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A discrete element study of the effect of particle shape on packing density of fine and cohesive powders

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Abstract

Fine and cohesive powders typically exhibit low packing density, with solid volume fraction around 0.3. Discrete element modelling (DEM) of particulate materials and processes typically employs spherical particles which have much larger solid fractions (e.g. 0.64 for dense random packing of frictionless spheres). In this work a range of quasi-spherical particles are designed, represented by a number of small satellites connected rigidly to a larger centre sphere. Using DEM, packing density is found to be controlled by the interplay between particle shape, size and inter-particle cohesion and friction. Low packing density is obtained for an appropriate combination of (1) particle shape that allows the creation of geometrically loose structures via separation of the central particles by the satellites, (2) particle size that should be sufficiently small so that adhesive forces between particles become dominant over gravity, (3) adhesive forces, determined from surface energy, should be sufficiently large, and (4) friction (static friction was found to have a dominant role compared to rolling friction, but negligible compared to adhesive forces for small particle size). By using the proposed quasi-spherical particle designs it becomes possible to calibrate more realistic DEM models for particulate processes that reproduces not only packing, but also other behaviours of bulk powders.

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References

  1. German RM (1989) Particle packing characteristics. Metal Powder Industries Federation

  2. White HE, Walton SF (1937) Particle packing and particle shape. J Am Ceram Soc 20(1–12):155–166

    Google Scholar 

  3. Allen JRL (ed) (1982) Chapter 4 packing of sedimentary particles, in developments in sedimentology. Elsevier, Amsterdam, pp 137–177

    Google Scholar 

  4. Rothon RN (2003) Particulate-filled polymer composites. Rapra Technology Limited, Shrewsbury

    Google Scholar 

  5. Dias R et al (2004) Particulate binary mixtures: dependence of packing porosity on particle size ratio. Ind Eng Chem Res 43(24):7912–7919

    Google Scholar 

  6. Sohn HY, Moreland C (1968) The effect of particle size distribution on packing density. Can J Chem Eng 46(3):162–167

    Google Scholar 

  7. Ye X et al (2018) Novel powder packing theory with bimodal particle size distribution-application in superalloy. Adv Powder Technol 29(9):2280–2287

    Google Scholar 

  8. Farr R, Groot R (2009) Close packing density of polydisperse hard spheres. J Chem Phys 131:244104

    Google Scholar 

  9. Krupp H (1967) Particle adhesion theory and experiment. Adv Colloid Interface Sci 1(2):111–239

    Google Scholar 

  10. Yu AB, Bridgwater J, Burbidge A (1997) On the modelling of the packing of fine particles. Powder Technol 92(3):185–194

    Google Scholar 

  11. Visser J (1989) Van der Waals and other cohesive forces affecting powder fluidization. Powder Technol 58(1):1–10

    Google Scholar 

  12. Bruni G (2005) An investigation of the influence of fines size distribution and high temperature on the fluidization behaviour of gas fluidized beds linked with rheological studies. Department of Chemical Engineering, University College London, London

  13. Yu AB, Standish N, Lu L (1995) Coal agglomeration and its effect on bulk density. Powder Technol 82(2):177–189

    Google Scholar 

  14. Holubec I, D'Appolonia E (1973) Effect of particle shape on the engineering properties of granular soils. American Society for Testing and Materials, West Conshohocken

    Google Scholar 

  15. Youd TL (1973) Factors controlling maximum and minimum densities of sands. Evaluation of relative density and its role in geotechnical projects involving cohesion less soils (523)

  16. Rouse P, Fannin RJ, Shuttle DA (2008) Influence of roundness on the void ratio and strength of uniform sand. Geotechnique 58:227–231

    Google Scholar 

  17. Cho G-C, Dodds J, Santamarina J (2006) Particle shape effects on packing density, stiffness, and strength: natural and crushed sands. Geotechn Geoenviron Eng 132(5):591–602

    Google Scholar 

  18. Nolan GT, Kavanagh PE (1995) Random packing of nonspherical particles. Powder Technol 84(3):199–205

    Google Scholar 

  19. Yang RY, Zou RP, Yu AB (2003) Effect of material properties on the packing of fine particles. J Appl Phys 94:3025–3034

