Flows of dense granular media

Annual Review of Fluid Mechanics

Volumn 40, Issue , 2008, Pages 1-24

  Forterre, Yoël ^a   Pouliquen, Olivier ^a  

^a AIX MARSEILLE UNIVERSITÉ   (France)

Author keywords

Friction; Granular flows; Instability; Rheology; Shallow water; Visco plasticity

Indexed keywords

COMPUTER SIMULATION; CONSTITUTIVE EQUATIONS; FRICTION; GRANULAR MATERIALS; RHEOLOGY; VISCOPLASTICITY;

DENSE FLOW; GRANULAR FLOW; VISCO-PLASTIC CONSTITUTIVE LAW;

FLOW OF SOLIDS;

COMPUTER SIMULATION; CONSTITUTIVE EQUATIONS; FLOW OF SOLIDS; FRICTION; GRANULAR MATERIALS; RHEOLOGY; VISCOPLASTICITY;

CONSTITUTIVE EQUATION; FLUID FLOW; FRICTION; GRANULAR MEDIUM; RHEOLOGY; VISCOPLASTICITY;

EID: 39049128968     PISSN: 00664189     EISSN: None     Source Type: Book Series    
DOI: 10.1146/annurev.fluid.40.111406.102142     Document Type: Review

References (111)

