Liquid–solid-like transition in quasi-one-dimensional driven granular media


The theory of non-ideal gases at thermodynamic equilibrium, for instance the van der Waals gas model, has played a central role in our understanding of coexisting phases, as well as the transitions between them. In contrast, the theory fails with granular matter because collisions between the grains dissipate energy, and their macroscopic size renders thermal fluctuations negligible. When a mass of grains is subjected to mechanical vibration, it can make a transition to a fluid state. In this state, granular matter exhibits patterns and instabilities that resemble those of molecular fluids. Here, we report a granular solid–liquid phase transition in a vibrating granular monolayer. Unexpectedly, the transition is mediated by waves and is triggered by a negative compressibility, as for van der Waals phase coexistence, although the system does not satisfy the hypotheses used to understand atomic systems. The dynamic behaviour that we observe—coalescence, coagulation and wave propagation—is common to a wide class of phase transitions. We have combined experimental, numerical and theoretical studies to build a theoretical framework for this transition.

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Figure 1: Schematic representation of the system.
Figure 2: Solid–liquid coexistence in the confined system.
Figure 3: Pressure versus density measurements.
Figure 4: Density and longitudinal momentum space–time diagrams for early stages of the solid cluster formation.


  1. 1

    Jaeger, H. M., Nagel, S. R. & Behringer, R. P. Granular solids, liquids, and gases. Rev. Mod. Phys. 68, 1259–1273 (1996).

    ADS  Article  Google Scholar 

  2. 2

    Aranson, I. S. & Tsimring, L. S. Patterns and collective behavior in granular media: Theoretical concepts. Rev. Mod. Phys. 78, 641–692 (2006).

    ADS  Article  Google Scholar 

  3. 3

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

    ADS  Article  Google Scholar 

  4. 4

    Fauve, S., Douady, S. & Laroche, C. Collective behaviors of granular masses under vertical vibrations. J. Physique 50, 187–191 (1989).

    Google Scholar 

  5. 5

    Ramírez, R., Risso, D. & Cordero, P. Thermal convection in fluidized granular systems. Phys. Rev. Lett. 85, 1230–1233 (2000).

    ADS  Article  Google Scholar 

  6. 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).

    ADS  Article  Google Scholar 

  7. 7

    Melo, F., Umbanhowar, P. & Swinney, H. L. Hexagons, kinks and disorder in oscillated granular layers. Phys. Rev. Lett. 75, 3838–3841 (1995).

    ADS  Article  Google Scholar 

  8. 8

    Umbanhowar, P. B., Melo, F. & Swinney, H. L. Localized excitations in a vertically vibrated granular layer. Nature 382, 793–796 (1996).

    ADS  Article  Google Scholar 

  9. 9

    Mujica, N. & Melo, F. Solid–liquid transition and hydrodynamic surface waves in vibrated granular layers. Phys. Rev. Lett. 80, 5121–5124 (1998).

    ADS  Article  Google Scholar 

  10. 10

    Olafsen, J. S. & Urbach, J. S. Clustering, order, and collapse in a driven granular monolayer. Phys. Rev. Lett. 81, 4369–4372 (1998).

    ADS  Article  Google Scholar 

  11. 11

    Cafiero, R., Luding, S. & Herrmann, H. J. Two-dimensional granular gas of inelastic spheres with multiplicative driving. Phys. Rev. Lett. 84, 6014–6017 (2000).

    ADS  Article  Google Scholar 

  12. 12

    Aranson, I. S. et al. Electrostatically driven granular media: Phase transitions and coarsening. Phys. Rev. Lett. 84, 3306–3309 (2000).

    ADS  Article  Google Scholar 

  13. 13

    Aranson, I. S., Meerson, B., Sasorov, P. V. & Vinokur, V. M. Phase separation and coarsening in electrostatically driven granular media. Phys. Rev. Lett. 88, 204301 (2002).

