Skip to main content
Log in

Effect of the confinement on the properties of ultrasonic vibrated granular gases

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

Abstract

The properties of a ultrasonic vibrated granular gas are investigated by using an event-driven Molecular Dynamics simulation of inelastic hard spheres that are fluidized by a vibrating bottom wall (sonotrode) in boxes with different geometries showing either no or an increased confinement. It appears that geometry controls dramatically not only the distribution of wall impacts and their velocity and impact angles, but also more fundamental properties of the granular gas such as temperature and density. For geometries displaying an acute angle (prism), stacking is found, which induces a strong temperature and density gradient. The underlying origin of such phenomena for the granular gas arises from the spatial limitation, confinement, combined with the inelastic collisions induced by closely located side walls. It underscores the possibility that kinetic and thermodynamic properties of granular gases can be changed by simple geometries inducing spatial limitation.

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

Access this article

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

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10

Similar content being viewed by others

References

  1. Goldhirsch, I.: Rapid granular flows. Annu. Rev. Fluid Mech. 35, 267–293 (2003)

    Article  MathSciNet  ADS  Google Scholar 

  2. de Gennes, P.-G.: Granular matter : A tentative view. Rev. Mod. Phys. 71, S374–S382 (1999)

    Article  Google Scholar 

  3. Capriz, G., Giovine, P. (eds.): Mathematical Models of Granular Matter. Springer, Berlin (2008)

    MATH  Google Scholar 

  4. Brillantov, N.V., Pöschel, T.: Kinetic Theory of Granular Gases. Oxford University Press, Oxford (2004)

    Book  Google Scholar 

  5. Nicodemi, M.: Dynamical response functions in models of vibrated granular media. Phys. Rev. Lett. 82, 3734–3737 (1999)

    Article  ADS  Google Scholar 

  6. Nicodemi, M., Coniglio, A.: Aging in out of equilibrium dynamics of models for granular media. Phys. Rev. Lett. 82, 916–919 (1999)

    Article  ADS  Google Scholar 

  7. Talbot, J., Viot, P.: Wall-enhanced convection in vibrofluidized granular systems. Phys. Rev. Lett. 89, 064301 (2002)

    Article  ADS  Google Scholar 

  8. Johnson, O., Toussaint, R., Maloy, K.J., Flekkoy, E.G.: Pattern formation during air injection into granular materials confined in a circular Hele-Shaw cell. Phys. Rev. E 74(1–13), 011301 (2006)

    Article  ADS  Google Scholar 

  9. Kudrolli, A.: Size separation in vibrated granular matter. Rep. Prog. Phys. 67, 209–247 (2004)

    Article  ADS  Google Scholar 

  10. Ferreira, J.A.M., Boorrego, L.F.P., Costa, J.D.M.: Effects of surface treatments on the fatigue of notched bend specimens. Fatigue Fract. Eng. Mater. Struct. 19, 111–117 (1996)

    Google Scholar 

  11. Zum Gahr, K.-H.: Microstructure and Wear of Materials. Tribology Series. Elsevier, Amsterdam (1987)

    Google Scholar 

  12. Micoulaut, M., Retraint, D., Viot, P., François, M.: Heterogeneousutrasonic shot peening: Experiment and simulation. In: Proceedings of the International Conference on Shot Peening, 9, 119-125 (2005)

  13. Micoulaut, M., Mechkov, S., Retraint, D., François, M., Viot, P.: Granular gases in mechanical engineering: On the origin of heterogeneous ultrasonic shot peening. Granul. Matter 9, 25–33 (2007)

    Article  MATH  Google Scholar 

  14. Lu, J., Peyre, P., Nonga, C.O., Benamar, A., Flavenot, J.F.: Residual Stress and Mechanical Surface Treatments. SEM, Baltimore (1994)

    Google Scholar 

  15. Badreddine, J., Rouhaud, E., Micoulaut, M., Retraint, D., Remy, S., François, M., Baboeuf, G., Desfontaine, V.: Simulation and experimental approach for shot velocity evaluation in ultrasonic shot peening. Mécanique et Industrie 12, 223–229 (2011)

    Article  Google Scholar 

  16. Wang, K., Tao, N.R., Liu, G., Lu, J., Lu, K.: Plastic strain-induced grain refinement at the nanometer scale in copper. Acta Materialia 54, 5281–5291 (2006)

