A Fluctuating Energy Model for Dense Granular Flows

  • Riccardo Artoni
  • Andrea Santomaso
  • Paolo Canu


We address the slow, dense flow of granular materials as a continuum with the incompressible Navier-Stokes equations plus the fluctuating energy balance for granular temperature. The pseudo-fluid is given an apparent viscosity, for which we choose an Arrhenius-like dependence on granular temperature; the fluctuating energy balance includes a ‘mobility enhancing’ term due to shear stress and a jamming, dissipative term which we assume to depend on the isotropic part of the stress tensor and on shear rate. After having proposed a ‘chemical’ interpretation of the phenomenology described by the model in terms of reaction rates, we report results for some 2-D standard geometries of flow, which agree semi-quantitatively with experimental and DEM observations. In particular, our model well reproduces the formation of stagnant zones of a characteristic shape (e.g. wedge-shaped static zones in a silo with flat bottom) without prescribing them a-priori with erosion techniques.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Jaeger, H. M., Nagel, S. R., and Behringer, R. P. (1996) Rev. Mod. Phys. 68(4), 1259–1273. CrossRefGoogle Scholar
  2. 2.
    King, P., Lopez-Alcaraz, P., Pacheco-Martinez, H., Clement, C., Smith, A., and Swift, M. (2007) Eur Phys J E Soft Matter 22(3), 219–226. CrossRefGoogle Scholar
  3. 3.
    Cundall, P. A. and Strack, O. D. L. (1979) Géotechnique 29(1), 47–65. CrossRefGoogle Scholar
  4. 4.
    Pouliquen, O. and Chevoir, F. (2002) Comptes Rendus Physique 3, 163–175. CrossRefGoogle Scholar
  5. 5.
    GDR Midi (2004) Eur. Phys. J. E 14(4), 341–365. CrossRefGoogle Scholar
  6. 6.
    Jop, P., Forterre, Y., and Pouliquen, O. (2006) Nature 441, 727–730. CrossRefGoogle Scholar
  7. 7.
    Pouliquen, O., Cassar, C., Forterre, Y., Jop, P., and Nicolas, M. (2006) In Proc. Powders & Grains 2005: A. A. Balkema, Rotterdam. Google Scholar
  8. 8.
    da Cruz, F., Emam, S., Prochnow, M., Roux, J.-J., and Chevoir, F. (2005) Phys. Rev. E 72, 021309. CrossRefGoogle Scholar
  9. 9.
    Goddard, J. D. (1986) Acta Mechanica 63(1-4), 3–13. zbMATHCrossRefGoogle Scholar
  10. 10.
    Babić, M. (1997) Int. J. Engng. Sci. 35(5), 523–548. zbMATHCrossRefGoogle Scholar
  11. 11.
    Goddard, J. D. (to appear) In Mathematical models of granular matter, Lecture Notes in Mathematics. Berlin: Springer. Google Scholar
  12. 12.
    Savage, S. B. (1998) J. Fluid Mech. 377, 1–26. zbMATHCrossRefMathSciNetGoogle Scholar
  13. 13.
    Artoni, R., Santomaso, A., and Canu, P. (to appear) Europhys. Lett. e-print: cond-mat/0705.3726.
  14. 14.
    Hibler, W. D. (1977) J. Geophys. Res. 82, 3932–3938. CrossRefGoogle Scholar
  15. 15.
    Doolittle, A. K. (1951) J. Appl. Phys. 22, 1031–1035. CrossRefGoogle Scholar
  16. 16.
    Cohen, M. H. and Grest, G. S. Aug 1979 Phys. Rev. B 20(3), 1077–1098. CrossRefGoogle Scholar
  17. 17.
    Edwards, S. F. and Oakeshott, R. B. S. (1989) Physica A 157, 1080–1090. CrossRefMathSciNetGoogle Scholar
  18. 18.
    Losert, W., Bocquet, L., Lubensky, T. C., and Gollub, J. P. Phys. Rev. Lett. 85(7), 1428–1431. Google Scholar
  19. 19.
    Bocquet, L., Losert, W., Schalk, D., Lubensky, T. C., and Gollub, J. P. Phys. Rev. E 65, 011307. Google Scholar
  20. 20.
    Bocquet, L., Errami, J., and Lubensky, T. C. Oct 2002 Phys. Rev. Lett. 89(18), 184301. CrossRefGoogle Scholar
  21. 21.
    Brown, R. L. and Hawksley, P. G. W. (1947) Fuel 27, 159–173. Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Riccardo Artoni
    • 1
  • Andrea Santomaso
    • 1
  • Paolo Canu
    • 1
  1. 1.Dipartimento di Principi e Impianti di Ingegneria Chimica “I. Sorgato”Università di PadovaPadovaItaly

Personalised recommendations