1932

Abstract

Accurate continuum models of flow and segregation of dense granular flows are now possible. This is the result of extensive comparisons, over the last several years, of computer simulations of increasing accuracy and scale, experiments, and continuum models, in a variety of flows and for a variety of mixtures. Computer simulations—discrete element methods (DEM)—yield remarkably detailed views of granular flow and segregation. Conti-nuum models, however, offer the best possibility for parametric studies of outcomes in what could be a prohibitively large space resulting from the competition between three distinct driving mechanisms: advection, diffusion, and segregation. We present a continuum transport equation–based framework, informed by phenomenological constitutive equations, that accurately predicts segregation in many settings, both industrial and natural. Three-way comparisons among experiments, DEM, and theory are offered wherever possible to validate the approach. In addition to the flows and mixtures described here, many straightforward extensions of the framework appear possible.

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2019-06-07
2024-06-19
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Literature Cited

  1. 1.
    Ottino JM, Khakhar DV 2000. Mixing and segregation of granular materials. Annu. Rev. Fluid Mech. 32:55–91
    [Google Scholar]
  2. 2.
    Makse HA, Havlin S, King PR, Stanley HE 1997. Spontaneous stratification in granular mixtures. Nature 386:379–82
    [Google Scholar]
  3. 3.
    Pereira GG, Cleary PW 2017. Segregation due to particle shape of a granular mixture in a slowly rotating tumbler. Granul. Matter 19:23
    [Google Scholar]
  4. 4.
    Zhao Y, Xiao H, Umbanhowar PB, Lueptow RM 2017. Simulation and modeling of segregating rods in quasi-2D bounded heap flow. AIChE J. 64:1550–63
    [Google Scholar]
  5. 5.
    Tripathi A, Khakhar DV 2013. Density difference-driven segregation in a dense granular flow. J. Fluid. Mech. 717:643–69
    [Google Scholar]
  6. 6.
    Gillemot KA, Somfai E, Börzsönyi T 2017. Shear-driven segregation of dry granular materials with different friction coefficients. Soft Matter 13:415–20
    [Google Scholar]
  7. 7.
    Wornyoh EA, Jasti VK, Higgs CF III 2007. A review of dry particulate lubrication: powder and granular materials. ASME J. Tribol. 129:438–49
    [Google Scholar]
  8. 8.
    Fan Y, Jacob KV, Freireich B, Lueptow RM 2017. Segregation of granular materials in bounded heap flow: a review. Powder Technol. 312:67–88
    [Google Scholar]
  9. 9.
    Arndt T, Brucks A, Ottino JM, Lueptow RM 2006. Creeping granular motion under variable gravity levels. Phys. Rev. E 74:031307
    [Google Scholar]
  10. 10.
    Kudrolli A 2004. Size separation in vibrated granular matter. Rep. Prog. Phys. 67:209–47
    [Google Scholar]
  11. 11.
    Iverson RM 1997. The physics of debris flows. Rev. Geophys. 35:245–96
    [Google Scholar]
  12. 12.
    Gray JMNT, Hutter K 1997. Pattern formation in granular avalanches. Continuum Mech. Therm. 9:341–45
    [Google Scholar]
  13. 13.
    Jaeger HM, Nagel SR, Behringer RP 1996. Granular solids, liquids, and gases. Rev. Mod. Phys. 68:1259
    [Google Scholar]
  14. 14.
    Forterre Y, Pouliquen O 2008. Flows of dense granular media. Annu. Rev. Fluid Mech. 40:1–24
    [Google Scholar]
  15. 15.
    Duran J 2000.Sands, Powders, and Grains: An Introduction to the Physics of Granular Materials Berlin: Springer
  16. 16.
    Ennis BJ, Green J, Davies R 1994. Legacy of neglect in the United States. Chem. Eng. Prog. 90:32–43
    [Google Scholar]
  17. 17.
