Analyses of slow high-concentration flows of granular materials

Journal of Fluid Mechanics

Volumn 377, Issue , 1998, Pages 1-26

  Savage, S B ^a  

^a MCGILL UNIVERSITY   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

BOUNDARY LAYER FLOW; CONTINUUM MECHANICS; DEFORMATION; GRANULAR MATERIALS;

GRANULAR FLOW;

SHEAR FLOW;

EID: 0032305779     PISSN: 00221120     EISSN: None     Source Type: Journal    
DOI: 10.1017/S0022112098002936     Document Type: Article

References (89)

1. ABAQUS/Standard 1994 Users Manual, Vols. I and II. Hibbitt, Karlsson & Sorensen, Inc., Pawtucket, Rhode Island.
2. ANDERSON, K. G., JACKSON, R. 1992 A comparison of the solutions of some proposed equations of motion of granular materials for fully developed flow down inclines. J. Fluid Mech. 241, 145-168.
3. BAGNOLD, R. A. 1954 Experiments on a gravity free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. R. Soc. Lond. A 225, 49-63.
4. BEHRINGER, R. P. & BAXTER, G. W. 1994 Pattern formation and complexity in granular flows. In Granular Matter (ed. A. Mehta), pp. 85-119. Springer.
5. BOLZON, G., SCHREFLER, B. A. & ZIENKIEWICZ, O. C. 1996 Elastoplastic soil constitutive laws generalized to partially saturated states. Géotechnique 46, 279-289.
6. CHAPMAN, S. & COWLING, T. G. 1970 The Mathematical Theory of Non-Uniform Gases, 3rd edn. Cambridge University Press.
7. CHEN, C. L. 1988 Generalized visco-plastic modelling of debris flow. J. Hydraul. Engng ASCE 114, 237-258.
8. CHEN, W. F. & MIZUNO, E. 1990 Nonlinear Analysis in Soil Mechanics. Elsevier.
9. CLIFT, R. 1993 An Occamist review of fluidized bed modelling. In Fluid Particle Processes: Fundamentals and Applications (ed. A. W. Weimer, J. C. Chen, L.-S. Fan & W. C. Yang). AIChE Symposium Series No. 296, vol. 89, pp. 1-17.
10. COLE, G. H. A. 1967 The Statistical Theory of Classical Simple Dense Fluids. Pergamon.
11. COWIN, S. C. 1977 The theory of static loads in bins. Trans. ASME E: J. Appl. Mech. 44, 409-412.
12. DING, J. & GIDASPOW, D. 1990 A bubbling fluidization model using kinetic theory of granular flow. AIChE J. 36, 523-538.
13. DRESCHER, A. & DE JOSSELIN DE JONG, G. 1972 Photoelastic verification of a mechanical model for the flow of a granular material. J. Mech. Phys. Solids 20. 337-351.
14. EISENSCHITZ, R. 1958 Statistical Theory of Irreversible Processes. Oxford University Press.
15. FLECK, N. A. & HUTCHINSON, J. W. 1997 Strain gradient plasticity. Adv. Appl. Mech. 33, 295-361.
16. GIDASPOW, D. 1994 Multiphase Flow and Fluidization. Academic.
17. GOLDHIRSCH, I. 1995 Microstructures and kinetics in rapid granular flows. In Traffic and Granular Flows, pp. 251-266. World Scientific.
18. GOLDSHTEIN, A. & SHAPIRO, M. 1995 Mechanics of collisional motion of granular materials. Part 1. General hydrodynamic equations. J. Fluid Mech. 282, 75-114.
19. GOLDHIRSCH, I. & SELA, N. 1996 Origin of normal stress differences in rapid granular flows. Phys. Rev. E 54, 4458-4461.
20. GOLDSHTEIN, A., SHAPIRO, M., MOLDAVSKY, L. & FICHMAN, M. 1995 Mechanics of collisional motion of granular materials. Part 2. Propagation through vibrofluidized garanular layers. J. Fluid Mech. 287, 349-382.
21. GUTFRAIND, R. & POULIQUEN, O. 1996 Study of the origin of shear zones in quasi-static vertical chute flows using discrete element simulations. Mech. Mater. 24, 273-285.
