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Impact dynamics and power-law scaling behavior of wet agglomerates

Abstract

We investigate the impact dynamics of a single wet agglomerate composed of primary spherical particles impacting a flat plane by using three-dimensional discrete element method simulations. The primary particle is assumed to be rigid and interacted with its near-neighboring particles by introducing approximate analytical expressions of capillary cohesion forces and lubrication forces induced from the liquid in addition to their elastic and frictional interactions. The paper analyzes the mechanical strength, the deformation, and the connectivity of wet particle agglomerate during the impact as well as in its early-stage impact and the final-stage deposition. We show that the mechanical strength, deformation, and connectivity of granule strongly depend on the key parameters (the liquid–vapor surface tension, the liquid viscosity, and the impact speed of agglomerate). In particular, the early-stage strength and the height of wet agglomerate at its final-stage deposition nicely behave as a function of the Capillary–Stokes inertial number that combines the Capillary number and Stokes number, and the macroscopic strength of the agglomerate at its early-stage impact has the microscopic origin from the normal compressive forces between primary particles. These observations are consistent that represent the relationship between the rheological properties and the liquid properties and the impact conditions of wet granular materials.

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References

  1. 1.

    Nimmo J (2005) Aggregation|physical aspects. In: Hillel D (ed) Encyclopedia of soils in the environment. Elsevier, Oxford, pp 28–35

    Chapter  Google Scholar 

  2. 2.

    Sarkar J, Dubey D (2016) Failure regimes of single wet granular aggregate under shear. J Non-Newton Fluid Mech 234:236–248

    MathSciNet  Article  Google Scholar 

  3. 3.

    Ennis BJ, Tardos G, Pfeffer R (1991) A microlevel-based characterization of granulation phenomena. Powder Technol 65(1):257–272

    Article  Google Scholar 

  4. 4.

    Rondet E, Delalonde M, Ruiz T, Desfoursb JP (2010) Fractal formation description of agglomeration in low shear mixer. Chem Eng J 164:376–382

    Article  Google Scholar 

  5. 5.

    Barkouti A, Rondet E, Delalonde M, Ruiz T (2012) Influence of physicochemical binder properties on agglomeration of wheat powder in couscous grain. J Food Eng 111:234–240

    Article  Google Scholar 

  6. 6.

    Nosrati A, Addai-Mensah J, Robinson DJ (2012) Drum agglomeration behavior of nickel laterite ore: effect of process variables. Hydrometallurgy 125–126:90–99

    Article  Google Scholar 

  7. 7.

    Chien SH, Carmona G, Prochnow LI, Austin ER (2003) Cadmium availability from granulated and bulk-blended phosphate-potassium fertilizers. J Environ Qual 32(5):1911–1914

    Article  Google Scholar 

  8. 8.

    Suresh P, Sreedhar I, Vaidhiswaran R, Venugopal A (2017) A comprehensive review on process and engineering aspects of pharmaceutical wet granulation. Chem Eng J 328:785–815

    Article  Google Scholar 

  9. 9.

    Lian G, Thornton C, Adams MJ (1998) Discrete particle simulation of agglomerate impact coalescence. Chem Eng Sci 53(19):3381–3391

    Article  Google Scholar 

  10. 10.

    Kafui K, Thornton C (2000) Numerical simulations of impact breakage of a spherical crystalline agglomerate. Powder Technol 109(1):113–132

    Article  Google Scholar 

  11. 11.

    Mishra B, Thornton C (2001) Impact breakage of particle agglomerates. Int J Miner Process 61(4):225–239

    Article  Google Scholar 

  12. 12.

    Thornton C, Ciomocos MT, Adams MJ (2004) Numerical simulations of diametrical compression tests on agglomerates. Powder Technol 140:258–267

    Article  Google Scholar 

  13. 13.

    Liu L, Kafui K, Thornton C (2010) Impact breakage of spherical, cuboidal and cylindrical agglomerates. Powder Technol 199(2):189–196

    Article  Google Scholar 

  14. 14.

