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Tapped granular column dynamics: simulations, experiments and modeling


This paper communicates the results of a synergistic investigation that initiates our long term research goal of developing a continuum model capable of predicting a variety of granular flows. We consider an ostensibly simple system consisting of a column of inelastic spheres subjected to discrete taps in the form of half sine wave pulses of amplitude a/d and period \(\tau \). A three-pronged approach is used, consisting of discrete element simulations based on linear loading-unloading contacts, experimental validation, and preliminary comparisons with our continuum model in the form of an integro-partial differential equation.

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    The sharp gradient up to this peak is due to the scale of the horizontal axis.

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    The choice to utilize continuous vibration, as opposed to discrete taps, arises from the fact that as the number of particles in our system is altered, the motion of the oscillating base used to excite particles may be influenced by the varying mass, resulting in an unequal provision of energy to the different systems, and hence a lack of consistency in our results. The use of continuous vibrations allows feedback from an accelerometer to be used in order to ensure a driving strength which is consistent to within 0.1 % in all cases.

    Fig. 9

    Schematic diagram of the PEPT system and a photo of the camera

  3. 3.

    The number of repeated runs for the three-dimensional systems was limited to this value due to the considerable amount of time required for the highest-N runs combined with the costs associated with the use of the PEPT facility. It should be noted, however, that the minimal variance observed in the data for our 3D systems (see Fig. 10) indicates that the number of runs conducted was indeed adequate to produce good statistics.


  1. 1.

    Valverde JM, Castellanos A (2007) Compaction of fine powders: from fluidized agglomerates to primary particles. Granul Matter 9(1–2):19–24

    Google Scholar 

  2. 2.

    Rosato AD, Dybenko O, Ratnaswamy V, Horntrop D, Kondic L (2010) Microstructure evolution in density relaxation by tapping. Phys Rev E 81:061301

    Article  Google Scholar 

  3. 3.

    Richard P, Philippe P, Barbe F, Bourles S, Thibault X, Bideau D (2003) Analysis by x-ray microtomography of a granular packing undergoing compaction. Phys Rev E 68(2):020301

    Article  Google Scholar 

  4. 4.

    Richard P, Nicodemi M, Delannay R, Ribiere P, Bideau D (2005) Slow relaxation and compaction of granular systems. Nat Mater 4(2):121–128

    Article  Google Scholar 

  5. 5.

    Luding S, Nicolas M, Pouliquen O (2000) A minimal model for slow dynamics: compaction of granular media under vibration or shear. In: Kolymbas D, Fellin W (eds) Compaction of soils, granulates and powders. A. A. Balkema, Rotterdam, p 241

    Google Scholar 

  6. 6.

    Linz S, Dohle A (1999) Minimal relaxation law for compaction of tapped granular matter. Phys Rev E 60(5):5737–5741

    Article  Google Scholar 

  7. 7.

    Dobry R, Whitman RV (1973) Compaction of sand on a vertically vibrated table. American Society of Testing Materials, Philadelphia

    Google Scholar 

  8. 8.

    Ayer JE, Soppet FE (1965) Vibratory compaction: I, compaction of spherical shapes. J Am Ceram Soc 48(4):180

    Article  Google Scholar 

  9. 9.

    Wildman RD, Parker DJ (2002) Coexistence of two granular temperatures in binary vibrofluidized beds. Phys Rev Lett 88(6):064301

    Article  Google Scholar 

  10. 10.

    Wildman RD, Huntley JM, Parker DJ (2001) Granular temperature profiles in three-dimensional vibrofluidized granular beds. Phys Rev E 63(6 I):061311

    Article  Google Scholar 

  11. 11.

    Warr S, Huntley JM, Jacques GTH (1995) Fluidization of a two-dimensional granular system: experimental study and scaling behavior. Phys Rev E 52(5):5583–5595

    Article  Google Scholar 

  12. 12.

    Wakou J, Ochiai A, Isobe M (2008) A Langevin approach to one-dimensional granular media fluidized by vibrations. J Phys Soc Jpn 77(3):034402

    Article  Google Scholar 

  13. 13.

    Brey JJ, Ruiz-Montero MJ, Moreno F, Garcia-Rojo R (2002) Transversal inhomogeneities in dilute vibrofluidized granular fluids. Phys Rev E 65(6):061302

    Article  Google Scholar 

  14. 14.

    Yoon DK, Jenkins JT (2006) The influence of different species’ granular temperatures on segregation in a binary mixture of dissipative grains. Phys Fluids 18(7):073301:073303–073306

    Article  Google Scholar 

  15. 15.

    Windows-Yule CR, Parker DJ (2015) Density-driven segregation in binary and ternary granular systems. Kona Powder Particle 32:163–175. doi:10.14356/kona.2015004

    Article  Google Scholar 

  16. 16.

