, Chem. Eng. Sci., Volume 52 (1997), pp. 913-933

[78] K.G. Anderson; R. Jackson A comparison of the solutions of some proposed equations of motion of granular materials for fully developed flow down inclines, J. Fluid Mech., Volume 241 (1992), pp. 145-168

[79] W. Losert; L. Bocquet; T.C. Lubensky; J.P. Gollub Particle dynamics in sheared granular matter, Phys. Rev. Lett., Volume 85 (2000), pp. 1428-1432

[80] L. Bocquet; W. Losert; D. Schalk; T.C. Lubensky; J.P. Gollub Granular shear flow dynamics and forces: experiments and continuum theory, Phys. Rev. E, Volume 65 (2002), p. 011307

[81] S.B. Savage Analyses of slow high-concentration flows of granular materials, J. Fluid Mech., Volume 377 (1998), pp. 1-26

[82] I.S. Aranson; L.S. Tsimring Continuum description of avalanches in granular media, Phys. Rev. E, Volume 64 (2001), p. 020301

[83] I.S. Aranson; L.S. Tsimring Continuum theory of partially fluidized granular flows (2001) | arXiv

[84] A. Lemaı̂tre The origin of a repose angle: kinetics of rearrangement for granular materials | arXiv

[85] M.L. Falk; S.A. Langer Dynamics of viscoplastic deformation in amorphous solids, Phys. Rev. E, Volume 57 (1998), pp. 7192-7208

[86] P. Mills; D. Loggia; M. Tixier Model for a stationary dense granular flow along an inclined wall, Europhys. Lett., Volume 45 (1999), pp. 733-738

[87] P. Mills; M. Tixier; D. Loggia Influence of roughness and dilatancy for dense granular flow along an inclined wall, Eur. Phys. J. E, Volume 1 (2000), pp. 5-8

[88] J.T. Jenkins, F. Chevoir, Dense plane flows of frictional spheres down a bumpy, frictional incline, preprint, 2001

[89] B. Andreotti; S. Douady Selection of velocity profile and flow depth in granular flows, Phys. Rev. E, Volume 63 (2001), p. 031305

[90] O. Pouliquen; Y. Forterre; S. Ledizes Dense granular flows down incline as a self activated process, Adv. Complex Systems, Volume 4 (2001), pp. 441-450

[91] S. Douady; B. Andreotti; A. Daerr; P. Cladé From a grain to avalanches: on the physics of granular surface flows, C. R. Phys., Volume 3 (2002), pp. 177-186

[92] A. Aradian; E. Raphaël; P.G. de Gennes C. R. Phys., 3 (2002), pp. 187-196

Cité par Sources :

Commentaires - Politique