    Cundall P, Strack O 1979. Discrete numerical model for granular assemblies. Géotechnique 29:47–65
    [Google Scholar]
  18. 18.
    Walther JH, Sbalzarini IF 2009. Large-scale parallel discrete element simulations of granular flow. Eng. Comput. 26:688–97
    [Google Scholar]
  19. 19.
    Windows-Yule CRK, Tunuguntla DR, Parker DJ 2016. Numerical modelling of granular flows: a reality check. Comput. Part. Mech. 3:311–32
    [Google Scholar]
  20. 20.
    William JC 1976. The segregation of particulate materials. A review. Powder Technol. 15:245–51
    [Google Scholar]
  21. 21.
    Gray JMNT 2018. Particle segregation in dense granular flows. Annu. Rev. Fluid Mech. 50:407–33
    [Google Scholar]
  22. 22.
    Fan Y, Boukerkour Y, Blanc T, Umbanhowar PB, Ottino JM, Lueptow RM 2012. Stratification, segregation, and mixing of granular materials in quasi-two-dimensional bounded heaps. Phys. Rev. E 86:051305
    [Google Scholar]
  23. 23.
    Baxter J, Tuzun U, Heyes D, Hayati I, Fredlund P 1998. Stratification in poured granular heaps. Nature 391:136
    [Google Scholar]
  24. 24.
    Lecocq N, Vandewalle N 2000. Stripes ordering in self-stratification experiments of binary and ternary granular mixtures. Phys. Rev. E 62:8241–44
    [Google Scholar]
  25. 25.
    Alder BJ, Wainwright TE 1957. Phase transition for a hard sphere system. J. Chem. Phys. 27:1208–9
    [Google Scholar]
  26. 26.
    Hill KM, Fan Y 2016. Granular temperature and segregation in dense sheared particulate mixtures. KONA Powder Part. J. 33:150–68
    [Google Scholar]
  27. 27.
    Woodhouse MJ, Thornton AR, Johnson CG, Kokelaar BP, Gray JMNT 2012. Segregation-induced fingering instabilities in granular free-surface flows. J. Fluid. Mech. 709:543–80
    [Google Scholar]
  28. 28.
    Savage S, Lun C 1988. Particle size segregation in inclined chute flow of dry cohesionless granular solids. J. Fluid. Mech. 189:311–35
    [Google Scholar]
  29. 29.
    Dolgunin V, Ukolov A 1995. Segregation modeling of particle rapid gravity flow. Powder Technol. 83:95–103
    [Google Scholar]
  30. 30.
    Dolgunin V, Kudy A, Ukolov A 1998. Development of the model of segregation of particles undergoing granular flow down an inclined chute. Powder Technol. 96:211–18
    [Google Scholar]
  31. 31.
    Gray JMNT, Chugunov VA 2006. Particle-size segregation and diffusive remixing in shallow granular avalanches. J. Fluid. Mech. 569:365–98
    [Google Scholar]
  32. 32.
    Gray JMNT, Ancey C 2011. Multi-component particle-size segregation in shallow granular avalanches. J. Fluid. Mech. 678:535–88
    [Google Scholar]
  33. 33.
    Fan Y, Schlick CP, Umbanhowar PB, Ottino JM, Lueptow RM 2014. Modelling size segregation of granular materials: the roles of segregation, advection and diffusion. J. Fluid. Mech. 741:252–79
    [Google Scholar]
  34. 34.
    Fan Y, Umbanhowar PB, Ottino JM, Lueptow RM 2013. Kinematics of monodisperse and bidisperse granular flows in quasi-two-dimensional bounded heaps. Proc. R. Soc. A 469:20130235
    [Google Scholar]
  35. 35.
    Xiao H, Umbanhowar PB, Ottino JM, Lueptow RM 2016. Modelling density segregation in flowing bidisperse granular materials. Proc. R. Soc. A 472:20150856
    [Google Scholar]
  36. 36.
