Towards a theoretical picture of dense granular flows down inclines
Source abstract
Abstract
Unlike most fluids, granular materials include coexisting solid, liquid or gaseous regions, which produce a rich variety of complex flows. Dense flows down inclines preserve this complexity but remain simple enough for detailed analysis. In this review we survey recent advances in this rapidly evolving area of granular flow, with the aim of providing an organized, synthetic review of phenomena and a characterization of the state of understanding. The perspective that we adopt is influenced by the hope of obtaining a theory for dense, inclined flows that is based on assumptions that can be tested in physical experiments and numerical simulations, and that uses input parameters that can be independently measured. We focus on dense granular flows over three kinds of inclined surfaces: flat-frictional, bumpy-frictional and erodible. The wealth of information generated by experiments and numerical simulations for these flows has led to meaningful tests of relatively simple existing theories.
Source: europepmc · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: Granular flow and fluidized beds · Landslides and related hazards · Fluid Dynamics and Heat Transfer
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (88)
Show source-provided references
1. Maloney, C. & Lemaître, A. Universal breakdown of elasticity at the onset of material failure. Phys. Rev. Lett. 93, 195501 (2004).10.1103/PhysRevLett.93.195501 ↗
2. Johnson, W. L. Bulk glass-forming metallic alloys: science and technology. Mater. Res. Soc. Bull. 24, 42–56 (1999).10.1557/S0883769400053252 ↗
3. Azanza, E., Chevoir, F. & Moucheront, P. Experimental study of collisional granular flows down an inclined plane. J. Fluid Mech. 400, 199–227 (1999).10.1017/S0022112099006461 ↗
4. Forterre, Y. & Pouliquen, O. Longitudinal vortices in granular flow. Phys. Rev. Lett. 86, 5886–5889 (2001).10.1103/PhysRevLett.86.5886 ↗
5. Xu, H., Louge, M., & Reeves, A. Solutions of the kinetic theory for bounded collisional granular flows. Continuum Mech. Thermodyn. 15, 321–349 (2003).10.1007/s00161-003-0116-6 ↗
6. Louge, M. Y. & Keast, S. C. On dense granular flows down flat frictional inclines. Phys. Fluids 13, 1213–1233 (2001).10.1063/1.1358870 ↗
7. Pouliquen, O. Scaling laws in granular flows down a bumpy inclined plane. Phys. Fluids 11, 542–548 (1999).10.1063/1.869928 ↗
8. Taberlet, N. et al. Super stable granular heap in thin channel. Phys. Rev. Lett. 91, 264301 (2003).10.1103/PhysRevLett.91.264301 ↗
9. Silbert, L. E. et al. Granular flow down an inclined plane: Bagnold scaling and rheology. Phys. Rev. E 64, 51302 (2001).10.1103/PhysRevE.64.051302 ↗
10. GDR MiDi. On dense granular flows. Eur. Phys. J. E 14, 341–365 (2004).10.1140/epje/i2003-10153-0 ↗
11. Pouliquen, O. & Chevoir, F. Dense flows of dry granular materials. C. R. Acad. Sci. Paris, Phys. 3, 163–175 (2002).
12. Campbell, C. S. Rapid granular flows. Annu. Rev. Fluid Mech. 22, 57–92 (1990).10.1146/annurev.fl.22.010190.000421 ↗
13. Goldhirsch, I. Rapid granular flows. Annu. Rev. Fluid Mech. 35, 267–292 (2003).10.1146/annurev.fluid.35.101101.161114 ↗
