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Brazil nut effect in a rectangular plate under horizontal vibration

Abstract

An intruder to a group of identical small beads enclosed in a rectangular plate will gradually migrate to either the center or one side of the plate when the plate is subjected to a horizontal vibration. By considering probabilities for a bead to move into and off the space between the intruder and the near side of the plate, we predict that the size ratio and the mass ratio of the intruder to small bead have equal but opposite effects in determining the direction of migration. The prediction is confirmed by a molecular dynamics simulation.

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References

  1. 1

    Rosato A., Strandburg K.J., Prinz F., Swendsen R.H.: Why the Brazil nuts are on tops: size segregation of particulate matter by shaking. Phys. Rev. Lett. 58, 1038 (1987). doi:10.1103/PhysRevLett.58.1038

  2. 2

    Jullien R., Meakin P., Pavlovitch A.: Three-dimension model for particle-size segregation by shaking. Phys. Rev. Lett. 69, 640 (1992). doi:10.1103/PhysRevLett.69.640

  3. 3

    Vanel L., Rosato A.D., Dave R.N.: Rise-time regimes a large sphere in vibrated bulk solids. Phys. Rev. Lett. 78, 1255 (1997). doi:10.1103/PhysRevLett.78.1255

  4. 4

    Knight J.B., Jaeger H.M., Nagel S.R.: Vibration-induced sized separation in granular media: the convection connection. Phys. Rev. Lett. 70, 3728 (1993). doi:10.1103/PhysRevLett.70.3728

  5. 5

    Hong D.C., Quinn P.V., Luding S.: Reverse Brazil nut problem: competition between percolation and condensation. Phys. Rev. Lett. 86, 3423 (2001). doi:10.1103/PhysRevLett.86.3423

  6. 6

    Trujillo L., Alam M., Herrmann H.J.: Segregation in a fluidized binary granular mixture: competition between buoyancy and geometric forces. Europhys. Lett. 64, 190 (2003). doi:10.1209/epl/i2003-00287-1

  7. 7

    Brey J.J., Ruiz-Montero M.J., Moreno F.: Energy partition and segregation for an intruder in a vibrated granular system under gravity. Phys. Rev. Lett. 95, 098001 (2005). doi:10.1103/PhysRevLett.95.098001

  8. 8

    Yan X., Shi Q., Hou M., Lu K., Chan C.K.: Effects of air on the segregation of particles in a shaken granular bed. Phys. Rev. Lett. 91, 14302 (2003). doi:10.1103/PhysRevLett.91.014302

  9. 9

    Breu A.P.J., Ensner H.M., Kruelle C.A., Rehberg I.: Reversing the Brazil-nut effect: competition between percolation and condensation. Phys. Rev. Lett. 90, 014302 (2003). doi:10.1103/PhysRevLett.90.014302

  10. 10

    Schroter M., Ulrich S., Kreft J., Swift J.B., Swinney H.L.: Mechanisms in the size segregation of a binary granular mixture. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 011307 (2006). doi:10.1103/PhysRevE.74.011307

  11. 11

    Schnautz T., Brito R., Kruelle C.A., Rehberg I.: A horizontal Brazil-nut effect and its reverse. Phys. Rev. Lett. 95, 028001 (2005). doi:10.1103/PhysRevLett.95.028001

  12. 12

    Chung F.F., Liu R.-T., Liaw S.-S., Kor J.: Horizontal size segregation in granular matter. Phys. Soc. 50, 224 (2007)

  13. 13

    Luding S., Herrmann H.J., Blumen A.: Scaling behavior of 2-dimensional arrays of beads under external vibrations. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 50, 3100 (1994). doi:10.1103/PhysRevE.50.3100

  14. 14

    Kondic L.: Dynamics of spherical particles on a surface: collision-induced sliding and other effects. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 60, 751 (1999). doi:10.1103/PhysRevE.60.751

  15. 15

    Painter B., Dutt M., Behringer R.P.: Energy dissipation and clustering for a cooling material on a substrate. Physica D 175, 43 (2003). doi:10.1016/S0167-2789(02)00566-3

  16. 16

    Dutt M., Behringer R.P.: Effects of surface friction on a two-dimensional granular system: cooling bound system. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 70, 061304 (2004). doi:10.1103/PhysRevE.70.061304

  17. 17

    Liboff, R.L. (ed.): Kinetic Theory—Classical, Quantum, and Relativistic Descriptions, 2nd edn. Wiley, New York (1998)

  18. 18

    Ciamarra M.P., Coniglio A., Nicodemi M.: Shear instabilities in granular mixtures. Phys. Rev. Lett. 94, 188001 (2005). doi:10.1103/PhysRevLett.94.188001

  19. 19

    Reis P.M., Sykes T., Mullin T.: Phases of granular segregation in a binary mixture. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 74, 051306 (2006). doi:10.1103/PhysRevE.74.051306

  20. 20

    Scherer M.A., Buchholtz V., Pöschel T., Rehberg I.: Swirling granular matter: from rotation to reptation. Phys. Rev. E Stat. Phys. Plasmas Fluids Relat. Interdiscip. Topics 54, R4560 (1996). doi:10.1103/PhysRevE.54.R4560

  21. 21

    Chung F.F., Ju C.-Y., Liaw S.-S.: Spiral trajectory in the horizontal Brazil nut effect. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 77, 061304 (2008). doi:10.1103/PhysRevE.77.061304

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Correspondence to Sy-Sang Liaw.

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Chung, F.F., Liaw, S. & Ju, C. Brazil nut effect in a rectangular plate under horizontal vibration. Granular Matter 11, 79–86 (2009). https://doi.org/10.1007/s10035-008-0122-2

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Keywords

  • Segregation
  • Vibration
  • Horizontal
  • Brazil nut effect