Mixing and segregation of granular materials

Annual Review of Fluid Mechanics

Volumn 32, Issue , 2000, Pages 55-91

  Ottino, J M ^a   Khakhar, D V ^b  

^a Northwestern University   (United States)

^b INDIAN INSTITUTE OF TECHNOLOGY BOMBAY   (India)

Author keywords

Chaos; Complex systems; Granular flow; Granular materials; Mixing

Indexed keywords

FLOW OF FLUIDS; MIXING; MONTE CARLO METHODS; SEPARATION;

FLOW-INDUCED SEGREGATION;

GRANULAR MATERIALS;

CHAOS; GRANULAR SOLID; MIXING; REVIEW; SEGREGATION; SOLID FLOW;

EID: 0034592314     PISSN: 00664189     EISSN: None     Source Type: Journal    
DOI: 10.1146/annurev.fluid.32.1.55     Document Type: Article

References (115)

1. Abdel-Ghani M, Petrie JG, Seville JPK, Clift R. 1991. Mechanical properties of cohesive particulate solids. Powder Technol. 65: 113-23
2. Adams MJ, Edmonson B. 1987. Forces between particles in continuous and discrete fluid media. In Tribology in Particulate Technology, ed. BJ Briscoe, MJ Adams, pp. 154-72. Philadelphia: Adam Hilger
3. Albert R, Albert I, Hornbaker D, Schiffer P, Barabasi A-L. 1997. The angle of repose in wet and dry granular media. Phys. Rev. E 56:R6371-76
4. Allen MP, Tildesley DJ. 1987. Computer Simulation of Liquids. Oxford, UK: Oxford Univ.
5. Alonzos M, Satoh M, Miyanami K. 1991. Optimum combination of size ratio, density ratio and concentration to minimize free surface segregation. Powder Technol. 68:145-52
6. Aref H. 1990. Chaotic advection of fluid particles. Philos. Trans. R. Soc. London Ser. A 333:273-88
7. Arnarson BÖ, Willits JT. 1998. Thermal diffusion in binary mixtures of smooth, nearly elastic spheres with and without gravity. Phys. Fluids 10:1324-1328
8. Bagnold RA. 1954. Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc. R. Soc. London Ser. A 255:49-63
9. Baumann G, Janosi IM, Wolf DE. 1995. Surface properties and flow of granular material in a two dimensional rotating drum, Phys. Rev. E 51:1879-88
10. Bird RB, Stewart WE, Lightfoot EN. 1960. Transport phenomena. New York: Wiley & Sons 780 pp.
11. Bocquet L, Charlaix E, Ciliberto S, Crassous J. 1998. Moisture-induced aging in granular media and the kinetics of capillary condensation. Nature 396:735-37
12. Boutreux T, de Gennes PG. 1996. Surface flows of granular mixtures. I. General principles and minimal model. J. Phys. I, France 6:1295-304
13. Bridgwater J. 1976. Fundamental powder mixing mechanisms. Powder Technol. 15:215-36
14. Bridgewater J. 1995. Particle technology. Chem. Eng. Sci. 50:4081-89
15. Bridgwater J, Cooke MH, Scott AM. 1978. Interparticle percolation: equipment development and mean percolation velocities. Trans. Inst. Chem. Eng. 56:157-67
16. Bridgwater J, Foo WS, Stephens DJ. 1985. Particle mixing and segregation in failure zones - theory and experiment. Powder Technol. 41:147-58
17. Brone D, Alexander A, Muzzio FJ. 1998. Quantitative characterization of mixing of dry powders in V-blenders, AIChE J. 44:271-78
18. Brone D, Wightman C, Connor K, Alexander A, Muzzio FJ, Robinson P. 1997. Using flow perturbations to enhance mixing of dry powders in V-blenders. Powder Technol. 91:165-72
19. Campbell CS. 1997. Self-diffusion in granular shear flows. J. Fluid Mech. 348:85-101
20. Cantalaube F, Bideau D. 1995. Radial segregation in a 2D drum: experimental analysis. Europhys. Lett. 30:133-38
21. Choo K, Molteno TCA, Morris SW. 1997. Travelling granular segregation patterns in a long drum mixer. Phys. Rev. Lett. 79:4994-97
22. Cleary PW, Metcalfe G, Liffman K. 1998. How well do discrete element granular flow models capture the essentials of mixing processes? Appl. Math. Model. 22:995-1008
23. Clément E, Rajchenbach J, Duran J. 1995. Mixing of a granular material in a bidimensional rotating drum. Europhys. Lett. 30:7-12
24. Cooke MH, Bridgwater J. 1979. Interparticle percolation: a statistical mechanical interpretation. I&EC Fundam. 18:25-27
25. Cundall PA, Strack DL. 1979. A discrete numerical model for granular assemblies. Géotechnique 29:47-65