    Article  Google Scholar 

  17. Goldsmith, W.: The Theory and Physical Behaviour of Colliding Solids. Dover Ed, London (1990)

    Google Scholar 

  18. Hertzsch, J.M., Spahn, F., Brilliantov, N.V.: On low-velocity collisions of viscoelastoc particles. J. Phys. II 5, 1725–1735 (1995)

    Article  Google Scholar 

  19. Brilliantov, N.V., Spahn, F., Hertzsch, J.M., Pöschel, T.: Models for collisions in granular gases. Phys. Rev. E 53, 5382–5392 (1996)

    Article  ADS  Google Scholar 

  20. Schwager, T., Pöschel, T.: Coefficient of normal restitution of viscous particles and cooling rate of granular gases. Phys. Rev. E 57, 650–654 (1998)

    Article  ADS  Google Scholar 

  21. Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1985)

  22. Zener, C.: The intrinsic inelasticity of large plates. Phys. Rev. 59, 669–673 (1941)

    Google Scholar 

  23. Sondergaard, R., Chaney, K., Brennen, C.E.: Measurements of solid spheres bouncing off flat plates. J. Appl. Mech. 57, 694 (1990)

    Article  ADS  Google Scholar 

  24. Micoulaut, M., Retraint, D., Viot, P., Francois, M.: Grenaillage ultrasonore hétérogène. Actes du 17ème Congrès Français de Mécanique 689, 1–6 (2005)

    Google Scholar 

  25. McNamara, S., Falcon, E.: Simulation of vibrated granular medium with impact-velocity-dependent restitution coefficient. Phys. Rev. E 71, 031302 (2005)

    Article  ADS  Google Scholar 

  26. Brach, R.M.: Impact dynamics with applications to solid particle erosion. Int. J. Impact Eng. 7, 37–53 (1988)

    Article  Google Scholar 

  27. Talbot, J., Viot, P.: Torroidal convection roll in a three-dimensional granular system. Physica A 317, 672–676 (2002)

    Article  ADS  Google Scholar 

  28. O’Hern, C.S., Silbert, L.E., Liu, A.J., Nagel, S.R.: Jamming at zero temperature and zero applied stress: The epitome of disorder. Phys. Rev. E 68, 011306 (2003)

    Article  ADS  Google Scholar 

  29. Torquato, S., Truskett, T.M., Debenedetti, P.M.: Is random close packing of spheres well defined. Phys. Rev. Lett. 84, 2064–2067 (2000)

    Article  ADS  Google Scholar 

  30. Berthier, L., Jacquin, H., Zamponi, F.: Microscopic theory of the jamming transition of harmonic spheres. Phys. Rev. E 84, 051103 (2011)

    Article  ADS  Google Scholar 

  31. Viswanathan, H., Wildman, R.D., Huntley, J.M., Martin, T.W.: Comparison of kinetic theory predictions with experimental results for a vibrated three-dimensional granular bed. Phys. Fluids 18, 113302 (2006)

    Article  ADS  Google Scholar 

  32. Wildman, R.D., Huntley, J.M., Parker, D.J.: Granular temperature profiles in three-dimensional vibrofluidized granular beds. Phys. Rev. E 63, 061311 (2001)

    Article  ADS  Google Scholar 

  33. Javier Brey, J., Ruiz-Montero, M.J., Moreno, F.: Hydrodynamics of an open vibrated granular system. Phys. Rev. E 63, 061305 (2001)

    Article  ADS  Google Scholar 

Download references

Acknowledgments

It is a pleasure to acknowledge ongoing discussions and support from D. Le Saunier, V. Desfontaine, G. Doubre, S. Mechkov, M. Prioul, P. Renaud, J. Talbot and P. Viot. SNECMA (Groupe Safran) and SONATS (Europe technologies Group) are gratefully acknowledged for financial support.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to M. Micoulaut.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Supplementary material 1 (mpg 3028 KB)

Supplementary material 2 (mpg 7708 KB)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Badreddine, J., Micoulaut, M., Rouhaud, E. et al. Effect of the confinement on the properties of ultrasonic vibrated granular gases. Granular Matter 15, 367–376 (2013). https://doi.org/10.1007/s10035-013-0397-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10035-013-0397-9

Keywords

Navigation