Granular Matter

, Volume 16, Issue 2, pp 175–183 | Cite as

Flow profile of granular avalanches with imposed vertical vibration

  • Nora C. Swisher
  • Brian C. UtterEmail author
Original Paper


We report experimental results on the effect of imposed vertical vibration on the flow of pentagonal grains in a two-dimensional rotation drum. While dimensionless acceleration \(\varGamma \) can be tuned either by increasing vibration frequency or amplitude, the former leads to stabilization an increase in the angle of repose while the latter leads to destabilization and a decrease in the critical angle for failure. Increased vibration amplitude leads to continuous avalanching and a more uniform flow profile, with a flowing layer composed of increasingly long-lived, shallower avalanches before a continuous flow regime is reached. The slope and grain-scale roughness of the surface decrease and interface curvature increases as vibration amplitude is increased and collective motion allows relaxation of the surface. While qualitative flow characteristics are similar both with and without vibration, vibration allows the system to evolve continuously in a nearly steady-state profile.


Avalanche Vibration Rotating drum Pentagons 



We gratefully acknowledge the support of the Research Corporation (Cottrell College Science Award No. CC7145/7266) and DOD ASSURE Grant # DMR-0353773.


  1. 1.
    Otsuki, M., Hayakawa, H.: Critical scaling near jamming transition for frictional granular particles. Phys. Rev. E 83, 051301 (2011)ADSCrossRefGoogle Scholar
  2. 2.
    Coussot, P., Roussel, N., Jarny, S., Chanson, H.: Continuous or catastrophic solid–liquid transition in jammed systems. Phys. Fluids 17, 011704 (2005)ADSCrossRefGoogle Scholar
  3. 3.
    Luck, J.M., Mehta, A.: Dynamics at the angle of repose: jamming, bistability, and collapse. J. Stat. Mech. Theor. Exp. 2004, P10015 (2004)Google Scholar
  4. 4.
    Olson, J., Priester, M., Luo, J., Chopra, S., Zieve, R.J.: Packing fractions and maximum angles of stability of granular materials. Phys. Rev. E 72, 031302 (2005)ADSCrossRefGoogle Scholar
  5. 5.
    Grasselli, Y., Herrmann, H.J.: On the angles of dry granular heaps. Phys. A 246, 301 (1997)CrossRefGoogle Scholar
  6. 6.
    Liu, A.J., Nagel, S.: Nonlinear dynamics: jamming is not just cool any more. Nature 396, 21 (1998)ADSCrossRefGoogle Scholar
  7. 7.
    Papanikolaou, S., Dimiduk, D.M., Choi, W., Sethna, J.P., Uchic, M.D., Christopher, F., Woodward, C.F., Zapperi, S.: Quasi-periodic events in crystal plasticity and the self-organized avalanche oscillator. Nature 490, 517 (2012)ADSCrossRefGoogle Scholar
  8. 8.
    Amon, D.L., Niculescu, T., Utter, B.C.: Granular avalanches in a two-dimensional rotating drum with imposed vertical vibration. Phys. Rev. E 88, 012203 (2013)ADSCrossRefGoogle Scholar
  9. 9.
    Ottino, J.M., Khakhar, D.V.: Mixing and segregation of granular materials. Annu. Rev. Fluid Mech. 32, 55 (2000)ADSCrossRefMathSciNetGoogle Scholar
  10. 10.
    Kabla, A., Debrégeas, G., Di Meglio, J., Senden, T.J.: X-ray observation of micro-failures in granular piles approaching an avalanche. Europhys. Lett. 71, 932 (2005)ADSCrossRefGoogle Scholar
  11. 11.
    Fischer, R., Gondret, P., Perrin, B., Rabaud, M.: Dynamics of dry granular avalanches. Phys. Rev. E 78, 021302 (2008)ADSCrossRefGoogle Scholar
  12. 12.
    Fischer, R., Gondret, P., Rabaud, M.: Transition by intermittency in granular matter: from discontinuous avalanches to continuous flow. Phys. Rev. Lett. 103, 128002 (2009)ADSCrossRefGoogle Scholar
  13. 13.