    Vo T-T, Mutabaruka P, Nezamabadi S, Delenne J-Y, Izard E, Pellenq R, Radjai F (2018) Mechanical strength of wet particle agglomerates. Mech Res Commun 92:1–7

    Article  Google Scholar 

  15. 15.

    Khalilitehrani M, Olsson J, Rasmuson A, Daryosh F (2018) A regime map for the normal surface impact of wet and dry agglomerates. AIChE J 64(6):1975–1985

    Article  Google Scholar 

  16. 16.

    Vo T-T, Nezamabadi S, Mutabaruka P, Delenne J-Y, Izard E, Pellenq R, Radjai F (2019) Agglomeration of wet particles in dense granular flows. Eur Phys J E 42(9):127

    Article  Google Scholar 

  17. 17.

    Vo T-T, Mutabaruka P, Nezamabadi S, Delenne J-Y, Radjai F (2020) Evolution of wet agglomerates inside inertial shear flow of dry granular materials. Phys Rev E 101:032906

    Article  Google Scholar 

  18. 18.

    Tong Z, Yang R, Yu A, Adi S, Chan H (2009) Numerical modelling of the breakage of loose agglomerates of fine particles. Powder Technol 196(2):213–221

    Article  Google Scholar 

  19. 19.

    Vo TT (2019) Modeling the rheology of wet granular materials. Thesis, Université de Montpellier

  20. 20.

    Talu I, Tardos GI, Khan MI (2000) Computer simulation of wet granulation. Powder Technol 110:59–75

    Article  Google Scholar 

  21. 21.

    Iveson S, Beathe J, Page N (2002) The dynamic strength of partially saturated powder compacts: the effect of liquid properties. Powder Technol 127:149–161

    Article  Google Scholar 

  22. 22.

    Ghadiri M, Salman AD, Hounslow M, Hassanpour A, York DW (2011) Editorial: Special issue—agglomeration. Chem Eng Res Des 89(5):499

    Article  Google Scholar 

  23. 23.

    Nguyen D, Rasmuson A, Thalberg K, Niklasson Björn I (2015) A breakage and adhesion regime map for the normal impact of loose agglomerates with a spherical target. AIChE J 61(12):4059–4068

    Article  Google Scholar 

  24. 24.

    Rahmanian N, Ghadiri M (2013) Strength and structure of granules produced in continuous granulators. Powder Technol 233:227–233

    Article  Google Scholar 

  25. 25.

    Khalifa A, Breuer M (2020) Data-driven model for the breakage of dry monodisperse agglomerates by wall impact applicable for multiphase flow simulations. Powder Technol 376:241–253

  26. 26.

    Ning Z, Boerefijn R, Ghadiri M, Thornton C (1997) Distinct element simulation of impact breakage of lactose agglomerates. Adv Powder Technol 8(1):15–37

    Article  Google Scholar 

  27. 27.

    Thornton C, Ciomocos M, Adams M (1999) Numerical simulations of agglomerate impact breakage. Powder Technol 105(1):74–82

    Article  Google Scholar 

  28. 28.

    Liu L, Thornton C, Shaw SJ, Tadjouddine EM (2016) Discrete element modelling of agglomerate impact using autoadhesive elastic–plastic particles. Powder Technol 297:81–88

    Article  Google Scholar 

  29. 29.

    Deng X, Davé RN (2017) Breakage of fractal agglomerates. Chem Eng Sci 161:117–126

    Article  Google Scholar 

  30. 30.

    Vo T-T (2021) Scaling behavior of the tensile strength of viscocohesive granular aggregates. Phys Rev E 103:042902

    Article  Google Scholar 

  31. 31.

    Zhang L, Wu C-Y (2020) Discrete element analysis of normal elastic impact of wet particles. Powder Technol 362:628–634

    Article  Google Scholar 

  32. 32.

    Chen H, Liu W, Zheng Z, Li S (2021) Impact dynamics of wet agglomerates onto rigid surfaces. Powder Technol 379:296–306

    Article  Google Scholar 

  33. 33.

    Vo T-T, Nezamabadi S, Mutabaruka P, Delenne J-Y, Radjai F (2020) Additive rheology of complex granular flows. Nat Commun 11:1476

    Article  Google Scholar 

  34. 34.

    Radjai F, Topin V, Richefeu V, Voivret C, Delenne J-Y, Azéma E, El Youssoufi MS (2010) Force transmission in cohesive granular media. In: Goddard JD, Jenkins JT, Giovine P (eds) Mathematical modeling and physical instances of granular flows. AIP, Dabaka, pp 240–260

    Google Scholar 

  35. 35.

    Bagnold RA (1954) Experiments on a gravity-free dispersion of large solid spheres in a Newtonian fluid under shear. Proc R Soc Lond 225:49–63

    Google Scholar 

  36. 36.

    da Cruz F, Emam S, Prochnow M, Roux J-N, Chevoir F (2005) Rheophysics of dense granular materials: discrete simulation of plane shear flows. Phys Rev E 72:021309

    Article  Google Scholar 

  37. 37.

    Khalilitehrani M, Olsson J, Daryosh F, Rasmuson A (2019) The morphology of the deposited particles after a wet agglomerate normal surface impact. Powder Technol 345:796–803

    Article  Google Scholar 

  38. 38.

    Azéma E, Sánchez P, Scheeres DJ (2018) Scaling behavior of cohesive self-gravitating aggregates. Phys Rev E 98:030901

    Article  Google Scholar 

  39. 39.

    Vo T-T (2020) Erosion dynamics of wet particle agglomerates. Comput Part Mech 8:601–612

    Article  Google Scholar 

  40. 40.

    Trulsson M, Andreotti B, Claudin P (2012) Transition from the viscous to inertial regime in dense suspensions. Phys Rev Lett 109:118305

    Article  Google Scholar 

  41. 41.

    Amarsid L, Delenne J-Y, Mutabaruka P, Monerie Y, Perales F, Radjai F (2017) Viscoinertial regime of immersed granular flows. Phys Rev E 96:012901

    Article  Google Scholar 

  42. 42.

    Vo T-T (2020) Rheology and granular texture of viscoinertial simple shear flows. J Rheol 64(5):1133–1145

    Article  Google Scholar 

  43. 43.

    Radjai F, Dubois F (2011) Discrete-element modeling of granular materials. Wiley, New York

    Google Scholar 

  44. 44.

    Richefeu V, ElYoussoufi S, Azéma E, Radjai F (2009) Force distribution in cohesive and non cohesive granular media. Powder Technol 190:258263

    Article  Google Scholar 

  45. 45.

    Matuttis H, Luding S, Herrmann H (2000) Discrete element simulations of dense packings and heaps made of spherical and non-spherical particles. Powder Technol 109(1):278–292

    Article  Google Scholar 

  46. 46.

    Lian G, Thornton C, Adams M (1993) A theoretical study of the liquid bridge forces between two rigid spherical bodies. J Colloid Interface Sci 161:138–147

    Article  Google Scholar 

  47. 47.

    Scheel M, Seemann R, Brinkmann M, Michiel MD, Sheppard A, Herminghaus S (2008) Liquid distribution and cohesion in wet granular assemblies beyond the capillary bridge regime. J Phys Condens Matter 20(49):494236

    Article  Google Scholar 

  48. 48.

    Delenne J-Y, Richefeu V, Radjai F. (2015) Liquid clustering and capillary pressure in granular media. J Fluid Mech 762:R5

  49. 49.

    Richefeu V, El Youssoufi MS, Radjaï F (2007) Shear strength of unsaturated soils: experiments, dem simulations, and micromechanical analysis. In: Theoretical and numerical unsaturated soil mechanics. Springer, Berlin Heidelberg, pp 83–91

  50. 50.

    Willett C, Adans M, Johnson S, Seville J (2000) Capillary bridges between two spherical bodies. Langmuir 16:9396–9405

    Article  Google Scholar 

  51. 51.