    Google Scholar 

  20. Kallus Y (2016) The random packing density of nearly spherical particles. Soft Matter 12(18):4123–4128

    Google Scholar 

  21. Baserinia R, Sinka IC (2018) Mass flow rate of fine and cohesive powders under differential air pressure. Powder Technol 334:173–182

    Google Scholar 

  22. Marigo M, Stitt EH (2015) Discrete element method (DEM) for industrial applications: comments on calibration and validation for the modelling of cylindrical pellets. KONA Powder Part J 32:236–252

    Google Scholar 

  23. Ketterhagen WR, Ende MT, Hancock BC (2009) Process modeling in the pharmaceutical industry using the discrete element method. J Pharm Sci 98(2):442–470

    Google Scholar 

  24. Gantt JA, Gatzke EP (2005) High-shear granulation modeling using a discrete element simulation approach. Powder Technol 156(2):195–212

    Google Scholar 

  25. Hassanpour A et al (2009) Effect of granulation scale-up on the strength of granules. Powder Technol 189(2):304–312

    Google Scholar 

  26. Wu C-Y (2008) DEM simulations of die filling during pharmaceutical tabletting. Particuology 6(6):412–418

    Google Scholar 

  27. Guo Y et al (2010) Numerical analysis of density-induced segregation during die filling. Powder Technol 197(1):111–119

    Google Scholar 

  28. Cleary PW, Sawley ML (2002) DEM modelling of industrial granular flows: 3D case studies and the effect of particle shape on hopper discharge. Appl Math Modelling 26(2):89–111

    MATH  Google Scholar 

  29. Anand A et al (2008) Predicting discharge dynamics from a rectangular hopper using the discrete element method (DEM). Chem Eng Sci 63(24):5821–5830

    Google Scholar 

  30. Ketterhagen WR et al (2009) Predicting the flow mode from hoppers using the discrete element method. Powder Technol 195(1):1–10

    Google Scholar 

  31. Arratia PE et al (2006) A study of the mixing and segregation mechanisms in the Bohle Tote blender via DEM simulations. Powder Technol 164(1):50–57

    Google Scholar 

  32. Xu Y et al (2010) 2D DEM simulation of particle mixing in rotating drum: a parametric study. Particuology 8(2):141–149

    Google Scholar 

  33. Alizadeh E, Bertrand F, Chaouki J (2014) Discrete element simulation of particle mixing and segregation in a tetrapodal blender. Comput Chem Eng 64:1–12

    Google Scholar 

  34. Zhang ZP et al (2001) A simulation study of the effects of dynamic variables on the packing of spheres. Powder Technol 116(1):23–32

    Google Scholar 

  35. Gan JQ, Yu AB, Zhou ZY (2016) DEM simulation on the packing of fine ellipsoids. Chem Eng Sci 156:64–76

    Google Scholar 

  36. Cundall PA, Strack O (1979) A discrete numerical mode for granular assemblies. Geotechnique 29:47–65

    Google Scholar 

  37. Tanaka K et al (2001) Numerical and experimental studies for the impact of projectiles on granular materials. In: Levy A, Kalman H (eds) Handbook of powder technology. Elsevier, Amsterdam, pp 263–270

    Google Scholar 

  38. Wills BA, Finch JA (2016) Chapter 17—modeling and characterization. In: Wills BA, Finch JA (eds) Wills' mineral processing technology, 8th edn. Butterworth-Heinemann, Boston, pp 449–462

    Google Scholar 

  39. Fortin J, Millet O, Saxcé GD (2004) Numerical simulation of granular materials by an improved discrete element method. Int J Numer Methods Eng 62:639–663

    MathSciNet  MATH  Google Scholar 

  40. Mindlin RD (1949) Compliance of elastic bodies in contact. Trans ASME J Appl Mech 16:259–268

    MathSciNet  MATH  Google Scholar 

  41. Hertz H (1982) Über die Berührung fester elastischer Körper. Journal für die Reine und Angewandte Mathematik 92:156–171

    MATH  Google Scholar 

  42. Johnson KL, Kendall K, Roberts AD (1971) Surface energy and contact of elastic solids. Proc R Soc Lond A Math Phys Sci 324:301–313

    Google Scholar 

  43. Mishra BK, Thornton C, Bhimji D (2002) A preliminary numerical investigation of agglomeration in a rotary drum. Miner Eng 15(1):27–33