    Williams JC (1976) The segregation of particulate materials: a review. Powder Technol 15:245–251

    Article  Google Scholar 

  17. 17.

    Vanel L, Rosato AD, Dave RN (1997) Rise regimes of a single large sphere in a vibrated bed. Phys Rev Lett 78:1255–1258

    Article  Google Scholar 

  18. 18.

    Shishodia N, Wassgren CR (2001) Particle segregation in vibrofluidized beds due to buoyant forces. Phys Rev Lett 87(8):084302

    Article  Google Scholar 

  19. 19.

    Sanders DA, Swift MR, Bowley RM, King PJ (2006) The attraction of Brazil nuts. Europhys Lett 73(3):349–355

    Article  Google Scholar 

  20. 20.

    Rosato AD, Blackmore DL, Zhang N, Lan Y (2002) A perspective on vibration-induced size segregation of granular materials. Chem Eng Sci 57(2):265–275

    Article  Google Scholar 

  21. 21.

    Poschel T, Herrmann HJ (1995) Size segregation and convection. Europhys Lett 29(2):123–128

    Article  Google Scholar 

  22. 22.

    Metzger MJ, Remy B, Glasser BJ (2011) All the Brazil nuts are not on top: vibration induced granular size segregation of binary, ternary and multi-sized mixtures. Powder Technol 205(1–3):42–51

    Article  Google Scholar 

  23. 23.

    Liffman K, Muniandy K, Rhodes M, Gutteridge D, Metcalfe G (2001) A segregation mechanisms in vertically shaken bed. Granul Matter 3:205–214

    Article  Google Scholar 

  24. 24.

    Huerta DA, Ruiz-Suarez JC (2004) Vibration-induced granular segregation: a phenomenon driven by three mechanisms. Phys Rev Lett 92(11):114301–114301

    Article  Google Scholar 

  25. 25.

    Harwood CF (1977) Powder segregation due to vibration. Powder Technol 16:51–57

    Article  Google Scholar 

  26. 26.

    Ellenberger J, Vandu CO, Krishna R (2006) Vibration-induced granular segregation in a pseudo-2D column: the (reverse) Brazil nut effect. Powder Technol 164(3):168–173

    Article  Google Scholar 

  27. 27.

    Duran J, Rajchenbach J, Clement E (1993) Arching effect model for particle size segregation. Phys Rev Lett 70:2431–2434

    Article  Google Scholar 

  28. 28.

    Ahmad K, Smalley IJ (1973) Observation of particle segregation in vibrated granular systems. Powder Technol 8:69–75

    Article  Google Scholar 

  29. 29.

    Bonneau L, Andreotti B, Clement E (2007) Surface elastic waves in granular media under gravity and their relation to booming avalanches. Phys Rev E 75(1):016602. doi:10.1103/PhysRevE.75.016602

    Article  Google Scholar 

  30. 30.

    Conway SL, Coldfarb DJ, Glasser BJ (2003) Free surface waves in wall-bounded granular flows. Phys Rev Lett 90(7):074301

    Article  Google Scholar 

  31. 31.

    Luding S (1997) Surface waves and pattern formation in vibrated granular media. In: Behringer R, Jenkins JT (eds) Powders and grains 1997. A. A. Balkema, Amsterdam

    Google Scholar 

  32. 32.

    Pak HK, Behringer PR (1993) Surface waves in vertically vibrated granular materials. Phys Rev Lett 71(12):1835–1838

    Article  Google Scholar 

  33. 33.

    Blackmore D, Rosato A, Tricoche X, Urban K, Zuo L (2014) Analysis, simulation and visualization of 1D tapping via reduced dynamical systems models. Physica D 273–74:14–27. doi:10.1016/j.physd.2014.01.009

    Article  Google Scholar 

  34. 34.

    Blackmore D, Rosato A, Tricoche X, Urban K, Ratnaswamy V (2011) Tapping dynamics for a column of particles and beyond. J Mech Mater Struct 6(1–4):71–86. doi:10.2140/jomms.2011.6.71

    Article  Google Scholar 

  35. 35.

    Dybenko O, Rosato AD, Horntrop D (2007) Three-dimensional Monte Carlo simulations of density relaxation. Kona Powder Particle 25:133–144

    Article  Google Scholar 

  36. 36.

    Falcon E, Laroche C, Fauve S, Coste C (1998) Collision of a 1-D column of beads with a wall. Eur Phys J B 5(1):111–131

    Article  Google Scholar 

  37. 37.

    Cundall PA (1974) Rational design of tunnel supports: a computer model for rock-mass behavior using interactive graphics for input and output of geometrical data. U. S. Army Corp. of Engineers, Omaha

    Google Scholar 

  38. 38.

