Skip to main content
SpringerLink
Log in

Collective motion of inelastic particles between two oscillating walls

  • Original Paper
  • Published:
Granular Matter Aims and scope Submit manuscript

Abstract

This study theoretically considers the motion of N identical inelastic particles between two oscillating walls. The particles’ average energy increases abruptly at certain critical filling fractions, wherein the system changes into a solid-like phase with particles clustered in their compact form. Molecular dynamics simulations of the system show that the critical filling fraction is a decreasing function of vibration amplitude independent of vibration frequency, which is consistent with previous experimental results. This study considers the entire group of particles as a giant pseudo-particle with an effective size and an effective coefficient of restitution. The N-particles system is then analytically treated as a one-particle problem. The critical filling fraction’s dependence on vibration amplitude can be explained as a necessary condition for a stable resonant solution. The fluctuation to the system’s mean flow energy is also studied to show the relation between the granular temperature and the system phase.

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

    Article  ADS  Google Scholar 

  2. Clement E., Vanel L., Rajchenbach J., Duran J.: Pattern formation in a vibrated two-dimensional granular layer. Phys. Rev. E 53, 2972 (1996)

    Article  ADS  Google Scholar 

  3. Rosato A., Strandburg Katherine J., Prinz Friedrich, Swendsen Robert H.: Why the Brazil nuts are on top: size segregation of particulate matter by shaking. Phys. Rev. Lett. 58, 1038 (1987)

    Article  MathSciNet  ADS  Google Scholar 

  4. Schnautz T., Brito R., Kruelle C.A., Rehberg I.: A horizontal brazil-but effect and its reverse. Phys. Rev. Lett. 95, 028001 (2005)

    Article  ADS  Google Scholar 

  5. Chung F.F., Liaw S.-S., Ju C.-Y.: Brazil nut effect in a rectangular plate under horizontal vibration. Granular Matter 11, 79 (2009)

    Article  MATH  Google Scholar 

  6. Clement E., Rajchenbach J.: Fluidization of a bidimensional powder. Europhys. Lett. 16, 133–138 (1991)

    Article  ADS  Google Scholar 

  7. Gallas J.A.C., Herrmann H.J., Sokolowski S.: Molecular dynamics simulation of powder fluidization in two dimensions. Phys. A 189, 437–446 (1992)

    Article  Google Scholar 

  8. Olafsen J.S., Urbach J.S.: Cluster, order, and collapse in a driven granular monolayer. Phys. Rev. Lett. 81, 4369 (1998)

    Article  ADS  Google Scholar 

  9. Quinn P.V., Hong D.C.: Liquid–solid transition of hard spheres under gravity. Phys. Rev. E 62, 8295 (2000)

    Article  ADS  Google Scholar 

  10. To K., Lai P.-Y., Pak H.K.: Jamming of granular flow in a two-dimensional hopper. Phys. Rev. Lett. 86, 71 (2001)

    Article  ADS  Google Scholar 

  11. Reis P.M., Ingale R.A.M.D.: Crystallization of a quasi-two-dimensional granular fluid. Shattuck Phys. Rev. Lett. 96, 258001 (2006)

    Article  ADS  Google Scholar 

  12. Reis P.M., Ingale R.A., Shattuck M.D.: Caging dynamics in a granular fluid. Phys. Rev. Lett. 98, 188301 (2007)

    Article  ADS  Google Scholar 

  13. Jenkins J.T., Richman M.W.: Kinetic theory for plane flows of dense gas of identical, rough, inelastic, circular disks. Phys. Fluids 28(12), 3485 (1985)

    Article  ADS  MATH  Google Scholar 

  14. Grossman E.L., Zhou Tong, Ben-Naim E.: Towards granular hydrodynamics in two dimensions. Phys. Rev. E 55, 4200 (1997)

    Article  ADS  Google Scholar 

  15. Goldshtein A., Alexeev A., Shapiro M.: Hydrodynamics of resonance oscillations of columns of inelastic particles. Phys. Rev. E 59, 6967 (1999)

    Article  ADS  Google Scholar 

  16. Pieranski P.: Jumping particle model. Period doubling cascade in an experimental system. J. Phys. 44, 573–578 (1983)

    Article  MathSciNet  Google Scholar 

  17. Burkhardt T.W., Kotsev S.N.: Equilibrium statistic of an inelastically bouncing ball, subject to gravity and a random force. Phys. Rev. E 73, 046121 (2006)

    Article  ADS  Google Scholar 

  18. Barroso J.J., Carneiro M.V., Macau E.E.N.: Bouncing ball problem: stability of the periodic modes. Phys. Rev. E 79, 026206 (2009)

    Article  MathSciNet  ADS  Google Scholar 

  19. Luck J.M., Mehta A.: Bouncing ball with a finite restitution: chattering, locking, and chaos. Phys. Rev. E 48, 3988 (1993)