    Pignatel F, Asselin C, Krieger L, Christov IC, Ottino JM, Lueptow RM 2012. Parameters and scalings for dry and immersed granular flowing layers in rotating tumblers. Phys. Rev. E 86:011304
    [Google Scholar]
  37. 37.
    Deng Z, Umbanhowar PB, Ottino JM, Lueptow RM 2018. Continuum modelling of segregating tridisperse granular chute flow. Proc. R. Soc. A 474:20170384
    [Google Scholar]
  38. 38.
    Christov IC, Lueptow RM, Ottino JM, Sturman R 2014. A study in three-dimensional chaotic dynamics: granular flow and transport in a bi-axial spherical tumbler. SIAM J. Appl. Dyn. Syst. 13:901–43
    [Google Scholar]
  39. 39.
    Midi GDR 2004. On dense granular flows. Eur. Phys. J. E 14:341–65
    [Google Scholar]
  40. 40.
    Henann DL, Kamrin K 2013. A predictive, size-dependent continuum model for dense granular flows. PNAS 110:6730–35
    [Google Scholar]
  41. 41.
    Pouliquen O, Cassar C, Jop P, Forterre Y, Nicolas M 2006. Flow of dense granular material: towards simple constitutive laws. J. Stat. Mech. Theory Exp. 2006:P07020
    [Google Scholar]
  42. 42.
    Jop P, Forterre Y, Pouliquen O 2006. A constitutive law for dense granular flows. Nature 441:727–30
    [Google Scholar]
  43. 43.
    Chauchat J, Médale M 2014. A three-dimensional numerical model for dense granular flows based on the rheology. J. Comput. Phys. 256:696–712
    [Google Scholar]
  44. 44.
    Savage S, Dai R 1993. Studies of granular shear flows. Wall slip velocities, ‘layering’ and self-diffusion. Mech. Mater. 16:225–38
    [Google Scholar]
  45. 45.
    Hsiau S, Hunt M 1993. Kinetic theory analysis of flow-induced particle diffusion and thermal conduction in granular material flows. J. Heat Transf. 115:541–48
    [Google Scholar]
  46. 46.
    Bridgwater J 1980. Self-diffusion coefficients in deforming powders. Powder Technol. 25:129–31
    [Google Scholar]
  47. 47.
    Natarajan V, Hunt M, Taylor E 1995. Local measurements of velocity fluctuations and diffusion coefficients for a granular material flow. J. Fluid. Mech. 304:1–25
    [Google Scholar]
  48. 48.
    Utter B, Behringer R 2004. Self-diffusion in dense granular shear flows. Phys. Rev. E 69:031308
    [Google Scholar]
  49. 49.
    Katsuragi H, Abate A, Durian D 2010. Jamming and growth of dynamical heterogeneities versus depth for granular heap flow. Soft Matter 6:3023–29
    [Google Scholar]
  50. 50.
    Fry AM, Umbanhowar PB, Ottino JM, Lueptow RM 2019. Diffusion, mixing, and segregation in confined granular flows. AIChE J 65875–81
    [Google Scholar]
  51. 51.
    Gray JMNT, Edwards AN 2014. A depth-averaged -rheology for shallow granular free-surface flows. J. Fluid. Mech. 755:503–34
    [Google Scholar]
  52. 52.
    Fan Y, Umbanhowar PB, Ottino JM, Lueptow RM 2015. Shear-rate-independent diffusion in granular flows. Phys. Rev. Lett. 115:088001
    [Google Scholar]
  53. 53.
    Bridgwater J 1994. Mixing and segregation mechanisms in particle flow. Granular Matter: An Interdisciplinary Approach A Mehta161–93 Berlin: Springer
    [Google Scholar]
  54. 54.
    Khola N, Wassgren C 2016. Correlations for shear-induced percolation segregation in granular shear flows. Powder Technol. 288:441–52
    [Google Scholar]
  55. 55.