14. Walton, O. R. in Particulate Two-Phase Flows (ed. Roco, M.) Ch. 25, 884–911 (Butterworth-Heinemann, Boston, 1993).
15. Foerster, S. F., Louge, M. Y., Chang, H. & Allia, K. Measurements of the collision properties of small spheres. Phys. Fluids 6, 1108–1115 (1994).10.1063/1.868282 ↗
16. Kharaz, A. H., Gorham, D. A. & Salman, A. D. An experimental study of the elastic rebound of spheres. Powder Technol. 120, 281–291 (2001).10.1016/S0032-5910(01)00283-2 ↗
17. Louge, M. Y. & Adams, M. E. Anomalous behavior of normal kinematic restitution in the oblique impacts of a hard sphere on an elastoplastic plate. Phys. Rev. E 65, 021303 (2002).10.1103/PhysRevE.65.021303 ↗
18. Thornton, C. Coefficient of restitution for collinear collisions of elastic perfectly plastic spheres. J. Appl. Mech. 64, 383–386 (1997).10.1115/1.2787319 ↗
19. Zhang, X. & Vu-Quoc, L. A method to extract the mechanical properties of particles in collision based on a new elasto-plastic normal force–displacement model. Mech. Mater. 34, 779–794 (2002).10.1016/S0167-6636(02)00181-3 ↗
20. Ahn, H., Brennen, C. E. & Sabersky, R. H. Measurements of velocity, velocity fluctuations, density, and stresses in chute flows of granular materials. J. Appl. Mech. 58, 792–803 (1991).10.1115/1.2897265 ↗
21. Drake, T. G. Granular flow: physical experiments and their implications for microstructural theories. J. Fluid Mech. 225, 121–151 (1991).10.1017/S0022112091001994 ↗
22. Berton, G., Delannay, R., Richard, P., Taberlet, N. & Valance, A. Two-dimensional inclined chute flows: transverse motion and segregation. Phys. Rev. E 68, 051303 (2003).10.1103/PhysRevE.68.051303 ↗
23. Hanes, D. M. & Walton, O. R. Simulations and physical measurements of glass spheres flowing down a bumpy incline. Powder Tech. 109, 133–144 (2000).10.1016/S0032-5910(99)00232-6 ↗
24. Walton, O. R. Numerical simulation of inclined chute flows of monodisperse, inelastic, frictional spheres. Mech. Mater. 16, 239–247 (1993).10.1016/0167-6636(93)90048-V ↗
25. Luding, S. in The Physics of Granular Media (eds Hinrichsen, H. & Wolf, D.) 299–324 (Wiley-VCH, Weinheim, 2004).
26. Moreau, J. J. Some numerical methods in multibody dynamics: applications to granular materials. Eur. J. Mech. A 13, 93–114 (1994).
27. Bi, W., Delannay, R., Richard, P., Taberlet, N. & Valance, A. 2D and 3D confined granular chute flows: experimental and numerical results. J. Phys. Condens. Matter 17, 1–24 (2005).10.1088/0953-8984/17/1/001 ↗
28. Johnson, P. C., Nott, P. & Jackson, R. Frictional–collisional equations of motion for particulate flows and their application to chutes. J. Fluid Mech. 210, 501–535 (1990).10.1017/S0022112090001380 ↗
29. Baumberger, T. & Caroli, C. Multicontact solid friction: a macroscopic probe of pinning and dissipation on the mesoscopic scale. Mater. Res. Soc. Bull. 23, 41–46 (1998).10.1557/S0883769400030621 ↗
30. Silbert, S. L., Landry, J. W. & Grest, G. S. Granular flow down a rough inclined plane; transition between thin and thick piles. Phys. Fluids 15, 1–10 (2003).10.1063/1.1521719 ↗
31. Louge, M. Y. Model for dense granular flows down bumpy inclines. Phys. Rev. E 67, 061303 (2003).10.1103/PhysRevE.67.061303 ↗
32. Daerr, A. & Douady, S. Two types of avalanche behaviour in granular media. Nature 399, 241–243 (1999).10.1038/20392 ↗