    Christov, I.C., Ottino, J.M., Lueptow, R.M.: Streamline jumping: a mixing mechanism. Phys. Rev. E 81, 046307 (2010)ADSCrossRefGoogle Scholar
  14. 14.
    Jain, N., Ottino, J.M., Lueptow, R.M.: An experimental study of the flowing granular layer in a rotating tumbler. Phys. Fluids 14, 572 (2002)ADSCrossRefGoogle Scholar
  15. 15.
    Gray, J.M.N.T.: Granular flow in partially filled slowly rotating drums. J. Fluid Mech. 441, 1 (2001)ADSCrossRefzbMATHMathSciNetGoogle Scholar
  16. 16.
    Orpe, A.V., Khakhar, D.V.: Scaling relations for granular flow in quasi-two-dimensional rotating cylinders. Phys. Rev. E 64, 031302 (2001)ADSCrossRefGoogle Scholar
  17. 17.
    Félix, G., Falk, V., D’Ortona, U.: Granular flows in a rotating drum: the scaling law between velocity and thickness of the flow. Eur. Phys. J. E 22, 25 (2007)CrossRefGoogle Scholar
  18. 18.
    Daerr, A., Douady, S.: Two types of avalanche behaviour in granular media. Nature 399, 241 (1999)ADSCrossRefGoogle Scholar
  19. 19.
    Rajchenbach, J.: Dynamics of grain avalanches. Phys. Rev. Lett. 88, 014301 (2002)ADSCrossRefGoogle Scholar
  20. 20.
    Scheller, T., Huss, C., Lumay, G., Vandewalle, N., Dorbolo, S.: Precursors to avalanches in a granular monolayer. Phys. Rev. E 74, 031311 (2006)ADSCrossRefGoogle Scholar
  21. 21.
    Staron, L., Radjai, F., Vilotte, J.-P.: Granular micro-structure and avalanche precursors. J. Stat. Mech. Theor. Exp. 2006, P07014 (2006)Google Scholar
  22. 22.
    Kiesgen De Richter, S., Le Caër, G., Delannay, R.: Dynamics of rearrangements during inclination of granular packings: the avalanche precursor regime. J. Stat. Mech. Theor. Exp. 2012, P04013 (2012)Google Scholar
  23. 23.
    Staron, L., Vilotte, J.-P., Radjai, F.: Preavalanche instabilities in a granular pile. Phys. Rev. Lett. 89, 204302 (2002)ADSCrossRefGoogle Scholar
  24. 24.
    Deboeuf, S., Dauchot, O., Staron, L., Mangeney, A., Vilotte, J.-P.: Jamming transition of a granular pile below the angle of repose. Eur. Phys. J B 36, 105 (2003)ADSCrossRefGoogle Scholar
  25. 25.
    Kiesgen De Richter, S., Zaitsev, V. Y., Richard, P., Delannay, R., Le Caër, G., Tournat, V.: Experimental evidence of ageing and slow restoration of the weak-contact conguration in tilted 3D granular packings. J. Stat. Mech. Theor. Exp. 2010, P11023 (2010)Google Scholar
  26. 26.
    Rajchenbach, J.: Flow in powders: from discrete avalanches to continuous regime. Phys. Rev. Lett. 65, 2221 (1990)ADSCrossRefGoogle Scholar
  27. 27.
    Liu, X.Y., Specht, E., Mellmann, J.: Slumping-rolling transition of granular solids in rotary kilns. Chem. Eng. Sci. 60, 3629 (2005)CrossRefGoogle Scholar
  28. 28.
    Sepúlveda, N., Krstulovic, G., Rica, S.: Scaling laws in granular continuous avalanches in a rotating drum. Phys. A 356, 178 (2005)CrossRefGoogle Scholar
  29. 29.
    Komatsu, T., Inagaki, S., Nakagawa, N., Nasuno, S.: Creep motion in a granular pile exhibiting steady surface flow. Phys. Rev. Lett. 86, 1757 (2001)ADSCrossRefGoogle Scholar
  30. 30.
    Aguirre, M.A., Calvo, A., Ippolito, I., Medus, A., Mancuso, M.: Rearrangements in a two-dimensional packing of disks. Phys. Rev. E 73, 041307 (2006)ADSCrossRefGoogle Scholar
  31. 31.
    Nowak, E., Knight, J., Povinelli, M., Jaeger, H., Nagel, S.: Reversibility and irreversibility in the packing of vibrated granular material. Powder Technol. 94, 79 (1997)CrossRefGoogle Scholar
  32. 32.
    Richard, P., Philippe, P., Barbe, F., Bourlès, S., Thibault, X., Bideau, D.: Analysis by x-ray microtomography of a granular packing undergoing compaction. Phys. Rev. E 68, 020301 (2003)ADSCrossRefGoogle Scholar