1. Ancey C, Coussot P, Evesque P. 1999. A theoretical framework for granular suspension in a steady simple shear flow. J. Rheol. 43:1673-99
2. Aradian A, Raphaël E, de Gennes PG. 2002. Surface flows of granular materials: a short introduction to some recent models. C. R. Phys. 3:187-96
3. Aranson IS, Tsimring LS. 2002. Continuum theory of partially fluidized granular flows. Phys. Rev. Lett. 65:061303
4. Aranson IS, Tsimring LS. 2006. Patterns and collective behavior in granular media: theoretical concepts. Rev. Mod. Phys. 78:641-92
5. Bagnold RA. 1954. Experiment on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. R. Soc. London Ser. A 225:49-63
6. Balmforth NJ, Kerswell RR. 2005. Granular collapse in two dimensions. J. Fluid Mech. 538:399-428
7. Balmforth NJ, Liu JJ. 2004. Roll waves in mud. J. Fluid Mech. 519:33-54
8. Baran O, Ertas D, Halsey TC, Grest GS, Lechman JB. 2006. Velocity correlations in dense gravity-driven granular chute flow. Phys. Rev. E 74:051302
9. Bocquet L, Losert W, Schalk D, Lubensky TC, Gollub JP. 2001. Granular shear flow dynamics and forces: experiments and continuum theory. Phys. Rev. E 65:011307
10. Bonamy D, Daviaud F, Laurent L, Bonetti M, Bouchaud JP. 2002. Multi-scale clustering in granular surface flows. Phys. Rev. Lett. 89:034301
11. Börzsönyi T, Halsey T, Ecke RE. 2005. Two scenarios for avalanche dynamics in inclined granular layers. Phys. Rev. Lett. 94:208001
12. Bouchaud JP, Cates M, Prakash JR, Edwards SF. 1994. A model for the dynamics of sandpile surfaces. J. Phys. 14:1383-410
13. Boutreux T, Raphaël E, de Gennes PG. 1998. Surface flows of granular material: a modified picture for thick avalanches. Phys. Rev. E 58:4692-700
14. Campbell CS. 1990. Rapid granular flows. Annu. Rev. Fluid Mech. 22:57-92
15. Campbell CS. 2002. Granular shear flows at the elastic limit. J. Fluid Mech. 465:261-91
16. Cassar C, Nicolas M, Pouliquen O. 2005. Submarine granular flows down inclined planes. Phys. Fluids 17:103301
17. Courrech du Pont S, Gondret P, Perrin B, Rabaud M. 2003. Wall effects on granular heap stability. Eur. Lett. 61:492-98
18. da Cruz F, Chevoir F, Bonn D, Coussot P. 2002. Viscosity bifurcation in granular materials, foams, and emulsions. Phys. Rev. E 66:051305
19. da Cruz F, Chevoir F, Roux JN, Iordanoff I. 2004. Macroscopic friction of dry granular materials. Tribol. Ser. 43:53-61
20. da Cruz F, Emam S, Prochnow M, Roux JN, Chevoir F. 2005. Rheophysics of dense granular materials: discrete simulation of plane shear flows. Phys. Rev. E 72:021309
21. Daerr A, Douady S. 1999a. Sensitivity of granular surface flows to preparation. Europhys. Lett. 47:324-30
22. Daerr A, Douady S. 1999b. Two types of avalanche behavior in granular media. Nature 399:241-43
23. Deboeuf S, Lajeunesse E, Dauchot O, Andreotti B. 2006. Flow rule, self-channelization and levees in unconfined granular flows. Phys. Rev. Lett. 97:158303
24. Depken M, van Saaloos W, van Hecke M. 2006. Continuum approach to wide shear zones in quasistatic granular matter. Phys. Rev. E 73:031302
25. Douady S, Andreotti B, Cladé P, Daerr A. 2001. The four avalanche fronts: a test case for granular surface flow modeling. Adv. Complex Syst. 4:509-22
26. Douady S, Andreotti B, Daerr A. 1999. On granular surface flow equations. Eur. Phys. J. B 11:131-42
27. Ertas D, Halsey TC. 2002. Granular gravitational collapse and chute flow. Eurphys. Lett. 60:931-37
28. Felix G, Thomas N. 2004. Relation between dry granular flow regimes and morphology of deposits: formation of levees in pyroclastic deposits. Earth Planet. Sci. Lett. 221:197-213
29. Felix G, Thomas N. 2005. Evidence of two effects in the size segregation process in dry granular media. Phys. Rev. E 70:051307
30. Fenistein D, van de Meent JW, van Hecke M. 2004. Universal and wide shear zones in granular bulk flow. Phys. Rev. Lett. 92:094301
31. Forterre Y. 2006. Kapiza waves as a test for three-dimensional granular flow rheology. J. Fluid Mech. 563:123-32
32. Forterre Y, Pouliquen O. 2002. Stability analysis of rapid granular chute flows: formation of longitudinal vortices. J. Fluid Mech. 467:361-87
33. Forterre Y, Pouliquen O. 2003. Long-surface-wave instability in dense granular flows. J. Fluid Mech. 486:21-50
34. Frigaard IA, Nouar C. 2005. On the usage of viscosity regularisation methods for visco-plastic fluid flow computation. J. Non-Newton. Fluid Mech. 127:1-26
35. GDR MiDi. 2004. On dense granular flows. Eur. Phys. J. E 14:341-65
36. Goddard JD. 1986. Dissipative materials as constitutive models for granular media. Acta Mech. 83:3-13
37. Goldhirsch I. 2003. Rapid granular flows. Annu. Rev. Fluid Mech. 35:267-93
38. Gray JMNT, Tai YC, Noelle S. 2003. Shock waves, dead zones and particle-free regions in rapid granular free-surface flows. J. Fluid Mech. 491:161-81
39. Greve R, Koch T, Hutter K. 1994. Unconfined flow of granular avalanches along a partly curved surface: experiments and theoretical predictions. Proc. R. Soc. London Ser. A 342:573-600