33. Silbert, L. E., Grest, G. S. & Plimpton, S. J. Boundary effects and self-organization in dense granular flows. Phys. Fluids 14, 1–10 (2002).10.1063/1.1487379 ↗
34. Mitarai, N. & Nakanishi, H. Bagnold scaling, density plateau, and kinetic theory analysis of dense granular flow. Phys. Rev. Lett. 94, 128001 (2005).10.1103/PhysRevLett.94.128001 ↗
35. Ancey, C. Dry granular flows down an inclined channel: experimental investigation on the frictional–collisional regime. Phys. Rev. E 65, 011304 (2001).10.1103/PhysRevE.65.011304 ↗
36. Hungr, O. & Morgenstern, N. R. Experiments on the flow behaviour of granular materials at high velocity in an open channel. Géotechnique 34, 405–413 (1984).10.1680/geot.1984.34.3.405 ↗
37. Jop, P., Forterre, Y. & Pouliquen, O. Crucial role of side walls for granular surface flows: consequences for rheology. J. Fluid Mech. 541, 167–192 (2005).10.1017/S0022112005005987 ↗
38. Rajchenbach, J. Granular flows. Adv. Phys. 49, 229–256 (2000).10.1080/000187300243372 ↗
39. Khakhar, D. V., Orpe, A. V., Andersen, P. & Ottino, J. M. Surface flows of granular materials: model and experiments in heap formation. J. Fluid Mech. 441, 255–264 (2001).10.1017/S0022112001005201 ↗
40. Komatsu, T. S., Inagaki, S., Nakagawa, N. & Nasuno, S. Creep motion in a granular pile exhibiting steady surface flow. Phys. Rev. Lett. 86, 1757–1760 (2001).10.1103/PhysRevLett.86.1757 ↗
41. Félix, G. & Thomas, N. Relation between dry granular flow regimes and morphology of deposits: formation of levees in pyroclastic deposits. Earth Planet. Sci. Lett. 221, 197–213 (2004).10.1016/S0012-821X(04)00111-6 ↗
42. Jenkins, J. T. in Dynamics: Models and Kinetic Methods for Non-Equilibrium Many Bodied Systems (ed. Karkheck, J.) 313–323 (Kluwer, Dordrecht, 2000).10.1007/978-94-011-4365-3_18 ↗
43. Chapman, S. & Cowling, T. G. The Mathematical Theory of Nonuniform Gases. (Cambridge Univ. Press, Cambridge, 1970).
44. Kirkwood, J. G. Selected Topics in Statistical Mechanics (Gordon & Breach, New York, 1967).
45. Jenkins, J. T. Rapid granular flow down inclines. Appl. Mech. Rev. 47, S240–S244 (1994).10.1115/1.3124415 ↗
46. Bocquet, L., Errami, L. J. & Lubensky, T. C. A hydrodynamic model of a jammed-to-flowing transition in gravity driven granular materials. Phys. Rev. Lett. 89, 184301 (2002).10.1103/PhysRevLett.89.184301 ↗
47. Savage, S. B. in Mechanics of Granular Materials: New Models and Constitutive Relations (eds Jenkins, J. T. & Satake, M.) 261–282 (Elsevier, Amsterdam, 1983).10.1016/B978-0-444-42192-0.50028-1 ↗
48. Mills, P., Tixier, M. & Loggia, D. Model for stationary dense granular flow along an inclined wall. Europhys. Lett. 45, 733–738 (1999).10.1209/epl/i1999-00229-y ↗
49. Ancey, C. & Evesque, P. Frictional–collisional regime for granular suspension flow down an inclined channel. Phys. Rev. E 62, 8349–8360 (2000).10.1103/PhysRevE.62.8349 ↗
50. Aranson, I. S. & Tsimring, L. S. Continuum description of partially fluidized granular flows. Phys. Rev. E 65, 061303 (2002).10.1103/PhysRevE.65.061303 ↗
51. Anderson, K. G. & Jackson, R. A. Comparison of the solutions of some proposed equations of motion of granular materials for fully developed flow down inclined planes. J. Fluid Mech. 241, 145–168 (1992).10.1017/S0022112092001988 ↗