    Komatsu T, Inagaki S, Nakagawa N, Nasuno S 2001. Creep motion in a granular pile exhibiting steady surface flow. Phys. Rev. Lett. 86:1757–60
    [Google Scholar]
  56. 56.
    Socie BA, Umbanhowar P, Lueptow RM, Jain N, Ottino JM 2005. Creeping motion in granular flow. Phys. Rev. E 71:031304
    [Google Scholar]
  57. 57.
    Chen K, Cole J, Conger C, Draskovic J, Lohr M et al. 2006. Granular materials: packing grains by thermal cycling. Nature 442:257
    [Google Scholar]
  58. 58.
    Bridgwater J, Cooke MH, Scott AM 1978. Interparticle percolation: equipment development and mean percolation velocities. Trans. Inst. Chem. Eng. 56:157–67
    [Google Scholar]
  59. 59.
    Guillard F, Forterre Y, Pouliquen O 2016. Scaling laws for segregation forces in dense sheared granular flows. J. Fluid. Mech. 807:R1
    [Google Scholar]
  60. 60.
    Liu S, McCarthy JJ 2017. Transport analogy for segregation and granular rheology. Phys. Rev. E 96:020901
    [Google Scholar]
  61. 61.
    van der Vaart K, van Schrojenstein Lantman MP, Weinhart T, Luding S, Ancey C, Thornton AR 2018. Segregation of large particles in dense granular flows suggests a granular Saffman effect. Phys. Rev. Fluids 3:074303
    [Google Scholar]
  62. 62.
    Bell N, Yu Y, Mucha PJ 2005. Particle-based simulation of granular materials. Proceedings of the 2005 ACM SIGGRAPH/Eurographics Symposium on Computer Animation77–86 New York: ACM
    [Google Scholar]
  63. 63.
    Luding S 2008. Introduction to discrete element methods. Eur. J. Environ. Civ. Eng. 12:785–826
    [Google Scholar]
  64. 64.
    Guo Y, Curtis JS 2015. Discrete element method simulations for complex granular flows. Annu. Rev. Fluid Mech. 47:21–46
    [Google Scholar]
  65. 65.
    Thornton A, Weinhart T, Luding S, Bokhove O 2012. Modeling of particle size segregation: calibration using the discrete particle method. Int. J. Mod. Phys. C 23:1240014
    [Google Scholar]
  66. 66.
    Schlick CP, Fan Y, Isner AB, Umbanhowar PB, Ottino JM, Lueptow RM 2015. Modeling segregation of bidisperse granular materials using physical control parameters in the quasi-2D bounded heap. AIChE J. 61:1524–34
    [Google Scholar]
  67. 67.
    Jones RP, Isner AB, Xiao H, Ottino JM, Umbanhowar PB, Lueptow RM 2018. Asymmetric concentration dependence of segregation fluxes in granular flows. Phys. Rev. Fluids 3:094304
    [Google Scholar]
  68. 68.
    Weinhart T, Hartkamp R, Thornton AR, Luding S 2013. Coarse-grained local and objective continuum description of three-dimensional granular flows down an inclined surface. Phys. Fluids 25:070605
    [Google Scholar]
  69. 69.
    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
    [Google Scholar]
  70. 70.
    Isner AB 2017. A quantitative study of size segregation in free surface granular flows. PhD Thesis, Northwestern Univ., Evanston, IL
    [Google Scholar]
  71. 71.
    Gray JMNT, Thornton AR 2005. A theory for particle size segregation in shallow granular free-surface flows. Proc. R. Soc. A 461:1447–73
    [Google Scholar]
  72. 72.
    Hill KM, Tan DS 2014. Segregation in dense sheared flows: gravity, temperature gradients, and stress partitioning. J. Fluid. Mech. 756:54–88
    [Google Scholar]
  73. 73.
    van der Vaart K, Gajjar P, Epely-Chauvin G, Andreini N, Gray JMNT, Ancey C 2015. Underlying asymmetry within particle size segregation. Phys. Rev. Lett. 114:238001
    [Google Scholar]
  74. 74.