40. Heinrich P, Piatanesi A, Hebért. 2001. Numerical modelling of tsunami generation and propagation from submarine slumps: the 1998 Papua New Guinea event. Geophys. J. Int. 145:97-111
41. Hill G, Yeung S, Koehler SA. 2005. Scaling vertical drag forces in granular media. Europhys. Lett.72:137-43
42. Hokanardottir KM, Hogg AJ. 2005. Oblique shocks in rapid granular flows. Phys. Fluids 17:077101
43. Jaeger HM, Nagel SR, Behringer RP. 1996. Granular solids, liquids, and gases. Rev. Mod. Phys. 68:1259-73
44. Jenkins JT. 2006. Dense shearing flows of inelastic disks. Phys. Fluids 18:103307
45. Jenkins JT, Richman MW. 1985. Kinetic theory for plane flows of a dense gas of identical, rough, inelastic, circular disks. Phys. Fluids 12:3485-94
46. Jenkins JT, Savage SB. 1983. At theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. J. Fluid Mech. 130:187-202
47. Johnson PC, Jackson R. 1987. Frictional-collisional constitutive relations for granular materials, with application to plane shearing. J. Fluid Mech. 176:67-93
48. Jop P, Forterre Y, Pouliquen O. 2005. Crucial role of sidewalls in granular surface flows: consequences for the rheology. J. Fluid Mech. 541:167-92
49. Jop P, Forterre Y, Pouliquen O. 2006. A constitutive law for dense granular flows. Nature 441:727-30
50. Josserand C, Lagre PY, Lhuillier D. 2006. Granular pressure and the thickness of a layer jamming on a rough incline. Europhys. Lett. 73:363-69
51. Kamrin K, Bazant MZ. 2007. A stochastic flow rule for granular materials. Phys. Rev. E. In press
52. Khakhar DV, Orpe AV, Andersen P, Ottino JM. 2001. Surface flow of granular materials: model and experinents in heap formation. J. Fluid Mech. 441:255-64
53. Komatsu TS, Inagaki S, Nakagawa N, Nasumo S. 2001. Creep motion in a granular pile exhibiting steady surface flow. Phys. Rev. Lett. 86:1757-60
54. Kumaran V. 2006. The constitutive relation for the granular flow of rough particles, and its application to the flow down an inclined plane. J. Fluid Mech. 561:1-42
55. Lajeunesse E, Mangeney-Castelnau A, Vilotte JP. 2004. Spreading of a granular mass on a horizontal plane. Phys. Fluids 16:2371-81
56. Lajeunesse E, Monnier JB, Homsy GM. 2005. Granular slumping on a horizontal surface. Phys. Fluids 17:103302
57. Lemaitre A. 2002. Origin of a repose angle: kinetics of rearrangement for granular materials. Phys. Rev. Lett. 89:064303
58. Lemieux PA, Durian DJ. 2000. From avalanches to fluid flow: a continuum picture of grain dynamics down a heap. Phys. Rev. Lett. 85:4273-76
59. Liu AJ, Nagel SR. 1998. Jamming is not just cool any more. Nature 396:21-22
60. Lois G, Lemaitre A, Carlson J. 2005. Numerical tests of consitutive laws for dense granular flows. Phys. Rev. E 72:051303
61. Lois G, Lemaitre A, Carlson JM. 2006. Emergence of multi-contact interactions in contact dynamics simulations of granular shear flows. Europhys. Lett. 76:318-24
62. Losert W, Bocquet L, Lubensky TC, Gollub JP. 2000. Particle dynamics in sheared granular matter. Phys. Rev. Lett. 85:1428-31
63. Louge MY. 2003. Model for dense granular flows down bumpy inclines. Phys. Rev. E 67:061303
64. Louge M, Valance A, Taberlet N, Richard P, Delannay R. 2005. Volume fraction profile in channeled granular flows down an erodible incline. Proc. Powders Grains, Stuttgart, Ger. Leiden: Balkema Publ.
65. Lube G, Huppert HE, Sparks RSJ, Hallworth M. 2004. Axisymmetric collapse of granular columns. J. Fluid Mech. 508:175-99
66. Lun CKK, Savage SB, Jeffrey DJ, Chepurniy N. 1984. Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flow field. J. Fluid Mech. 140:223-56
67. Mangeney-Castelnau A, Bouchut F, Thomas N, Vilotte JP, Bristeau M-O. 2007. Numerical modeling of self-channeling granular flows and of their levee/channel deposits. J. Geophys. Res. 112:F02017
68. Mangeney-Castelnau A, Bouchut F, Vilotte JP, Lajeunesse E, Aubertin A, Pirulli M. 2005. On the use of Saint-Venant equations to simulate the spreading of a granular mass. J. Geophys. Res. 110:B09103
69. Mills P, Loggia D, Tixier M. 1999. Model for a stationary dense granular flow along an inclined wall. Europhys. Lett. 45:733-38
70. Mitarai N, Nakanishi H. 2004. Linear stability analysis of rapid granular flow on a slope and density wave formation. J. Fluid Mech. 507:309-34
71. Mohan LS, Rao KK, Nott PR. 2002. A frictional Cosserat model for the slow shearing of granular materials. J. Fluid Mech. 457:377-409
72. Mueth DM, Debregeas GF, Karczmar GS, Eng PJ, Nagel SR, Jaeger HM. 2000. Signatures of granular microstructure in dense shear flows. Nature 406:385-89
73. Naaim M, Vial S, Couture R. 1997. Saint-Venant approach for rock avalanches modelling. Multiple Scale Analyses Coupled Phys. Syst.: Saint-Venant Symp. Paris: Presse École Natl. Ponts Chaussées
74. Orpe A, Khakhar DV. 2007. Rheology of surface granular flows. J. Fluid Mech. 571:1-32
75. Ottino JM, Khakhar DV. 2000. Mixing and segregation of granular materials. Annu. Rev. Fluid Mech. 32:55-91