52. Pouliquen, O., Forterre, Y. & Ledizes, S. Dense granular flow down incline as a self-activated process. Adv. Complex Syst. 4, 441–450 (2001).10.1142/S0219525901000358 ↗
53. Lemaitre, A. Origin of a repose angle: kinetics of rearrangement for granular materials. Phys. Rev. Lett. 89, 064303 (2002).10.1103/PhysRevLett.89.064303 ↗
54. Pouliquen, O. On the shape of granular fronts down rough inclined planes. Phys. Fluids 11, 1956–1958 (1999).10.1063/1.870057 ↗
55. Jenkins, J. T. & Savage, S. B. A theory for the rapid flow of identical, smooth, nearly elastic, spherical particles. J. Fluid Mech. 130, 187–202 (1983).10.1017/S0022112083001044 ↗
56. Lun, C. K. K., Savage, S. B., Jeffrey, D. J. & Chepurniy, N. Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flow field. J. Fluid Mech. 140, 223–256 (1984).10.1017/S0022112084000586 ↗
57. Jenkins, J. T. & Richman, M. W. Grad's 13-moment system for a dense gas of inelastic spheres. Arch. Rat. Mech. Anal. 87, 355–377 (1985).10.1007/BF00250919 ↗
58. Jenkins, J. T. & Zhang, C. Kinetic theory for nearly elastic, slightly frictional spheres. Phys. Fluids 14, 1228–1235 (2002).10.1063/1.1449466 ↗
59. Lun, C. K. K. Kinetic theory for granular flow of dense, slightly inelastic, slightly rough spheres. J. Fluid Mech. 223, 539–559 (1991).
60. Chou, C. -S. & Richman, M. W. Constitutive theory for homogeneous granular shear flows of highly elastic spheres. Physica A 259, 430–448 (1998).10.1016/S0378-4371(98)00265-9 ↗
61. Sela, N. & Goldhirsch, I. Hydrodynamic equations for rapid flows of smooth inelastic spheres, to Burnett order. J. Fluid Mech. 361, 41–74 (1998).10.1017/S0022112098008660 ↗
62. Montanero, J. M., Garzo, V., Santos, A. & Brey, J. J. Kinetic theory of simple granular shear flows of smooth hard spheres. J. Fluid Mech. 389, 391–411 (1999).10.1017/S0022112099005182 ↗
63. Richman, M. W. Boundary conditions based on a modified Maxwellian velocity distribution for flows of identical, smooth, nearly elastic spheres. Acta Mech. 75, 227–240 (1988).10.1007/BF01174637 ↗
64. Richman, M. W. & Marciniec, R. P. Gravity-driven granular flows of smooth, inelastic spheres down bumpy inclines. J. Appl. Mech. 57, 1036–1043 (1990).10.1115/1.2897623 ↗
65. Nishimura, K., Kosugi, K. & Nakagawa, M. Experiments on ice-sphere flows along an inclined chute. Mech. Mater. 16, 205–209 (1993).10.1016/0167-6636(93)90044-R ↗
66. Silbert, L. E., Ertas, D., Grest, G. S., Halsey, T. C. & Levine, D. Analogies between granular jamming and the liquid-glass transition. Phys. Rev. E 65, 051307 (2002).10.1103/PhysRevE.65.051307 ↗
67. Aranson, I. S. & Tsimring, L. S. Continuum description of avalanches in granular media. Phys. Rev. E 64, 020301 (2001).10.1103/PhysRevE.64.020301 ↗
68. Wolfson, D., Tsimring, L. S. & Aranson, I. S. Partially fluidized shear granular flows: continuum theory and MD simulations. Phys. Rev. Lett. 90, 254301 (2003).10.1103/PhysRevLett.90.254301 ↗
69. Mills, P., Tixier, M. & Loggia, D. Influence of roughness and dilatancy for dense granular flow along an inclined wall. Eur. Phys. J. E 1, 5–8 (2000).10.1007/s101890050002 ↗
70. Chevoir, F., Prochnow, M., Jenkins, J. T. & Mills, P. in Powders and Grains 01 (ed. Kishino, Y.) 373–376 (Balkema, Lisse, 2001).