    Hajra SK, Shi D, McCarthy J 2012. Granular mixing and segregation in zigzag chute flow. Phys. Rev. E 86:061318
    [Google Scholar]
  75. 75.
    Gajjar P, Gray JMNT 2014. Asymmetric flux models for particle-size segregation in granular avalanches. J. Fluid. Mech. 757:297–329
    [Google Scholar]
  76. 76.
    Cooke MH, Bridgwater J 1979. Interparticle percolation: a statistical mechanical interpretation. Ind. Eng. Chem. Fund. 18:25–27
    [Google Scholar]
  77. 77.
    Hill KM, Fan Y 2008. Isolating segregation mechanisms in a split-bottom cell. Phys. Rev. Lett. 101:088001
    [Google Scholar]
  78. 78.
    Golick LA, Daniels KE 2009. Mixing and segregation rates in sheared granular materials. Phys. Rev. E 80:042301
    [Google Scholar]
  79. 79.
    Fry AM, Umbanhowar PB, Ottino JM, Lueptow RM 2018. Effect of pressure on segregation in granular shear flows. Phys. Rev. E 97:062906
    [Google Scholar]
  80. 80.
    Schlick CP, Isner AB, Freireich BJ, Fan Y, Umbanhowar PB et al. 2016. A continuum approach for predicting segregation in flowing polydisperse granular materials. J. Fluid. Mech. 797:95–109
    [Google Scholar]
  81. 81.
    Marks B, Rognon P, Einav I 2012. Grainsize dynamics of polydisperse granular segregation down inclined planes. J. Fluid. Mech. 690:499–511
    [Google Scholar]
  82. 82.
    Marks B, Einav I 2015. A mixture of crushing and segregation: the complexity of grainsize in natural granular flows. Geophys. Res. Lett. 42:274–81
    [Google Scholar]
  83. 83.
    Deng Z, Umbanhowar PB, Ottino JM, Lueptow RM 2019. Modeling segregation of polydisperse granular materials in developing and transient free-surface flows. AIChE J. 65:882–93
    [Google Scholar]
  84. 84.
    Lueptow RM, Deng Z, Xiao H, Umbanhowar PB 2017. Modeling segregation in modulated granular flow. EPJ Web Conf. 140:03018
    [Google Scholar]
  85. 85.
    Jain N, Ottino JM, Lueptow RM 2005. Combined size and density segregation and mixing in noncircular tumblers. Phys. Rev. E 71:051301
    [Google Scholar]
  86. 86.
    Liao C, Hsiau S, Nien H 2014. Density-driven spontaneous streak segregation patterns in a thin rotating drum. Phys. Rev. E 89:062204
    [Google Scholar]
  87. 87.
    Liao C, Hsiau S, Nien H 2015. Effects of density ratio, rotation speed, and fill level on density-induced granular streak segregation in a rotating drum. Powder Technol. 284:514–20
    [Google Scholar]
  88. 88.
    Tunuguntla DR, Bokhove O, Thornton AR 2014. A mixture theory for size and density segregation in shallow granular free-surface flows. J. Fluid. Mech. 749:99–112
    [Google Scholar]
  89. 89.
    Fan Y, Hill K 2015. Shear-induced segregation of particles by material density. Phys. Rev. E 92:022211
    [Google Scholar]
  90. 90.
    Pouliquen O 1999. Scaling laws in granular flows down rough inclined planes. Phys. Fluids 11:542–48
    [Google Scholar]
  91. 91.
    Savage SB 1979. Gravity flow of cohesionless granular materials in chutes and channels. J. Fluid. Mech. 92:53–96
    [Google Scholar]
  92. 92.
    Khakhar DV, McCarthy JJ, Ottino JM 1999. Mixing and segregation of granular materials in chute flows. Chaos 9:594–610
    [Google Scholar]
  93. 93.
    Silbert LE, Ertaş 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
    [Google Scholar]
  94. 94.