26. Danckwerts PV. 1952. The definition and measurement of some characteristics of mixtures. Appl. Sci. Res. A 3:279-96
27. Das Gupta S, Bhatia SK, Khakhar DV. 1991. Axial segregation of particles in a horizontal rotating cylinder. Chem. Eng. Sci. 46:1513-17
28. de Haro ML, Cohen EGD, Kincaid JM. 1983. The Enskog theory for multicomponent mixtures. I. Linear transport theory. J. Chem. Phys. 78:2746-59
29. Dolgunin VN, Kudy AN, Ukolov AA. 1998. Development of the model of segregation of particles undergoing granular flow down an inclined plane. Powder Technol. 96:211-18
30. Dolgunin VN, Ukolov AA. 1995. Segregation modelling of particle rapid gravity flow. Powder Technol. 83:95-103
31. Donald MB, Roseman B. 1962. Mixing and demixing of solid particles. Part 1. Mechanisms in a horizontal drum mixer. Br. Chem. Eng. 7:749-52
32. Drahun JA, Bridgwater J. 1983. The mechanics of free surface segregation. Powder Technol. 36:39-53
33. Dury CM, Ristow GH. 1997. Radial segregation in a two-dimensional rotating drum. J. Phys. I, France 7:737-45
34. Elperin T, Vikhansky A. 1998a. Granular flow in a rotating cylindrical drum. Europhys. Lett. 42:619-23
35. Elperin T, Vikhansky A. 1998b. Kinematics of the mixing of granular materials in slowly rotating containers. Europhys. Lett. 43:17-22
36. Epstein IR, Showalter K. 1996. Nonlinear chemical dynamics: oscillations, patterns, and chaos. J. Phys. Chem. 100(31):13132-47
37. Fan LT, Chen YM, Lai FS. 1990. Recent developments in solids mixing. Powder Technol. 61:255-87
38. Fisher RA. 1926. On the capillary forces in an ideal soil. J. Agric. Sci. 16:491-505
39. Goldenfeld N, Kadanoff LP. 1999. Simple lessons from complexity. Science 284:87-89
40. Hehl M, Kroger H, Helmrich H, Schugerl K. 1978. Longitudinal mixing in horizontal drum reactors. Powder Technol. 20:29-37
41. Henein H, Brimacomble JK, Watkinson AP. 1983. Experimental study of transverse bed motion in rotary kilns. Metal. Trans. B 14:191-205
42. Hill KM, Kakalios J. 1995. Reversible axial segregation of rotating granular media. Phys. Rev. E 52:4393-400
43. Hill KM, Caprihan A, Kakalios J. 1997. Bulk segregation in a rotated granular material measured by magnetic resonance imaging. Phys. Rev. Lett. 78:50-53
44. Hill KM, Khakhar DV, Gilchrist JF, McCarthy JJ, Ottino JM. 1999a. Segregation-driven organization in chaotic granular flows. Proceedings of the National Academy of Sciences 96:11701-706
45. Hill KM, Gilchrist JF, Khakhar DV, McCarthy JJ, Ottino JM. 1999b. Mixing of granular materials: a test-bed dynamical system for pattern formation. Int. J. Bifurc. Chaos 9: 1467-84
46. Hirschfeld D, Rapaport DC. 1997. Molecular dynamics studies of grain segregation in a sheared flow. Phys. Rev. E 56:2012-18
47. Hirschfelder JO, Curtiss CF, Bird RB. 1954. Molecular Theory of Gases and Liquids. New York: Wiley & Sons 1219 pp.
48. Hogg R, Cahn DS, Healy TW, Fuerstenau DW. 1966. Diffusional mixing in an ideal system. Chem. Eng. Sci. 21:1025-38
49. Hogg R, Fuerstenau DW. 1972. Transverse mixing in rotating cylinders. Powder Technol. 6:139-48
50. Hornbaker D, Albert R, Albert I, Barabasi AL, Schieffer P. 1997. What keeps sandcastles standing. Nature 387:765-67
51. Hsiau SS, Hunt ML. 1996. Granular thermal diffusion in flows of binary-sized mixtures. Acta Mech. 114:121-37
52. Inoue I, Yamaguchi K, Sato K. 1970. Motion of a particle and mixing process in a horizontal drum mixer, Kagaku Kogaku 34:1323-30
53. Jackson R. 1986. Some features of the flow of granular materials and aerated granular materials. J. Rheol. 30:907-30
54. Jaeger HM, Nagel SR. 1992. The physics of the granular state. Science 255:1523-31
55. Jaeger HM, Nagel SR, Behringer RP. 1996a. Granular solids, liquids, and glasses. Rev. Mod. Phys. 68:1259-73
56. Jaeger HM, Nagel SR, Behringer RP. 1996b. The physics of granular materials. Phys. Today 49:32-38
57. Jenkins JT, Mancini F. 1989. Kinetic theory for binary mixtures of smooth, nearly elastic spheres. Phys. Fluids A 1:2050-57
