Skip to main content
SpringerLink
Log in

Vibration-induced arching in a deep granular bed

  • Published:
Granular Matter Aims and scope Submit manuscript

Abstract

Forced vertical vibration of a granular layer can drive flow phenomena such as heaping, convection, fluidization, densification, surface waves and arching. Food, mineral processing, and pharmaceuticals industries all utilize vibratory processes for the handling and transport of granular materials. Understanding how a granular material responds when subjected to vibration is essential for equipment design. Three-dimensional discrete element simulations have been used in this study to investigate the convective motion leading to arching in a vertically vibrated, deep granular bed. The undulating granular layer contains alternating regions that first compact and then relax. The dynamics of these regions may depend on material properties such as restitution and friction coefficients; as well as particle shape. The effects of these factors on the kinematics and dynamics of the arching pattern are investigated here. The arching pattern is found to arise from synchronised momentum transfer between the rise and fall of the deforming granular layer and horizontally travelling waves. The arching pattern was found to be stable across a broad range of restitution and friction levels and particle shapes. Particles with high restitution tend to disrupt the timing between the vertical and horizontal periodic flows and affect the stability of the pattern selection. Large friction results in shear resistance, higher bed pressures, lower bulk densities, and delays in the timing of the vertical and horizontal momentum transfer. Non-sphericity leads to increased dilation of the bed, slower sideways velocities, and increased loading on the floor and dissipation rate in the bed.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Cleary P.W.: Large scale industrial DEM modeling. Eng. Comput. 21, 169–204 (2004)

    Article  MATH  Google Scholar 

  2. Cleary, P.W.: Industrial particle flow modelling using DEM. Eng. Comput (2008, in press)

  3. Ketterhagen, W.R., Am Ende, M.T., Hancock, B.C.: Process modeling in the pharmaceutical industry using the Discrete Element Method. J. Pharm. Sci. 1–28 (2008). doi:10.1002/jps.21466

  4. Faraday M.: On a peculiar class of acoustical figures; and on certain forms assumed by groups of particles upon vibrating elastic surfaces. Philos. Trans. R. Soc. Lond. 52, 299–340 (1831)

    Google Scholar 

  5. Pak H., Behringer R.: Surface waves in vertically vibrated granular materials. Phys. Rev. Lett. 71, 1832–1835 (1993)

    Article  ADS  Google Scholar 

  6. Melo F., Umbanhowar P., Swinney H.L.: Transition to parametric wave patterns in a vertically oscillated granular layer. Phys. Rev. Lett. 72, 172–175 (1994)

    Article  ADS  Google Scholar 

  7. Gallas J.A.C., Herrmann H.J., Sokolowski S.: Convection cells in vibrating granular media. Phys. Rev. Lett. 69, 1371–1374 (1992)

    Article  ADS  Google Scholar 

  8. Liffman K., Muniandy K., Rhodes M., Gutteridge D., Metcalfe G.: A segregation mechanism in a vertically shaken bed. Gran. Mat. 3, 205–214 (2001)

    Article  Google Scholar 

  9. Wassgren C.R., Brennen C.E., Hunt M.L.: Vertical vibration of a deep bed of granular material in a container. J. Appl. Mech. 63, 712–719 (1996)

    Article  Google Scholar 

  10. Douady S., Fauve S., Laroche C.: Subharmonic instabilities and defect in a granular layer under vertical vibrations. Europhys. Lett. 8, 621–627 (1989)

    Article  ADS  Google Scholar 

  11. Clement E., Vanel L., Rajchenbach J., Duran J.: Pattern formation in a vibrated granular layer. Phys. Rev. E 53, 2972–2976 (1996)

    Article  ADS  Google Scholar 

  12. Clement E., Labous L.: Pattern formation in a vibrated granular layer: the pattern selection issue. Phys. Rev. E 62, 8314–8323 (2000)

    Article  ADS  Google Scholar 

  13. Sano O.: Dilatancy, buckling, and undulations on a vertically vibrating granular layer. Phys. Rev. E 72, 051302 (2005)

    Article  ADS  Google Scholar 

  14. Melo F., Umbanhower P.B., Swinney H.L.: Hexagons, kinks, and disorder in oscillated granular layers. Phys. Rev. Lett. 75, 3838 (1995)