22. GUTFRAIND, R., POULIQUEN, O. & SAVAGE, S. B. 1995 Molecular dynamic simulations of quasi-static granular chute flows. Proc. 10th ASCE Engineering Mechanics Conference, Boulder, May 21-24, vol. 2, pp. 794-797.
23. GUTT, G. M. & HAFF, P. K. 1988 Boundary conditions on continuum theories of granular flow. Brown Bag Preprint Series BB-70, Division of Physics, Mathematics, and Astronomy, Caltech, 24 pp.
24. HAFF, P. K. 1983 Grain flow as a fluid-mechanical phenomenon. J. Fluid Mech. 134, 401-430.
25. HIBLER, W. D. III 1977 A viscous sea ice law as a stochastic average of plasticity. J. Geophys. Res. 82, 3932-3938.
26. HIBLER, W. D. III 1979 A dynamic thermodynamic sea ice model. J. Phys. Oceanogr. 9, 817-846.
27. HINCH, J. 1995 Introduction to mobile particulate systems. In Mobile Particulate Systems (eds. E. Guazzelli & L. Oger), pp. 1-21. Kluwer.
28. HOPKINS, M. A. & SHEN, H. H. 1992 A Monte-Carlo solution for rapidly shearing granular flows based on the kinetic theory of dense gases. J. Fluid Mech. 244, 477-491.
29. HUI, K., & HAFF, P. K. 1986 Kinetic grain flow in a vertical channel, Intl J. Multiphase Flow 12, 289-298.
30. HUI, K., HAFF, P. K., UNGAR, J. E. & JACKSON, R. 1984 Boundary conditions for high shear grain flows. J. Fluid Mech. 145, 223-233.
31. JENIKE, A. W. 1961 Gravity flow of bulk solids. Univ. Utah. Engng Exp. Stn Bull. 108. University of Utah, Salt Lake City.
32. JENIKE, A. W. 1987 A theory of flow of particulate solids in converging and diverging channels based on a conical yield function. Powder Technol. 50, 229-236.
33. JENKINS, J. T. 1987a Balance laws and constitutive relations for rapid flows of granular materials. In Constitutive Models of Deformations (ed. J. Chandra & R. Srivastav), pp. 109-119. SIAM.
34. JENKINS, J. T. 1987b Rapid flows of granular materials. In Non-classical Continuum Mechanics: Abstract Techniques and Applications (ed. R. J. Kops & A. A. Lacey), pp. 213-224. Cambridge University Press,
35. JENKINS, J. T. & MCTIGUE, D. F. 1990 Transport processes in concentrated suspensions: the role of particle fluctuations. In Two Phase Flows and Waves (ed. D. D. Joseph and D. G. Schaeffer), pp. 70-79. Springer.
36. JENKINS, J. T. & MCTIGUE, D. F. 1995 Viscous fluctuations and the rheology of concentrated suspensions. submitted to J. Fluid Mech.
37. JENKINS, J. T. & RICHMAN, M. W. 1985 Grad's 13-moment system for a dense gas of inelastic spheres. Arch. Rat. Mech. Anal. 87, 355-377.
38. JENKINS, J. T. & RICHMAN, M. W. 1986 Boundary conditions for plane flows of smooth nearly elastic, circular disks. J. Fluid Mech. 171, 53-69.
39. JENKINS, J. T. & RICHMAN, M. W. 1988 Plane simple shear of smooth inelastic circular disks: the anisotropy of the second moment in the dilute and dense limits. J Fluid Mech. 192, 313-328.
40. JENKINS, J. T. & SAVAGE, S. B. 1983 A theory for the rapid flow of identical, smooth, nearly elastic particles. J. Fluid Mech. 130, 186-202.
41. JOHNSON, P. C. & JACKSON, R. 1987 Frictional-collisional constitutive relations for granular materials, with application to plane shearing. J. Fluid Mech. 176, 67-93.
42. JOHNSON, P. C., NOTT, P. & JACKSON, R. 1990 Frictional-collisional equations of motion for particulate flows and their application to chutes. J. Fluid Mech. 210, 501-535.