    Google Scholar 

  44. Li SQ, Marshall JS (2007) Discrete element simulation of micro-particle deposition on a cylindrical fiber in an array. J Aerosol Sci 38(10):1031–1046

    Google Scholar 

  45. Barthel E (2008) Adhesive elastic contacts: JKR and more. J Phys D Appl Phys 41(16):163001

    Google Scholar 

  46. Deng X, Scicolone JV, Davé RN (2013) Discrete element method simulation of cohesive particles mixing under magnetically assisted impaction. Powder Technol 243:96–109

    Google Scholar 

  47. Deng XL, Davé RN (2013) Dynamic simulation of particle packing influenced by size, aspect ratio and surface energy. Granular Matter 15(4):401–415

    Google Scholar 

  48. Cabiscol R, Finke JH, Kwade A (2018) Calibration and interpretation of DEM parameters for simulations of cylindrical tablets with multi-sphere approach. Powder Technol 327:232–245

    Google Scholar 

  49. Asaf Z, Rubinstein D, Shmulevich I (2007) Determination of discrete element model parameters required for soil tillage. Soil Tillage Res 92(1):227–242

    Google Scholar 

  50. Coetzee CJ (2017) Review: calibration of the discrete element method. Powder Technol 310:104–142

    Google Scholar 

  51. Coetzee CJ (2019) Particle upscaling: calibration and validation of the discrete element method. Powder Technol 344:487–503

    Google Scholar 

  52. Fangping Y et al (2019) Calibration and verification of DEM parameters for dynamic particle flow conditions using a backpropagation neural network. Adv Powder Technol 30(2):292–301

    Google Scholar 

  53. Roessler T, Katterfeld A (2019) DEM parameter calibration of cohesive bulk materials using a simple angle of repose test. Particuology 45:105–115

    Google Scholar 

  54. Boikov A, Savelev R, Payor V (2018) DEM calibration approach: random forest. J Phys 1118:012009

    Google Scholar 

  55. Coetzee CJ (2016) Calibration of the discrete element method and the effect of particle shape. Powder Technol 297:50–70

    Google Scholar 

  56. Do HQ, Aragón AM, Schott DL (2018) A calibration framework for discrete element model parameters using genetic algorithms. Adv Powder Technol 29(6):1393–1403

    Google Scholar 

  57. Baroutaji A et al (2017) Mechanics and computational modeling of pharmaceutical tabletting process. In: Reference module in materials science and materials engineering. Elsevier, Amsterdam

  58. Lemieux M et al (2008) Large-scale numerical investigation of solids mixing in a V-blender using the discrete element method. Powder Technol 181(2):205–216

    MathSciNet  Google Scholar 

  59. Bertrand F, Leclaire LA, Levecque G (2005) DEM-based models for the mixing of granular materials. Chem Eng Sci 60(8):2517–2531

    Google Scholar 

  60. Roskilly SJ et al (2010) Investigating the effect of shape on particle segregation using a Monte Carlo simulation. Powder Technol 203(2):211–222

    Google Scholar 

  61. Miyajima T, Yamamoto K-I, Sugimoto M (2001) Effect of particle shape on packing properties during tapping. Adv Powder Technol 12(1):117–134

    Google Scholar 

  62. Zhao S et al (2017) Particle shape effects on fabric of granular random packing. Powder Technol 310:175–186

    Google Scholar 

  63. Anikeenko AV, Medvedev NN (2007) Polytetrahedral nature of the dense disordered packings of hard spheres. Phys Rev Lett 98(23):235504

    Google Scholar 

  64. Klumov BA, Khrapak SA, Morfill GE (2011) Structural properties of dense hard sphere packings. Phys Rev B 83(18):184105

    Google Scholar 

  65. Onoda GY, Liniger EG (1990) Random loose packings of uniform spheres and the dilatancy onset. Phys Rev Lett 64(22):2727–2730

    Google Scholar 

  66. Jerkins M et al (2008) Onset of mechanical stability in random packings of frictional spheres. Phys Rev Lett 101(1):018301