    ADS  Article  Google Scholar 

  14. 14

    Prevost, A., Melby, P., Egolf, D. A. & Urbach, J. S. Non-equilibrium two-phase coexistence in a confined granular layer. Phys. Rev. E 70, 050301(R) (2004).

    ADS  Article  Google Scholar 

  15. 15

    Melby, P. et al. The dynamics of thin vibrated granular layers. J. Phys. Condens. Matter 17, S2689–S2704 (2005).

    Article  Google Scholar 

  16. 16

    Argentina, M., Clerc, M. G. & Soto, R. van der Waals-like transition in fluidized granular matter. Phys. Rev. Lett. 89, 044301 (2002).

    ADS  Article  Google Scholar 

  17. 17

    Cartes, C., Clerc, M. G. & Soto, R. van der Waals normal form for a one-dimensional hydrodynamic model. Phys. Rev. E 70, 031302 (2004).

    ADS  Article  Google Scholar 

  18. 18

    Schmidt, M. & Löwen, H. Phase diagram of hard spheres confined between two parallel plates. Phys. Rev. E 55, 7228–7241 (1997).

    ADS  Article  Google Scholar 

  19. 19

    Graham, R. & Tel, T. Nonequilibrium potential for coexisting attractors. Phys. Rev. A 33, 1322–1337 (1986).

    ADS  MathSciNet  Article  Google Scholar 

  20. 20

    Landau, L. D. & Lifschitz, D. Statistical Physics (Pergamon, Oxford, 1980).

    Google Scholar 

  21. 21

    Cross, M. C. & Hohenberg, P. C. Pattern formation outside of equilibrium. Rev. Mod. Phys. 65, 851–1112 (1993).

    ADS  Article  Google Scholar 

  22. 22

    Guton, J. D., San Miguel, M. & Sanhi, P. S. in Phase Transitions and Critical Phenomena Vol. 8 (eds Domb, D. & Lewowitz, J. L.) (Academic, London, 1983).

    Google Scholar 

  23. 23

    Josserand, C. & Rica, S. Coalescence and droplets in the subcritical nonlinear Schrödinger equation. Phys. Rev. Lett. 78, 1215–1218 (1997).

    ADS  Article  Google Scholar 

  24. 24

    Josserand, C. Dynamique des superfluides: Nucléation de vortex et transition de phase du premier ordre, Thèse de Doctorat de l’Université de Paris VI (1997).

  25. 25

    Clerc, M. G. & Escaff, D. Solitary waves in van der Waals-like transition in fluidized granular matter. Physica A 371, 33–36 (2006).

    ADS  Article  Google Scholar 

  26. 26

    Géminard, J.-C. & Laroche, C. Pressure measurement in two-dimensional horizontal granular gases. Phys. Rev. E 70, 021301 (2004).

    ADS  Article  Google Scholar 

  27. 27

    Crocker, J. C. & Grier, D. G. Methods of digital video microscopy for colloidal studies. J. Colloid Interface Sci. 179, 298–310 (1996).

    ADS  Article  Google Scholar 

  28. 28

    Risso, D., Soto, R., Godoy, S. & Cordero, P. Friction and convection in a vertically vibrated granular system. Phys. Rev. E 72, 011305 (2005).

    ADS  Article  Google Scholar 

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We gratefully acknowledge R. Soto and T. Witten for fruitful discussions and C. González for preliminary numerical simulations. The authors acknowledge support from CONICYT grants: FONDAP No. 11980002, Fondecyt No. 1070958 (P.C., D.R.), Fondecyt No. 1070346 (N.M.), Anillo No. ACT 15 of Programa Bicentenario en Ciencia y Tecnología (M.G.C., J.D., K.H., N.M., G.V.). K.H. was supported through the Inter-American Materials Collaboration under DMR-0303072.

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Clerc, M., Cordero, P., Dunstan, J. et al. Liquid–solid-like transition in quasi-one-dimensional driven granular media. Nature Phys 4, 249–254 (2008).

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