  33. 33.
    Jaeger, H., Liu, C.-h., Nagel, S.: Relaxation at the angle of repose. Phys. Rev. Lett. 62, 40 (1989)Google Scholar
  34. 34.
    Ciamarra, M., Coniglio, A., De Martino, D., Nicodemi, M.: Shear- and vibration-induced order-disorder transitions in granular media. Eur. Phys. J. E 24, 411 (2007)CrossRefGoogle Scholar
  35. 35.
    Rubin, D., Goldenson, N., Voth, G.: Failure and strengthening of granular slopes under horizontal vibration. Phys. Rev. E 74, 051307 (2006)ADSCrossRefGoogle Scholar
  36. 36.
    Metcalfe, G., Tennakoon, S., Kondic, L., Schaeffer, D., Behringer, R.: Granular friction, coulomb failure, and the fluid-solid transition for horizontally shaken granular materials. Phys. Rev. E 65, 031302 (2002)ADSCrossRefGoogle Scholar
  37. 37.
    Wassgren, C.R., Hunt, M.L., Freese, P.J., Palamara, J., Brennen, C.E.: Effects of vertical vibration on hopper flows of granular material. Phys. Fluids 14, 3439 (2002)ADSCrossRefGoogle Scholar
  38. 38.
    Sistla, P., Baran, O., Chen, Q., Fohanno, S., Poole, P.H., Maitinuzzi, R.J.: Bulk motion of granular matter in an agitated cylindrical bed. Phys. Rev. E 71, 011303 (2005) Google Scholar
  39. 39.
    Kim, K., Moon, J.K., Park, J.J., Kim, H.K., Pak, H.K.: Jamming transition in a highly dense granular system under vertical vibration. Phys. Rev. E 72, 011302 (2005)ADSCrossRefGoogle Scholar
  40. 40.
    King, P., Swift, M., Benedict, K., Routledge, A.: Surface stability of granular systems under horizontal and vertical vibration: the applicability of a coefficient of friction. Phys. Rev. E 62, 6982 (2000)ADSCrossRefGoogle Scholar
  41. 41.
    Vidales, A.M., Pugnaloni, L.A., Ippolito, I.: Compaction and arching in tapped pentagon deposits. Granul. Matter 11(1), 53 (2009)CrossRefzbMATHGoogle Scholar
  42. 42.
    Dijksman, J.A., Wortel, G., van Dellen, L., Dauchot, O., van Hecke, M.: Jamming, yielding and rheology of weakly vibrated granular media. Phys. Rev. Lett. 107, 108303 (2011)ADSCrossRefGoogle Scholar
  43. 43.
    Pak, H.K., Behringer, R.P.: Surface waves in vertically vibrated granular materials. Phys. Rev. Lett. 71, 1832 (1993)ADSCrossRefGoogle Scholar
  44. 44.
    Barker, G.C., Mehta, A.: Vibrated powders: structure, correlations, and dynamics. Phys. Rev. A 45, 3435 (1992)ADSCrossRefGoogle Scholar
  45. 45.
    Azéma, E., Estrada, N., Radja, F.: Nonlinear effects of particle shape angularity in sheared granular media. Phys. Rev. E 86, 041301 (2012)ADSCrossRefGoogle Scholar
  46. 46.
    Vidales, A.M., Pugnaloni, L.A., Ippolito, I.: Pentagon deposits unpack under gentle tapping. Phys. Rev. E 77, 051305 (2008)ADSCrossRefGoogle Scholar
  47. 47.
    Riley, G.S., Mann, G.R.: Effects of particle shape on angles of repose and bulk densities of a granular solid. Mater. Res. Bull. 7, 163 (1972)CrossRefGoogle Scholar
  48. 48.
    Gravish, N., Franklin, S.V., Hu, D.L., Goldman, D.I.: Entangled granular media. Phys. Rev. Lett. 108, 208001 (2012)ADSCrossRefGoogle Scholar
  49. 49.
    Jiao, Y., Stillinger, F.H., Torquato, S.: Distinctive features arising in maximally random jammed packings of superballs. Phys. Rev. E 81, 041304 (2010)ADSCrossRefMathSciNetGoogle Scholar
  50. 50.
    Tegzes, P., Vicsek, T., Schiffer, P.: Development of correlations in the dynamics of wet granular avalanches. Phys. Rev. E 67, 051303 (2003)ADSCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Department of Physics and AstronomyJames Madison UniversityHarrisonburgUSA

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