58. Johanson JR. 1978. Particle segregation and what to do about it. Chem. Eng. 85:183-88
59. Johnson PC, Jackson R. 1987. Frictional-collisional constitutive relations for granular materials, with application to plane shearing. J. Fluid Mech. 176:67-93
60. Julien R, Meakin P. 1990. A mechanism for particle size segregation in three dimensions. Nature 344:425-27
61. Khakhar DV, McCarthy JJ, Gilchrist JF, Ottino JM. 1999a. Chaotic mixing of granular materials in 2D tumbling mixers. CHAOS 9:195-205
62. Khakhar DV, McCarthy JJ, Ottino JM. 1999b. Mixing and segregation of granular materials in chute flows. CHAOS 9:594-610
63. Khakhar DV, McCarthy JJ, Ottino JM. 1997a. Radial segregation of materials in rotating cylinders. Phys. Fluids 9:3600-14
64. Khakhar DV, McCarthy JJ, Shinbrot T, Ottino JM. 1997b. Transverse flow and mixing of granular materials in a rotating cylinder. Phys. Fluids 9:31-43
65. Knight JB, Jaeger HM, Nagel SR. 1993. Vibration induced granular segregation in granular media: the convection connection. Phys. Rev. Lett. 70:3728-31
66. Kincaid JM, Cohen EGD, de Haro ML. 1987. The Enskog theory for multicomponent mixtures. IV. Thermal diffusion. J. Chem. Phys. 86:963-75
67. Koeppe JP, Enz M, Kakalios J. 1998. Phase diagram for avalanche stratification of granular media. Phys. Rev. E 58:R4104
68. Lacey PM. 1954. Developments in the theory of particle mixing. J. Appl. Chem. 4:257-68
69. Lehmberg J, Hehl M, Schugerl K. 1977. Transverse mixing and heat transfer in horizontal rotary drum reactors. Powder Technol. 18:149-63
70. Levitan B. 1998. Segregation and coarsening of a granular mixture in a rotating tube. Physica A 249:386-90
71. Lian G, Thornton C, Adams MJ. 1993. A theoretical study of liquid bridge forces between two rigid spherical bodies. J. Colloid Int. Sci. 161:138-47
72. Lian G, Thornton C, Adams MJ. 1998. Discrete particle simulation of agglomerate impact coalescence. Chem. Eng. Sci. 53:3381-91
73. 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
74. Makse HA, Havlin S, King PR, Stanley HE. 1997. Spontaneous stratification in granular mixtures. Nature 386:379-81
75. McCarthy JJ. 1998. Mixing, segregation, and flow of granular materials. PhD thesis. Evanston, Ill: Northwestern Univ.
76. McCarthy JJ, Ottino JM. 1997. Particle dynamics simulation: a hybrid technique applied to granular mixing. Powder Technol. 97:91-99
77. McCarthy JJ, Ottino JM. 1998. A computational study of granular mixing: the effect of particle cohesion. Proceedings of the Topical Conference on Advanced Technologies for Particle Processing, Amer. Inst. Chem. Eng. Annual Meeting, Miami Beach, FL. 552-58
78. McCarthy JJ, Shinbrot T, Metcalfe G, Wolf JE, Ottino JM. 1996. Mixing of granular materials in slowly rotated containers. AIChE J. 42:3351-63
79. Meloy TP, Mani BP, Clark NN. 1986. Particle shape analysis and separation techniques: a critical review. J. Powder Bulk Solids Technol. 10:15-20
80. Metcalfe G, Shattuck M. 1996. Pattern formation during mixing and segregation of flowing granular materials. Physica A 233:709-17
81. Metcalfe G, Shinbrot T, McCarthy JJ, Ottino JM. 1995. Avalanche mixing of granular solids. Nature 374:39-41
82. Mindlin RD. 1949. Compliance of elastic bodies in contact. J. Appl. Mech. 16:256-70
83. Muzzio FJ, Robinson P, Wightman C, Brone D. 1997. Sampling practices in powder blending. Int. J. Pharm. 155:153-78
84. Nakagawa M. 1994. Axial segregation of granular flows in a horizontal rotating cylinder. Chem. Eng. Sci. 49:2540-44
85. Nakagawa M, Altobelli, SA, Caprihan A, Fukushima E, Jeong EK. 1993. Non-invasive measurements of granular flows by magnetic resonance imaging. Exp. Fluids. 16:54-60
86. Nienow AW, Edwards MF, Harnby N. 1985. In Mixing in the Process Industries, ed. N Harnby, MF Edwards, AW Nienow, p. 1. London: Butterworths.
87. Nityanand N, Manley B, Henein H. 1986. An analysis of radial segregation for different sized spherical solids in rotary cylinders. Metal. Trans. B 17:247-57