43. KRAUSZ, A. S. & EYRING, H. 1975 Deformation Kinetics. Wiley.
44. KRUYT, N. 1990 Density effects in two-dimensional bins. Trans. ASME E: J. Appl. Mech. 57, 1032-1035.
45. LADE, P. V. 1977 Elasto-plastic stress-strain theory for cohesionless soil with curved yield surfaces. Intl J. Solids Struct. 13, 1019-1035.
46. LADE, P. V. & PRABUCKI, M.-J. 1995 Softening and preshearing effects in sand. Soils and Found., Japanese Geotechn. Soc. 35(4), 93-104.
47. LADE, P. V. & PRADEL, D. 1990 Instability and plastic flow of soils. I: Experimental observations. J. Engng Mech., ASCE 116, 2532-2550.
48. LAN, Y. & ROSATO, A. D. 1995 Macroscopic behavior of vibrating beds of smooth inelastic spheres. Phys. Fluids 7, 1818-1831.
49. LOUGE, M., MASTORAKOS, E. & JENKINS, J. T. 1991 The role of particle collisions in pneumatic transport. J. Fluid Mech. 231, 345-359.
50. LUN, C. K. K. 1991 Kinetic theory for granular flow of dense, slightly inelastic slightly rough spheres. J. Fluid Mech. 233, 539-559.
51. LUN, C. K. K. & BENT, A. A. 1994 Numerical simulations of inelastic frictional spheres in simple shear flow. J. Fluid Mech. 258, 335-353.
52. LUN, C. K. K. & SAVAGE, S. B. 1987 A simple kinetic theory for granular flow of rough, inelastic spherical particles. Trans. ASME E: J. Appl. Mech. 54, 47-53.
53. LUN, C. K. K., SAVAGE, S. B., JEFFREY, D. J. & CHEPURNIY, N. 1984 Kinetic theories for granular flow: inelastic particles in Couette flow and slightly inelastic particles in a general flowfield. J. Fluid Mech. 140, 223-256.
54. MCQUARRIE, D. A. 1976 Statistical Mechanics. Harper and Row.
55. MCTIGUE, D. F. & JENKINS, J. T. 1992 Channel flow of a concentrated suspension. In Advances in Micromechanics of Materials (ed. H. H. Shen, M. Satake, M. Mehrabadi, C. S. Chang & C. S. Campbell), pp. 381-390. Elsevier.
56. MROZ, Z., NORRIS, V. A. & ZIENKIEWICZ, O. C. 1979 Application of an anisotropic hardening model in the analysis of elasto-plastic deformation of soils. Géotechnique 29, 1-34.
57. MÜHLHAUS, H.-B. & VARDOULAKIS, I. 1987 The thickness of shear bands in granular materials. Gétechnique 37, 271-283.
58. NATARAJAN, V., HUNT M. & TAYLOR, H. 1995 Local measurements of velocity fluctuations and diffusion coefficients for granular material flow. J. Fluid Mech. 304, 1-25.
59. NEDDERMAN, R. M. & LAOHAKUL, C. 1980 The thickness of the shear zone of flowing granular materials. Powder Technol. 25, 91-100.
60. ODA, M., NEMAT-NASSER, S. & KONISHI, J. 1985 Stress induced anisotropy in granular masses. Soils and Foundations 25, 85-97.
61. POULIQUEN, O. & GUTFRAIND, R. 1996 Stress fluctuations and shear zones in quasi-static granular chute flows. Phys. Rev. E 53, 552-561.
62. PRADEL, D. & LADE, P. V. 1990 Instability and plastic flow of soils. II: Analytical Investigation. J. Engng Mech., ASCE. 116, 2551-2566.
63. RICHMAN, M. W. 1988 Boundary conditions based upon a modified Maxwellian velocity distribution for flows of identical, smooth, nearly elastic, spheres. Acta Mechanica 75, 227-240.
64. RICHMAN, M. W. 1989 The source of second moment in dilute granular flows of highly inelastic spheres. J. Rheol. 33, 1293-1306.
65. RICHMAN, M. W. & CHOU, C. S. 1988 Boundary effects on granular shear flows of smooth disks. Math. Phys. Z. Angew. 39, 885-901.