71. Bonamy, D. & Mills, P. Diphasic non-local model for granular surface flows. Europhys. Lett. 63, 42–48 (2003).10.1209/epl/i2003-00475-5 ↗
72. Rajchenbach, J. Dense, rapid flows of inelastic grains under gravity. Phys. Rev. Lett. 90, 144302 (2003).10.1103/PhysRevLett.90.144302 ↗
73. da Cruz, F., Emam, S., Prochnow, M., Roux, J. -N. & Chevoir, F. Rheophysics of dense granular materials: discrete simulation of plane shear flows. Phys. Rev. E 72, 021309 (2005).10.1103/PhysRevE.72.021309 ↗
74. Jop, P., Forterre, Y. & Pouliquen, O. A constitutive law for dense granular flows. Nature 441, 727–730 (2006).10.1038/nature04801 ↗
75. Campbell, C. S, Cleary, P. & Hopkins, M. A. Long run-out landslides: a study by computer simulation. J. Geophys. Res. 100, 8267–8283 (1995).10.1029/94JB00937 ↗
76. Campbell, C. S. Granular shear flow at the elastic limit. J. Fluid Mech. 465, 261–291 (2002).10.1017/S002211200200109X ↗
77. Babic, M., Shen, H. H. & Shen, H. T. The stress tensor in granular shear flows of uniform, deformable disks at high solids concentrations. J. Fluid Mech. 219, 81–118 (1990).10.1017/S0022112090002877 ↗
78. Zhang, D. Z. & Rauenzahn, R. M. Stress relaxation in dense and slow flows. J. Rheol. 44, 1019–1041 (2000).10.1122/1.1287287 ↗
79. Ertas, D. & Halsey, T. C. Granular gravitational collapse and chute flow. Europhys. Lett. 60, 931–937 (2002).10.1209/epl/i2002-00307-8 ↗
80. Wildman, R. D., Huntley, J. M., Hansen, J. -P. & Parker, D. J. Granular temperature profiles in three-dimensional vibrofluidized granular beds. Phys. Rev. E 63, 061311 (2001).10.1103/PhysRevE.63.061311 ↗
81. Fukushima, E. Granular flow studies by NMR: a chronology. Adv. Complex Syst. 4, 1–5 (2001).10.1142/S0219525901000413 ↗
82. Dixon, P. K. & Durian, D. J. Speckle visibility spectroscopy and variable granular fluidization. Phys. Rev. Lett. 90 184302 (2003).10.1103/PhysRevLett.90.184302 ↗
83. Pouliquen, O., Belzons, M. & Nicolas, M. Fluctuating particle motion during shear induced granular compaction. Phys. Rev. Lett. 91, 014301 (2003).10.1103/PhysRevLett.91.014301 ↗
84. Toiya, M., Stambaugh, J. & Losert, W. Transient and oscillatory granular shear flow. Phys. Rev. Lett. 93, 088001 (2004).10.1103/PhysRevLett.93.088001 ↗
85. Richard, P., Philippe, P., Barbe, F., Bourlè s, T. X. & Bideau, D. Analysis by x-ray microtomography of a granular packing undergoing compaction. Phys. Rev. E 68, 020301 (2003).10.1103/PhysRevE.68.020301 ↗
86. Jenkins, J. T. & Richman, M. Kinetic theory for plane flows of a dense gas of identical, rough, inelastic, circular disks. Phys. Fluids 28, 3485–3494 (1985).10.1063/1.865302 ↗
87. Verlet, L. & Levesque, D. Integral equations for classical fluids. III. The hard discs system. Mol. Phys. 46, 969–980 (1982).10.1080/00268978200101711 ↗
88. Luding, S. Global equation of state of two-dimensional hard sphere system. Phys. Rev. E 63, 042201 (2001).10.1103/PhysRevE.63.042201 ↗