88. Onuki A. 1997. Phase transitions of fluids in shear flow. J. Phys-Condens. Matter 9:6119-57
89. Ottino JM. 1989. The kinematics of mixing: stretching, chaos, and transport. Cambridge, UK: Cambridge Univ. Press
90. Ottino JM. 1990. Mixing, chaotic advection, and turbulence. Annu. Rev. Fluid Mech. 22:207-54
91. Ottino JM, Shinbrot T. 1999. Comparing extremes: mixing of fluids, mixing of solids. In Mixing: Chaos and Turbulence, ed. H. Chaté, E Villermaux, J-M Chomaz, pp. 163-86. NATO Sci. Ser. New York: Kluwer Acad./Plenum
92. Pierrat P, Caram HS. 1997. Tensile strength of wet granular materials. Powder Technol. 91:83-93
93. Polhausen E. 1921. Zur näherungsweisen Intergration der Differentialgleichung der laminaren Grenzschicht. Z. Angewal Mathemat. Mechan. 1:115-21
94. Poux M, Fayolle P, Bertrand J, Bridoux D, Bousquet J. 1991. Powder mixing: some practical rules applied to agitated systems. Powder Technol. 68:213-34
95. Prigozhin L, Kalman H. 1998. Radial mixing and segregation of a binary mixture in a rotating drum: model and experiment. Phys. Rev. E 57:2073-80
96. Rajchenbach J. 1990. Flow in powders: from discrete avalanches to continuous regime. Phys. Rev. Lett. 65:2221-24
97. Rajchenbach J, Clement E, Duran J. 1995. Experiments in model granular media: a study of gravity flows. In Fractal Aspects of Materials, ed. F Family, P Meakin, B Sapoval, R Wool, p. 525. Pittsburgh: MRS Symp.
98. Rao SJ, Bhatia SK, Khakhar DV. 1991. Axial transport of granular solids in rotating cylinders. Part 2. Experiments in a non-flow system. Powder Technol. 67:153-62
99. Ristow GH. 1994. Particle mass segregation in a two-dimensional rotating drum. Europhys. Lett. 28:97-101
100. Rosato A, ed. 1999. Segregation in Granular Flows. IUTAM Symp., June 5-10, Cape May, NJ. Dordrecht, The Netherlands: Kluwer
101. Rosato A, Prinze F, Standburg KJ, Svendsen R. 1987. Why Brazil nuts are on top: size segregation of particulate matter by shaking. Phys. Rev. Lett. 58:1038-40
102. Savage SB. 1993. Disorder, diffusion and structure formation in granular flow. In Disorder and Granular Media, ed. D. Bideau, A Hansen, pp. 255-85. Amsterdam: Elsevier
103. Savage SB, Lun CKK. 1988. Particle size segregation in inclined chute flow of cohesionless granular slids. J. Fluid Mech. 189:311-35
104. Schafer J, Dippel S, Wolf DE. 1996. Force schemes in simulation of granular materials. J. Physique I 6:5-20
105. Scott AM, Bridgwater J. 1976. Self-diffusion of spherical particles in a simple shear apparatus. Powder Technol. 14:177-83
106. Shinbrot T, Alexander AW, Muzzio FJ. 1999. Spontaneous chaotic mixing. Nature 397:675-78
107. Thornton C, Yin KK, Adams MJ. 1996. Numerical simulation of the impact fracture and fragmentation of agglomerates. J. Phys. D 29:424-35
108. Wagner AJ, Yeomans JM. 1998. Breakdown of scale invariance in the coarsening of phase separating binary fluids. Phys. Rev. Lett. 80:1429-32
109. Walton OR. 1993. Numerical simulation of inclined chute flows of monodisperse, inelastic, frictional spheres. Mech. Mater. 16:239-47
110. Wes GWJ, Drinkenburg AAH, Stemerding S. 1976. Solids mixing and residence time distributions in a horizontal rotary drum reactor. Powder Technol. 13:177-84
111. Wightman C, Muzzio FJ. 1998a. Mixing of granular material in a drum mixer undergoing rotational and rocking motions. I. Uniform particles. Powder Technol. 98:113-24
112. Wightman C, Muzzio FJ. 1998b. Mixing of granular material in a drum mixer undergoing rotational and rocking motions. II. Segregating particles. Powder Technol. 98:125-34
113. Williams JC. 1963. The segregation of powders and granular materials. Fuel Soc. J. 14:29-34
114. Williams JC. 1976. The segregation of particulate materials: a review. Powder Technol. 15:246-51
115. Zik O, Levine D, Lipson SG, Shtrikman S, Stavans J. 1994. Rotationally induced segregation of granular materials. Phys. Rev. Lett. 73:644-47