66. RICHMAN, M. W. & CHOU, C. S. 1992 Constitutive theory for homogeneous granular shear flows of highly inelastic spheres. submitted to J. Rheol.
67. SAVAGE, S. B. 1979 Gravity flow of cohesionless granular materials in chutes and channels. J. Fluid Mech. 92, 53-96.
68. SAVAGE, S. B. 1983 Granular flows down rough inclines - review and extension. In Mechanics of Gramular Materials: New Models and Constitutive Relations (ed. J. T. Jenkins & M. Satake), pp. 261-82. Elsevier.
69. SAVAGE, S. B. 1984 The mechanics of rapid granular flows. Adv. Appl. Mech. 24, 289-366.
70. SAVAGE, S. B. 1992 Numerical simulation of Couette flow of granular materials; Spatio-temporal coherence and 1/f noise. In Physics of Granular Media (ed. D. Bideau & J. Dodds), pp. 343-362. Nova Scientific Publishers.
71. SAVAGE, S. B. 1995 Flow of granular materials. In Proc. 15th Canadian Congress of Applied Mechanics, CANCAM 95 (ed. B. Tabarrok & S. Dost), pp. 62-73. University of Victoria.
72. SAVAGE, S. B. & JEFFREY, D. J. 1981 The stress tensor in a granular flow at high shear rates. J. Fluid Mech. 110, 255-272.
73. SCHOFIELD, A. N. & WROTH, C. P. 1968 Critical State Soil Mechanics. McGraw-Hill.
74. SELA, N. & GOLDHIRSCH, I. 1998 Hydrodynamical equations for rapid flows of smooth inelastic spheres Burnett order. J. Fluid Mech. 361, 41-74.
75. SELA, N., GOLDHIRSCH, I. & NOSKOWICZ, S. H. 1996 Kinetic theoretical study of a two-dimensional granular gas to Burnett order. Phys. Fluids 8, 2337-2353.
76. SINCLAIR, J. L. & JACKSON, R. 1989 Gas-particle flow in a vertical pipe with particle-particle interactions. AIChE J. 35, 1473-1486.
77. SUNDARAM, V. & COWIN, S. C. 1979 A reassessment of static bin pressure experiments. Powder Technol. 22, 23-32.
78. TAKAHASHI, T. 1981 Debris flow. Ann. Rev. Fluid. Mech. 13, 57-77.
79. TAKAHASHI, T. 1991 Debris Flow. A. A. Balkema.
80. TAKAHASHI, H. & YANI, H. 1973 Flow profile and void fraction of granular solids in a moving bed. Powder Technol. 7, 205-214.
81. TSUBAKI, T. & HASHIMOTO, H. 1983 Interparticle stresses and characteristics of debris flows. J. Hydrosc. Hydr. Engng, 1, 67-82.
82. VARDOULAKIS, I. G. & SULEM, J. 1995 Bifurcation Analysis in Geomechanics. Chapman & Hall.
83. VERMEER, P. A. 1984 A five-constant model unifying well-established concepts. In Constitutive Relations for Soils (ed. G. Gudehus, F. Darve, & I. Vardoulakis), pp. 175-197. A. A. Balkema.
84. WALTON, O. R. & BRAUN, R. L. 1986a Stress calculations for assemblies of inelastic spheres in uniform shear. Acta Mechanica 63, 73-86.
85. WALTON, O. R. & BRAUN, R. L. 1986b Viscosity and temperature calculations for assemblies of inelastic frictional disks. J. Rheol. 30, 949-980.
86. WALTON, O. R., BRAUN, R. L., MALLON, R. G., & CERVELLI, D. M. 1987 Particle-dynamics calculations of gravity flow of inelastic, frictional spheres. In Micromechanics of Granular Materials (ed. M. Satake & J. T. Jenkins). pp. 153-162. Elsevier.
87. WOOD, D. M. 1990 Soil Behaviour and Critical State Soil Mechanics. Cambridge University Press.
88. WOODS, L. C. 1975 The Thermodynamics of Fluid Systems. Oxford University Press.
89. WOODS, L. C. 1993 A Introduction to the Kinetic Theory of Gases and Magnetoplasmas. Oxford University Press.