    Moreno-Atanasio R (2012) Energy dissipation in agglomerates during normal impact. Powder Technol 223:12–18 (Invited papers from delegates of Chemeca 2010: The 40th Annual Australasian Chemical Engineering Conference)

    Article  Google Scholar 

  52. 52.

    Cundall PA, Strack ODL (1979) A discrete numerical model for granular assemblies. Géotechnique 29(1):47–65

    Article  Google Scholar 

  53. 53.

    Allen MP, Tildesley DJ (1987) Computer simulation of liquids. Oxford University Press, Oxford

    MATH  Google Scholar 

  54. 54.

    Luding S (1998) Collisions and contacts between two particles. In: Herrmann HJ, Hovi J-P, Luding S (eds) Physics of dry granular media—NATO ASI series E350. Kluwer Academic Publishers, Dordrecht, p 285

    Chapter  Google Scholar 

  55. 55.

    Thornton C (1999) Quasi-static shear deformation of a soft particle system. Powder Technol 109:179–191

    Article  Google Scholar 

  56. 56.

    Duran J, Reisinger A, de Gennes P (1999) Sands, powders, and grains: an introduction to the physics of granular materials, partially ordered systems. Springer, New York

    Google Scholar 

  57. 57.

    Richefeu V, El Youssoufi M, Radjai F (2006) Shear strength properties of wet granular materials. Phys Rev E 73:051304

    Article  Google Scholar 

  58. 58.

    Pitois O, Moucheront P, Chateau X (2000) Liquid bridge between two moving spheres: an experimental study of viscosity effects. J Colloid Interface Sci 231(1):26–31

    Article  Google Scholar 

  59. 59.

    Badetti M, Fall A, Hautemayou D, Chevoir F, Aimedieu P, Rodts S, Roux J-N (2018) Rheology and microstructure of unsaturated wet granular materials: experiments and simulations. J Rheol 62(5):1175–1186

    Article  Google Scholar 

  60. 60.

    Mikami T, Kamiya H, Horio M (1998) Numerical simulation of cohesive powder behavior in a fluidized bed. Chem Eng Sci 53(10):1927–1940

    Article  Google Scholar 

  61. 61.

    Rabinovich YI, Esayanur MS, Moudgil BM (2005) Capillary forces between two spheres with a fixed volume liquid bridge: theory and experiment. Langmuir 21:10992–10997

  62. 62.

    Richefeu V, Radjai F, Youssoufi MSE (2007) Stress transmission in wet granular materials. Eur Phys J E 21:359–369

  63. 63.

    Krizou N, Clark AH (2020) Power-law scaling of early-stage forces during granular impact. Phys Rev Lett 124:178002

    Article  Google Scholar 

  64. 64.

    Azéma E, Radjaï F (2014) Internal structure of inertial granular flows. Phys Rev Lett 112:078001

    Article  Google Scholar 

  65. 65.

    Azéma E, Linero S, Estrada N, Lizcano A (2017) Shear strength and microstructure of polydisperse packings: the effect of size span and shape of particle size distribution. Phys Rev E 96:022902

  66. 66.

    Cantor D, Azéma E, Sornay P, Radjai F (2018) Rheology and structure of polydisperse three-dimensional packings of spheres. Phys Rev E 98:052910

    Article  Google Scholar 

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Acknowledgements

This research is funded by Vietnam National Foundation for Science and Technology Development (NAFOSTED) under Grant Number 107.01-2020.24. The authors also gratefully acknowledge Prof. Ha H. Bui for his comprehensive review of this manuscript paper.

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Correspondence to Thanh-Trung Vo or Thi Lo Vu.

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Vo, TT., Nguyen, C.T., Nguyen, TK. et al. Impact dynamics and power-law scaling behavior of wet agglomerates. Comp. Part. Mech. (2021). https://doi.org/10.1007/s40571-021-00427-9

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Keywords

  • Granular matter
  • Agglomerate
  • Discrete element method
  • Impact
  • Capillary number
  • Stokes number