    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
    [Google Scholar]
  95. 95.
    Schlick CP, Isner AB, Umbanhowar PB, Lueptow RM, Ottino JM 2015. On mixing and segregation: from fluids and maps to granular solids and advection–diffusion systems. Ind. Eng. Chem. Res. 54:10465–71
    [Google Scholar]
  96. 96.
    Wiederseiner S, Andreini N, Épely Chauvin G, Moser G, Monnereau M et al. 2011. Experimental investigation into segregating granular flows down chutes. Phys. Fluids 23:013301
    [Google Scholar]
  97. 97.
    Khakhar DV, McCarthy JJ, Ottino JM 1997. Radial segregation of granular mixtures in rotating cylinders. Phys. Fluids 9:3600–14
    [Google Scholar]
  98. 98.
    Mellmann J 2001. The transverse motion of solids in rotating cylinders—forms of motion and transition behavior. Powder Technol. 118:251–70
    [Google Scholar]
  99. 99.
    Meier SW, Lueptow RM, Ottino JM 2007. A dynamical systems approach to mixing and segregation of granular materials in tumblers. Adv. Phys. 56:757–827
    [Google Scholar]
  100. 100.
    Schlick CP, Fan Y, Umbanhowar PB, Ottino JM, Lueptow RM 2015. Granular segregation in circular tumblers: theoretical model and scaling laws. J. Fluid. Mech. 765:632–52
    [Google Scholar]
  101. 101.
    Fiedor SJ, Ottino JM 2005. Mixing and segregation of granular matter: multi-lobe formation in time-periodic flows. J. Fluid. Mech. 533:223–36
    [Google Scholar]
  102. 102.
    Hill KM, Khakhar DV, Gilchrist JF, McCarthy JJ, Ottino JM 1999. Segregation-driven organization in chaotic granular flows. PNAS 96:11701–6
    [Google Scholar]
  103. 103.
    Meier SW, Cisar SE, Lueptow RM, Ottino JM 2006. Capturing patterns and symmetries in chaotic granular flow. Phys. Rev. E 74:031310
    [Google Scholar]
  104. 104.
    Zaman Z, Yu M, Park PP, Ottino JM, Lueptow RM, Umbanhowar PB 2018. Persistent structures in a three-dimensional dynamical system with flowing and non-flowing regions. Nat. Commun. 9:3122
    [Google Scholar]
  105. 105.
    Yu M, Umbanhowar PB, Ottino JM, Lueptow RM 2018. Segregation patterns in a fully-3D granular flow. arXiv:1901.02988 [cond-mat]
    [Google Scholar]
  106. 106.
    Samadani A, Kudrolli A 2000. Segregation transitions in wet granular matter. Phys. Rev. Lett. 85:5102–5
    [Google Scholar]
  107. 107.
    Li H, McCarthy JJ 2003. Controlling cohesive particle mixing and segregation. Phys. Rev. Lett. 90:184301
    [Google Scholar]
  108. 108.
    Liao CC, Hsiau SS, Tsai TH, Tai CH 2010. Segregation to mixing in wet granular matter under vibration. Chem. Eng. Sci. 65:1109–16
    [Google Scholar]
  109. 109.
    Liu P, Yang R, Yu A 2013. The effect of liquids on radial segregation of granular mixtures in rotating drums. Granul. Matter 15:427–36
    [Google Scholar]
  110. 110.
    Xiao H, Hruska J, Ottino JM, Lueptow RM, Umbanhowar PB 2018. Unsteady flows and inhomogeneous packing in damp granular heap flows. Phys. Rev. E 98:032906
    [Google Scholar]
  111. 111.
    Herminghaus S 2013.Wet Granular Matter: A Truly Complex Fluid Singapore: World Sci.
  112. 112.
    Guazzelli E, Pouliquen O 2018. Rheology of dense granular suspensions. J. Fluid. Mech. 852:P1
    [Google Scholar]
  113. 113.