    Google Scholar 

  67. Farrell GR, Martini KM, Menon N (2010) Loose packings of frictional spheres. Soft Matter 6:2925–2930

    Google Scholar 

  68. Kloss C et al (2012) Models, algorithms and validation for opensource DEM and CFD-DEM. Prog Comput Fluid Dyn Int J 12(2/3):140

    MathSciNet  Google Scholar 

  69. Garcia X et al (2009) A clustered overlapping sphere algorithm to represent real particles in discrete element modelling. Géotechnique. 59(9):779–784

    Google Scholar 

  70. Lu G, Third JR, Müller CR (2015) Discrete element models for non-spherical particle systems: from theoretical developments to applications. Chem Eng Sci 127:425–465

    Google Scholar 

  71. You Y, Zhao Y (2018) Discrete element modelling of ellipsoidal particles using super-ellipsoids and multi-spheres: a comparative study. Powder Technol 331:179–191

    Google Scholar 

  72. He Y et al (2018) Discrete modelling of the compaction of non-spherical particles using a multi-sphere approach. Miner Eng 117:108–116

    Google Scholar 

  73. Seelen LJH, Padding JT, Kuipers JAM (2018) A granular discrete element method for arbitrary convex particle shapes: method and packing generation. Chem Eng Sci 189:84–101

    Google Scholar 

  74. Tahmasebi P (2018) Packing of discrete and irregular particles. Comput Geotech 100:52–61

    Google Scholar 

  75. Majidi B et al (2015) Packing density of irregular shape particles: DEM simulations applied to anode-grade coke aggregates. Adv Powder Technol 26(4):1256–1262

    Google Scholar 

  76. Gan JQ, Zhou ZY, Yu AB (2017) Interparticle force analysis on the packing of fine ellipsoids. Powder Technol 320:610–624

    Google Scholar 

  77. Tangri H, Guo Y, Curtis JS (2017) Packing of cylindrical particles: DEM simulations and experimental measurements. Powder Technol 317:72–82

    Google Scholar 

  78. Parteli EJR et al (2014) Attractive particle interaction forces and packing density of fine glass powders. Sci Rep 4:6227–6227

    Google Scholar 

  79. Liu W et al (2015) Adhesive loose packings of small dry particles. Soft Matter 11(32):6492–6498

    Google Scholar 

  80. Liu W et al (2017) Effects of hydrodynamic interaction on random adhesive loose packings of micron-sized particles. EPJ Web Conf 140:08017

    Google Scholar 

  81. Elmsahli HS, Sinka IC (2019) Coupled CFD-DEM analysis of mass flow rate of fine and cohesive powders under differential air pressure. Int J Solids Struct. Manuscript submitted 2 November 2019, under review

  82. Thornton C, Cummins SJ, Cleary PW (2013) An investigation of the comparative behaviour of alternative contact force models during inelastic collisions. Powder Technol 233:30–46

    Google Scholar 

  83. Elmsahli HSM (2019) Numerical analysis of powder flow using computational fluid dynamics coupled with discrete element modelling. Ph.D. Thesis, University of Leicester

  84. Rhodes M (2008) Introduction to particle technology. Wiley, Great Britain

    Google Scholar 

  85. Ho R et al (2010) Determination of surface heterogeneity of d-mannitol by sessile drop contact angle and finite concentration inverse gas chromatography. Int J Pharm 387(1–2):79–86

    Article  Google Scholar 

  86. Karde V, Ghoroi C (2014) Influence of surface modification on wettability and surface energy characteristics of pharmaceutical excipient powders. Int J Pharm 475(1–2):351–363

    Article  Google Scholar 

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Acknowledgements

H.E. would like to thank Aljabal Algharbi University in Libya/Faculty of Engineering, Jadu, for presenting him with the opportunity to complete his Ph.D. He is also grateful to Libyan Cultural Affair in London for all the support and assistance given to him during his Ph.D. studies.

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  1. School of Engineering, University of Leicester, University Road, Leicester, LE1 7RH, UK

    H. S. Elmsahli & I. C. Sinka

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  1. H. S. Elmsahli
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Correspondence to I. C. Sinka.

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Elmsahli, H.S., Sinka, I.C. A discrete element study of the effect of particle shape on packing density of fine and cohesive powders. Comp. Part. Mech. 8, 183–200 (2021). https://doi.org/10.1007/s40571-020-00322-9

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