76. Pouliquen O. 1999a. Scaling laws in granular flows down rough inclined planes. Phys. Fluids 11:542-48
77. Pouliquen O. 1999b. On the shape of granular fronts down rough inclined planes. Phys. Fluids 11:1956-58
78. Pouliquen O. 2004. Velocity correlations in dense granular flows. Phys. Rev. Lett. 93:248001
79. Pouliquen O, Cassar C, Jop P, Forterre Y, Nicolas M. 2006. Flow of dense granular material: towards simple constitutive laws. J. Stat. Mech. 2006:P07020
80. Pouliquen O, Chevoir F. 2002. Dense flows of dry granular material. C. R. Phys. 3:163-75
81. Pouliquen O, Forterre Y. 2002. Friction law for dense granular flows: application to the motion of a mass down a rough inclined plane. J. Fluid Mech. 453:133-51
82. Pouliquen O, Forterre Y, Ledizes S. 2001. Slow dense granular flows as a self-induced process. Adv. Complex Syst. 4:441-50
83. Pouliquen O, Renaut N. 1996. Onset of granular flows on an inclined rough surface: dilatancy effects. J. Phys. II 6:923-35
84. Quartier L, Andreotti B, Douady S, Daerr A. 2000. Dynamics of a grains on a sandpile model. Phys. Rev. E 62:8299-307
85. Radjai F, Roux S. 2003. Turbulent-like behavior in quasi-static flow of granular media. Phys. Rev. Lett. 89:064302
86. Rajchenbach J. 2003. Dense, rapid flows of inelastic grains under gravity. Phys. Rev. Lett. 90:144302
87. Renouf M, Bonamy D, Dubois F, Alart P. 2005. Numerical simulation of two-dimensional steady granular flows in rotating drum: on surface flow rheology. Phys. Fluids 17:103303
88. Rognon PG, Roux J-N, Wolf D, Naaim M, Chevoir F. 2006. Rheophysics of cohesive granular materials. Europhys. Lett. 74:644-50
89. Roux J-N, Combes G. 2002. Quasistatic rheology and the origin of strain. C. R. Phys. 3:131-40
90. Roux S, Radjai F. 1998. Texture-dependent rigid-plastic behavior. In Physics of Dry Granular Media, ed. HJ Hermann, JP Hovi, S Luding, pp. 229-36. Dordrecht: Kluwer Acad.
91. Ruyer-Quil C, Manneville P. 2000. Improved modeling of flows down inclined planes. Eur. Phys. J. B 15:357-69
92. Savage SB. 1983. Granular flows down rough inclines: review and extension. In Mechanics of Granular Materials: New Models and Constitutive Equations, ed. JT Jenkins, M Satake, pp. 261-82. Amsterdam: Elsevier
93. Savage SB. 1984. The mechanics of rapid granular flows. Adv. Appl. Mech. 24:28966
94. Savage SB. 1998. Analyses of slow high-concentration flows of granular materials. J. Fluid Mech. 377:1-26
95. Savage SB, Hutter K. 1989. The motion of a finite mass of granular material down a rough incline. J. Fluid Mech. 199:177-215
96. Savage SB, Lun CKK. 1988. Particle size segregation in inclined chute flow of dry cohesionless granular solids. J. Fluid Mech. 189:311-35
97. Savage SB, Sayed M. 1984. Stresses developed by dry cohesionless granular materials sheared in an annular shear cell. J. Fluid Mech. 142:391-430
98. Schaeffer DG. 1987. Instability in the evolution equations describing incompressible granular flow. J. Differ. Equat. 66:19-50
99. Schofield A, Wroth P. 1968. Critical State Soil Mechanics. London: McGraw-Hill
100. Shen HH, Sankaran B. 2004. Internal time scales in a simple shear granular flow. Phys. Rev. E 70:051308
101. Silbert LE, Ertas D, Grest GS, Halsey TC, Levine D, Plimpton SJ. 2001. Granular flow down an inclined plane: Bagnold scaling and rheology. Phys. Rev. E 64:051302
102. Silbert LE, Landry JW, Grest GS. 2003. Granular flow down a rough inclined plane: transition between thin and thick piles. Phys. Fluids 15:1-10
103. Stickel JJ, Powell RL. 2005. Fluid mechanics and rheology of dense suspensions. Annu. Rev. Fluid Mech. 37:129-49
104. Swinney HL, Rericha EC. 2004. Pattern formation and shock waves in granular gases. In The Physics of Complex Systems (New Advances and Perspectives): Proc. Int. School Phys. Enrico Fermi, Course CLV 155, 173, ed. F Mallamace, HE Stanley, pp. 1-34. Amsterdam: IOS Press
105. Taberlet N, Richard P, Henry E, Delannay R. 2004. The growth of a super stable heap: an experimental and numerical study. Europhys. Lett. 68:515-21
106. Taberlet N, Richard P, Valance A, Delannay R, Losert W, et al. 2003. Super stable granular heap in a thin channel. Phys. Rev. Lett. 91:264301
107. Veje CT, Howell DW, Behringer RP. 1999. Kinematics of a two-dimensional granular Couette experiment at the transition to shearing. Phys. Rev. E 59:739-45
108. Volfson D, Tsimring LS, Aranson IS. 2003. Order parameter description of stationary partially fluidized shear granular flows. Phys. Rev. Lett. 90:254301
109. Wang ZT. 2004. A note on the velocity of granular flow down a bumpy inclined plane. Granul. Matter 6:67-69
110. Wieland JM, Gray JMNT, Hutter K. 1999. Channelized free-surface flow of cohesionless granular avalanches in a chute with shallow lateral curvature. J. Fluid Mech. 392:73-100
111. Wood DM. 1990. Soil Behaviour and Critical State Soil Mechanics. Cambridge, UK: Cambridge Univ. Press