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

    Article  Google Scholar 

  39. 39.

    Alder BJ, Wainwright TE (1956) Statistical mechanical theory of transport properties. In: Proceedings of the international union of pure and applied physics, Brussels

  40. 40.

    Alder BJ, Wright TEWA (1960) Studies in molecular dynamics. II. Behavior of a small number of elastic spheres. J Chem Phys 33(5):1439–1451

    MathSciNet  Article  Google Scholar 

  41. 41.

    Walton OR, Braun RL (1993) Simulation of rotary-drum and repose tests for frictional spheres and rigid sphere clusters. In: Joint DOE/NSF worksop on flow of particulates and fluids, Ithaca

  42. 42.

    Walton OR, Braun RL (1986) Stress calculations for assemblies of inelastic spheres in uniform shear. Acta Mech 63(1–4):73–86

    Article  Google Scholar 

  43. 43.

    Walton OR (1992) Numerical simulation of inelastic, frictional particle-particle interactions. In: Roco MC (ed) Particulate two-phase flow. Butterworths, Boston, pp 884–911

  44. 44.

    Goldsmith W (1960) Impact: the theory and physical behavior of colliding solids. Edward Arnold, London

    MATH  Google Scholar 

  45. 45.

    Dintwa E, Tijskens E, Ramon H (2008) On the accuracy of the Hertz model to describe the normal contact of soft elastic spheres. Granul Matter 10(3):209–221

    Article  MATH  Google Scholar 

  46. 46.

    Parker D, Forster R, Fowler P, Takhar P (2002) Positron emission particle tracking usingthe new Birmingham positron camera. Nucl Instr Methods Phys Res A 477:540–545

    Article  Google Scholar 

  47. 47.

    Wildman RD, Huntley JM, Hansen JP, Parker DJ, Allen DA (2000) Single-particle motion in three-dimensional vibrofluidized granular beds. Phys Rev E 62(3 B):3826–3835

    Article  Google Scholar 

  48. 48.

    Windows-Yule CR, Rosato AD, Rivas N, Parker DJ (2014) Influence of initial conditions on granular dynamics near the jamming transition. New J Phys 16:063016

    Article  Google Scholar 

  49. 49.

    Wildman RD, Huntley JM, Parker DJ (2001) Convection in highly fluidized three-dimensional granular beds. Phys Rev Lett 86:3304–3307

    Article  Google Scholar 

  50. 50.

    Windows-Yule CR, Rivas N, Parker DJ (2013) Thermal convection and temperature inhomogeneity in a vibrofluidized granular bed: the influence of sidewall dissipation. Phys Rev Lett 111:038001

    Article  Google Scholar 

  51. 51.

    Windows-Yule C, Weinhart T, Parker DJ, Thornton AR (2014) Effects of packing density on the segregative behaviors of granular systems. Phys Rev Lett 112:098001

    Article  Google Scholar 

  52. 52.

    Jenkins JT, Zhang C (2002) Kinetic theory for identical, frictional, nearly elastic spheres. Phys Fluids 14(3):1228–1235

    Article  Google Scholar 

  53. 53.

    McNamara S, Young WR (1994) Inelastic collapse in two dimensions. Phys Rev E 50(1):R28–R31

    Article  Google Scholar 

  54. 54.

    Blackmore D, Samulyak R, Rosato A (1999) New mathematical model for particle flow dynamics. J Nonlinear Math Phys 6:198–221

    MathSciNet  Article  MATH  Google Scholar 

  55. 55.

    Blackmore D, Urban K, Rosato A (2010) Integrability analysis of regular and fractional BSR fields. Condens Matter Phys 13(43403):1–7

    Google Scholar 

  56. 56.

    Wu H, Blackmore D (2015) Global well-posedness of the BSR model. In preparation

  57. 57.

    Stirkwerda JC (2004) Finite difference schemes and particle differential equations. SIAM, Philadelphia

    Book  Google Scholar 

  58. 58.

    Tadmor E (2002) Stability of Runga-Kutta schemes by the energy method. In: Estep D, Tavener S (eds) Collected lectures on the preservation of stability under discretization. SIAM, Philadelphia, pp 25–48

    Google Scholar 

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The work of the NJIT group was supported in part by NSF Grant CMMI-1029809. Experiments conducted at the University of Birmingham were made possible through financial support provided by the Hawkesworth Scholarship, set up by the late Dr. Michael Hawkesworth.

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Correspondence to A. D. Rosato.

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Rosato, A.D., Zuo, L., Blackmore, D. et al. Tapped granular column dynamics: simulations, experiments and modeling. Comp. Part. Mech. 3, 333–348 (2016).

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  • Granular column
  • Discrete element simulation
  • Positron emission tracking
  • Continuum model