    Fiedor SJ, Umbanhowar P, Ottino JM 2007. Effects of fluid viscosity on band segregation dynamics in bidisperse granular slurries. Phys. Rev. E 76:041303
    [Google Scholar]
  114. 114.
    Freireich B, Fan Y, Jacob K 2017. Segregation of fragile granular materials Paper presented at the 2017 Meeting of the American Institute of Chemical Engineers, Minneapolis
    [Google Scholar]
  115. 115.
    Larcher M, Jenkins JT 2015. The evolution of segregation in dense inclined flows of binary mixtures of spheres. J. Fluid. Mech. 782:405–29
    [Google Scholar]
  116. 116.
    Oyama Y 1939. The motion of binary particle in a horizontally rotating tube. Bull. Inst. Phys. Chem. Res. Jpn. Rep. 18:600–39
    [Google Scholar]
  117. 117.
    Zik O, Levine D, Lipson S, Shtrikman S, Stavans J 1994. Rotationally induced segregation of granular materials. Phys. Rev. Lett. 73:644–47
    [Google Scholar]
  118. 118.
    Hill K, Kakalios J 1995. Reversible axial segregation of rotating granular media. Phys. Rev. E 52:4393–400
    [Google Scholar]
  119. 119.
    Fiedor S, Ottino J 2003. Dynamics of axial segregation and coarsening of dry granular materials and slurries in circular and square tubes. Phys. Rev. Lett. 91:244301
    [Google Scholar]
  120. 120.
    Finger T, Voigt A, Stadler J, Niessen HG, Naji L, Stannarius R 2006. Coarsening of axial segregation patterns of slurries in a horizontally rotating drum. Phys. Rev. E 74:031312
    [Google Scholar]
  121. 121.
    Chen P, Lochman BJ, Ottino JM, Lueptow RM 2009. Inversion of band patterns in spherical tumblers. Phys. Rev. Lett. 102:148001
    [Google Scholar]
  122. 122.
    Pohlman NA, Meier SW, Lueptow RM, Ottino JM 2006. Surface velocity in three-dimensional granular tumblers. J. Fluid Mech. 560:355–68
    [Google Scholar]
  123. 123.
    Zaman Z, D'Ortona U, Umbanhowar PB, Ottino JM, Lueptow RM 2013. Slow axial drift in three-dimensional granular tumbler flow. Phys. Rev. E 88:012208
    [Google Scholar]
  124. 124.
    Xiao H, Fan Y, Jacob KV, Umbanhowar PB, Kodam M et al. 2019. Continuum modeling of granular segregation during hopper discharge. Chem. Eng. Sci. 193:188–204
    [Google Scholar]
  125. 125.
    Fan Y, Hill KM 2010. Shear-driven segregation of dense granular mixtures in a split-bottom cell. Phys. Rev. E 81:041303
    [Google Scholar]
  126. 126.
    Fan Y, Hill KM 2011. Theory for shear-induced segregation of dense granular mixtures. New J. Phys. 13:095009
    [Google Scholar]
  127. 127.
    Fan Y, Hill KM 2011. Phase transitions in shear-induced segregation of granular materials. Phys. Rev. Lett. 106:218301
    [Google Scholar]
  128. 128.
    Fan Y, Hill KM 2015. Shear-induced segregation of particles by material density. Phys. Rev. E 92:022211
    [Google Scholar]
  129. 129.
    Windows-Yule C, Scheper B, van der Horn A, Hainsworth N, Saunders J et al. 2016. Understanding and exploiting competing segregation mechanisms in horizontally rotated granular media. New J. Phys. 18:023013
    [Google Scholar]
  130. 130.
    Kouwenhoven J, Terpstra R 1970. Mixing and sorting of granules by tines. J. Agric. Eng. Res. 15:129–47
    [Google Scholar]
  131. 131.