    Article  MathSciNet  ADS  Google Scholar 

  20. Ulam, S.: Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability (University of California Press, Berkeley, 1961), Vol. 3, p. 315

  21. Warr S., Cooke W., Ball R.C., Huntley J.M.: Probability distribution functions for a single-particle vibrating in one dimension: experimental study and theoretical analysis. Phys. A 231, 551–574 (1996)

    Article  Google Scholar 

  22. Geminard J.-C., Laroche C.: Energy of a single bead bouncing on a vibrating plate: experiments and numerical simulations. Phys. Rev. E 68, 031305 (2003)

    Article  ADS  Google Scholar 

  23. Javier Brey J., Ruiz-Montero M.J., Moreno F.: Boundary conditions and normal state for a vibrated granular fluid. Phys. Rev. E 62, 5339 (2000)

    Article  ADS  Google Scholar 

  24. Straβburger G., Rehberg I.: Crystallization in a horizontally vibrated monolayer of spheres. Phys. Rev. E 62, 2517 (2000)

    Article  ADS  Google Scholar 

  25. Aumaitre S., Schnautz T., Kruelle C.A., Rehberg I.: Granular phase transition as a precondition for segregation. Phys. Rev. Lett. 90, 114302 (2003)

    Article  ADS  Google Scholar 

  26. Chung F.F., Liaw S.S., Ho M.C.: Energy and phase transition in a horizontally vibrating granular system. Granular Matter 12, 369–374 (2010)

    Article  Google Scholar 

  27. Helbing D., Farkas I.J., Vicsek T.: Freezing by heating in a driven mesoscopic system. Phys. Rev. Lett. 84, 1240 (2000)

    Article  ADS  Google Scholar 

  28. Dzubiella J., Hoffmann G.P., Lowen H.: Lane formation in colloidal mixtures driven by an external field. Phys. Rev. E 65, 021402 (2002)

    Article  ADS  Google Scholar 

  29. Bernu B., Mazighi R.: One-dimensional bounce of inelastically colliding marbles on a wall. J. Phys. A Math. Gen. 23, 5745–5754 (1990)

    Article  ADS  MATH  Google Scholar 

  30. McNamara S., Young W.R.: Inelastic collapse and clumping in a one-dimensional granular medium. Phys. Fluids A 4, 496 (1992)

    Article  ADS  Google Scholar 

  31. Luding S., Clement E., Blumen A., Rajchenbach J., Duran J.: Studies of columns of beads under external vibrations. Phys. Rev. E 49, 1634 (1994)

    Article  ADS  Google Scholar 

  32. Lee J.: Subharmonic motion of particles in a vibrating tube. Phys. Rev. E 58, R1218 (1998)

    Article  ADS  Google Scholar 

  33. Jiang Z.H., Wang Y.Y., Wu J.: Subharmonic motion of granular particles under vertical vibrations. Europhys. Lett. 74(3), 417 (2006)

    Article  ADS  Google Scholar 

  34. Chen W., To K.: Unusual diffusion in a quasi-two-dimensional granular gas. Phys. Rev. E 80, 061305 (2009)

    Article  ADS  Google Scholar 

  35. Hu G., Li Y., Hou M., To K.: Traveling shock front in quasi-two-dimensional granular flows. Phys. Rev. E 81, 011305 (2010)

    Article  ADS  Google Scholar 

  36. van Zon J.S., MacKintosh F.C.: Velocity distributions in dissipative granular gases. Phys. Rev. Lett. 93, 038001 (2004)

    Article  ADS  Google Scholar 

  37. Szymanski K., Labaye Y.: Energy dissipation in the dynamics of a bouncing ball. Phys. Rev. E 59, 2863 (1999)

    Article  ADS  Google Scholar 

  38. Kumaran V.: Temperature of a granular material “fluidized” by external vibrations. Phys. Rev. E 57, 5660 (1998)

    Article  ADS  Google Scholar 

  39. Carnahan N.F., Starling K.E.: Equations of state of non-attracting rigid spheres. J. Chem. Phys. 51, 635 (1969)

    Article  ADS  Google Scholar 

  40. Allen M.P., Tildesley D.J.: Computer Simulation of Liquids. Oxford University Press, UK (1987)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, National Chung-Hsing University, 250 Guo-Kuang Road, Taichung, 402, Taiwan

    Fei Fang Chung, Sy-Sang Liaw & Wei Chun Chang

Authors
  1. Fei Fang Chung
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sy-Sang Liaw
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wei Chun Chang
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fei Fang Chung.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Chung, F.F., Liaw, SS. & Chang, W.C. Collective motion of inelastic particles between two oscillating walls. Granular Matter 13, 787–794 (2011). https://doi.org/10.1007/s10035-011-0291-2

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10035-011-0291-2

Keywords

Search

Navigation