    Article  ADS  Google Scholar 

  15. Luding S., Clement E., Rajchenbach J., Duran J.: Simulations of pattern formation in vibrated granular media. Europhys. Lett. 36, 247–252 (1996)

    Article  ADS  Google Scholar 

  16. Yang S.C., Hsiau S.S.: Simulated study of the convection cells in a vibrated granular bed. Chem. Eng. Sci. 55, 3627–3637 (2000)

    Article  Google Scholar 

  17. Hsiau S.S., Wang P., Tai C.: Convection cells and segregation in a vibrated granular bed. AIChE J. 48, 1430–1438 (2002)

    Article  Google Scholar 

  18. Saez A., Vivanco F., Melo F.: Size segregation, convection, and arching effect. Phys. Rev. E 72, 021307 (2005)

    Article  ADS  Google Scholar 

  19. Yang S.C.: Density effect on mixing and segregation processes in a vibrated binary granular mixture. Powder Technol. 164, 65–74 (2006)

    Article  Google Scholar 

  20. Wassgren, C.R.: Vibration of granular materials. Ph.D. thesis, California Institute of Technology, CA, USA (1997)

  21. Bougie J., Kreft J., Swift J.B., Swinney H.L.: Onset of patterns in an oscillated granular layer: continuum and molecular dynamics simulations. Phys. Rev. E 71, 021301 (2005)

    Article  ADS  Google Scholar 

  22. Hsiau S.S., Wu M.S.: Arching phenomena in a vibrated granular bed. Adv. Powder Technol. 99, 185–193 (1998)

    Article  Google Scholar 

  23. Eshuis P., Van Der Weele K., VanDer Meer D., Bos R., Lohse D.: Phase diagram of vertically shaken granular matter. Phys. Fluids 19, 123301 (2007)

    Article  ADS  Google Scholar 

  24. Cleary P.W., Sinnott M.D., Morrison R.D.: Analysis of stirred mill performance using DEM simulation: Part 2—Coherent flow structures, liner stress and wear, mixing and transport. Min. Eng. 19, 1551–1572 (2006)

    Article  Google Scholar 

  25. Campbell C.S.: Rapid granular flows. Ann. Rev. Fluid Mech. 22, 57–92 (1990)

    Article  ADS  Google Scholar 

  26. Barker G.C.: Computer simulations of granular materials. In: Anita, M. (eds) Granular Matter: An Interdisciplinary Approach, Springer, New York (1994)

    Google Scholar 

  27. Walton, O.R.: Numerical simulation of inelastic frictional particle-particle interaction, chap 25. In: Roco, M.C. (ed.) Particulate two-phase flow, pp 884–911 (1994)

  28. Cleary P.W.: Discrete element modeling of industrial granular flow applications. TASK. Quart. Sci. Bull. 2, 385–416 (1998)

    Google Scholar 

  29. Schäfer J., Dippel S., Wolf D.E.: Force schemes in simulation of granular material. J. Phys. I France 6, 5 (1996)

    Article  Google Scholar 

  30. Sinnott, M., Cleary, P.W.: Mixing of dry powders with non-spherical shapes. Proceedings of the World Congress Chemical Engineering 7, Glasgow (2005)

  31. Cleary P.W.: DEM Modeling of particulate flow in a screw feeder. Prog. Comput. Fluid Dyn. 7, 128–138 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  32. Walton O.R.: Numerical simulation of inclined chute flows of monodisperse, inelastic, frictional spheres. Mech. Mater. 16, 239–247 (1993)

    Article  ADS  Google Scholar 

  33. Song C., Wang P., Makse H.A.: A phase diagram for jammed matter. Nature 453, 629–632 (2008)

    Article  ADS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CSIRO Mathematical and Information Sciences, Private Bag 33, Clayton South, VIC, 3168, Australia

    Matthew D. Sinnott & P. W. Cleary

Authors
  1. Matthew D. Sinnott
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. P. W. Cleary
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Matthew D. Sinnott.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sinnott, M.D., Cleary, P.W. Vibration-induced arching in a deep granular bed. Granular Matter 11, 345–364 (2009). https://doi.org/10.1007/s10035-009-0147-1

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10035-009-0147-1

Keywords

Search

Navigation