    Zhou YC, Yu AB, Bridgwater J 2003. Segregation of binary mixture of particles in a bladed mixer. J. Chem. Technol. Biotechnol. 78:187–93
    [Google Scholar]
  132. 132.
    Remy B, Khinast JG, Glasser BJ 2009. Discrete element simulation of free flowing grains in a four-bladed mixer. AIChE J. 55:2035–48
    [Google Scholar]
  133. 133.
    Remy B, Glasser BJ, Khinast JG 2009. The effect of mixer properties and fill level on granular flow in a bladed mixer. AIChE J. 56:336–53
    [Google Scholar]
  134. 134.
    Remy B, Canty TM, Khinast JG, Glasser BJ 2010. Experiments and simulations of cohesionless particles with varying roughness in a bladed mixer. Chem. Eng. Sci. 65:4557–71
    [Google Scholar]
  135. 135.
    Remy B, Khinast JG, Glasser BJ 2011. Polydisperse granular flows in a bladed mixer: experiments and simulations of cohesionless spheres. Chem. Eng. Sci. 66:1811–24
    [Google Scholar]
  136. 136.
    Radl S, Brandl D, Heimburg H, Glasser BJ, Khinast JG 2012. Flow and mixing of granular material over a single blade. Powder Technol. 226:199–212
    [Google Scholar]
  137. 137.
    Maladen RD, Ding Y, Li C, Goldman DI 2009. Undulatory swimming in sand: subsurface locomotion of the sandfish lizard. Science 325:314–18
    [Google Scholar]
  138. 138.
    Darbois Texier B, Ibarra A, Melo F 2017. Helical locomotion in a granular medium. Phys. Rev. Lett. 119:068003
    [Google Scholar]
  139. 139.
    Askari H, Kamrin K 2016. Intrusion rheology in grains and other flowable materials. Nat. Mater. 15:1274
    [Google Scholar]
  140. 139a.
    Liu Y, Gonzalez M, Wassgren C 2019. Modeling granular material segregation using a combined finite element method and advection-diffusion-segregation equation model. Powder Technol 346:38–48
    [Google Scholar]
  141. 140.
    Liu Y, Gonzalez M, Wassgren C 2018. Modeling granular material blending in a rotating drum using a finite element method and advection–diffusion equation multiscale model. AIChE J. 64:3277–92
    [Google Scholar]
  142. 141.
    Xiao H, Ottino JM, Lueptow RM, Umbanhowar PB 2017. Transient response in granular quasi-two-dimensional bounded heap flow. Phys. Rev. E 96:040902
    [Google Scholar]
  143. 142.
    East RD, McGuinness P, Box F, Mullin T, Zuriguel I 2014. Granular segregation in a thin drum rotating with periodic modulation. Phys. Rev. E 90:052205
    [Google Scholar]
  144. 143.
    Juarez G, Lueptow RM, Ottino JM, Sturman R, Wiggins S 2010. Mixing by cutting and shuffling. Europhys. Lett. 91:20003
    [Google Scholar]
  145. 144.
    Park PP, Umbanhowar PB, Ottino JM, Lueptow RM 2016. Mixing with piecewise isometries on a hemispherical shell. Chaos 26:073115
    [Google Scholar]
  146. 145.
    Smith LD, Park PP, Umbanhowar PB, Ottino JM, Lueptow RM 2017. Predicting mixing via resonances: application to spherical piecewise isometries. Phys. Rev. E 95:062210
    [Google Scholar]
  147. 146.
    Jain N, Khakhar DV, Lueptow RM, Ottino JM 2001. Self-organization in granular slurries. Phys. Rev. Lett. 86:3771
    [Google Scholar]
  148. 147.
    Bird RB, Stewart WE, Lightfoot EN 2007.Transport Phenomena New York: Wiley 2nd revis. ed.
  149. 148.
    Ottino JM, Ranz WE, Macosko CW 1979. A lamellar model for analysis of liquid–liquid mixing. Chem. Eng. Sci. 34:877–90
    [Google Scholar]
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