Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Testing the thermodynamic approach to granular matter with a numerical model of a decisive experiment

Nature volume 415, pages 614–617 (2002)Cite this article

Abstract

Edwards has proposed1,2,3 a thermodynamic description of dense, slowly flowing granular matter, in which the grains (the ‘atoms’ of the system) interact with inelastic forces and enduring contacts. In Edwards' ensemble—one of the very few generalizations of standard statistical mechanics—thermodynamic quantities are computed as flat averages over configurations in which the grains are static or jammed, leading to a natural definition of configurational temperature. But the approach is not justified from first principles and hence, in the absence of explicit tests of its validity, has not been widely accepted. Here we report a numerical experiment involving a realistic model of slowly sheared granular matter; our results strongly support the thermodynamic description. Considering particles of different sizes in a slowly sheared dense granular system, we extract an effective temperature from a relation connecting their diffusivity and mobility. We then perform an explicit computation to show that the effective temperature measured from this relation coincides with the Edwards configurational temperature. Our approach, which is specifically conceived to be reproducible in the laboratory, may thus render the Edwards temperature accessible to experiments.

Your institute does not have access to this article

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

Buy

All prices are NET prices.

Figure 1: Diffusion (a) and response function (b) for the large and small particles in a sheared granular material measured perpendicular to the shear plane as a function of time in MD steps.
Figure 2: Parametric plot of diffusion versus response function for small and large grains interacting with tangential forces and without tangential forces (Coulomb frictionless).
Figure 3: Annealing procedure to calculate TEdw at different elastic compressional energies.

References

  1. Edwards, S. F. in Granular Matter: An Interdisciplinary Approach (ed. Mehta, A.) 121–140 (Springer, New York, 1994).

    Book  Google Scholar 

  2. Edwards, S. F. in Disorder in Condensed Matter Physics (eds Blackman, J. & Taguena, J.) 147–154 (Oxford Univ. Press, Oxford, 1991).

    Google Scholar 

  3. Mehta, A. & Edwards, S. F. Statistical mechanics of powder mixtures. Physica A 157, 1091–1097 (1989).

    ADS  MathSciNet  Article  Google Scholar 

  4. Cugliandolo, L. F., Kurchan, J. & Peliti, L. Energy flow, partial equilibration, and effective temperatures in systems with slow dynamics. Phys. Rev. E 55, 3898–3914 (1997).

    ADS  CAS  Article  Google Scholar 

  5. Kurchan, J. in Jamming and Rheology: Constrained Dynamics on Microscopic and Macroscopic Scales (eds Liu, A. & Nagel, S. R.) 72–79 (Taylor and Francis, London, 2001).

    Google Scholar 

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

    ADS  CAS  Article  Google Scholar 

  7. Barrat, A., Kurchan, J., Loreto, V. & Sellitto, M. Edwards measures for powders and glasses. Phys. Rev. Lett. 85, 5034–5037 (2000).

    ADS  CAS  Article  Google Scholar 

  8. Javier Brey, J., Prados, A. & Sanchez-Rey, B. Thermodynamic description in a simple model for granular compaction. Physica A 275, 310–324 (2000).

    ADS  Article  Google Scholar 

  9. Lefevre, A. & Dean, D. S. Tapping spin-glasses and ferromagnets on random graphs. Phys. Rev. Lett. 86, 5639–5642 (2001).

    ADS  Article  Google Scholar 

  10. Sciortino, F. & Tartaglia, P. Extension of the fluctuation-dissipation theorem to the physical aging of a model glass-forming liquid. Phys. Rev. Lett. 86, 107–110 (2001).

    ADS  CAS  Article  Google Scholar 

  11. Nowak, E. R., Knight, J. B., Ben-Naim, E., Jaeger, H. M. & Nagel, S. R. Density fluctuations in vibrated granular materials. Phys. Rev. E 57, 1971–1974 (1998).

    ADS  CAS  Article  Google Scholar 

  12. Johnson, K. L. Contact Mechanics (Cambridge Univ. Press, Cambridge, 1985).

    Book  Google Scholar 

  13. Cundall, P. A. & Strack, O. D. L. A Discrete numerical model for granular assemblies. Géotechnique 29, 47–65 (1979).

    Article  Google Scholar 

  14. Schäfer, J., Dippel, S. & Wolf, D. E. Force schemes in simulations of granular materials. J. Phys. I (France) 6, 5–20 (1996).

    Article  Google Scholar 

  15. Makse, H. A., Johnson, D. L. & Schwartz, L. M. Packing of compressible granular materials. Phys. Rev. Lett. 84, 4160–4163 (2000).

    ADS  CAS  Article  Google Scholar 

  16. Allen, M. P. & Tildesley, D. J. Computer Simulations of Liquids (Clarendon, Oxford, 1987).

    MATH  Google Scholar 

  17. Savage, S. B. The mechanics of rapid granular flows. Adv. Appl. Mech. 24, 289–365 (1994).

    Article  Google Scholar 

  18. Durian, D. J. Foam mechanics at the bubble scale. Phys. Rev. Lett. 75, 4780–4783 (1995).

    ADS  CAS  Article  Google Scholar 

  19. Lacasse, M.-D., Grest, G. S., Levine, D., Mason, T. G. & Weitz, D. A. Model for the elasticity of compressed emulsions. Phys. Rev. Lett. 76, 3448–3451 (1996).

    ADS  CAS  Article  Google Scholar 

  20. Langer, S. A. & Liu, A. J. Sheared foam as a supercooled liquid? Europhys. Lett. 49, 68–73 (2000).

    ADS  CAS  Article  Google Scholar 

  21. Herrmann, H. J., Hovi, J. P. & Luding, S. (eds) Physics of Dry Granular Matter (Kluwer, Dordrecht, 1998).

    Book  Google Scholar 

  22. Ottino, J. M. & Khakhar, D. V. Mixing and segregation of granular materials. Annu. Rev. Fluid Mech. 32, 55–91 (2000).

    ADS  MathSciNet  Article  Google Scholar 

  23. Hoover, W. G. et al. Lennard-Jones triple-point bulk and shear viscosities. Green-Kubo theory, Hamiltonian mechanics, and non-equilibrium molecular dynamics. Phys. Rev. A 22, 1690–1697 (1980).

    ADS  CAS  Article  Google Scholar 

  24. Drescher, A. & de Josselin de Jong, G. Photoelastic verification of a numerical model for the flow of a granular material. J. Mech. Phys. Solids 20, 337–351 (1972).

    ADS  Article  Google Scholar 

  25. Liu, C.-H. et al. Force fluctuations in bead packs. Science 269, 513–515 (1995).

    ADS  CAS  Article  Google Scholar 

  26. 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 

Download references

Acknowledgements

This work was partially supported by The Petroleum Research Fund.

Author information

Authors and Affiliations

  1. Levich Institute and Physics Department, City College of the City University of New York, New York, 10031, New York, USA

    Hernán A. Makse

  2. PMMH, Ecole Supérieure de Physique et Chimie Industrielles, 10 rue Vauquelin, Paris, 75231, France

    Jorge Kurchan

Authors
  1. Hernán A. Makse
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jorge Kurchan
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hernán A. Makse.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Makse, H., Kurchan, J. Testing the thermodynamic approach to granular matter with a numerical model of a decisive experiment. Nature 415, 614–617 (2002). https://doi.org/10.1038/415614a

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/415614a

Further reading

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing