- Physical Review Journals
All JournalsPhysics Magazine

Physical Review E

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Granular rheology: A tale of three time scales

O. Coquand1,2,*, W. T. Kranz3,1,†, and M. Sperl1,3,‡

  • *Contact author: olivier.coquand@univ-perp.fr
  • †Contact author: kranz@thp.uni-koeln.de
  • ‡Contact author: matthias.sperl@dlr.de
PDF

Phys. Rev. E 112, 035405 – Published 2 September, 2025

DOI: https://doi.org/10.1103/8gv1-9sb1

Abstract

We adapt statistical models of the physics of complex fluids to study the rheology of granular liquids. This allows us to provide laws of granular rheology based on first principles, which compare well with previously established phenomenological laws. In particular, the very successful law of μ(I) rheology can be understood within our model as the lowest order nontrivial Padé approximant of the macroscopic laws of rheology if one takes into account processes taking place at three distinct types of time scales: Collisions occurring at microscopic scales, collective motions like cage effect taking place at intermediate, mesoscopic scales, and finally advection that takes place at the macroscopic time scale. Our model's ability to describe granular physics outside of the Bagnold scaling regime allows for a natural extension to the rheology of granular suspensions.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (65)

  1. S. Savage, J. Fluid Mech. 92, 53 (1979).
  2. S. Savage and K. Hutter, J. Fluid Mech. 199, 177 (1989).
  3. S. Savage, J. Fluid Mech. 377, 1 (1998).
  4. O. Pouliquen, Phys. Fluids 11, 542 (1999).
  5. O. Pouliquen and Y. Forterre, J. Fluid Mech. 453, 133 (2002).
  6. K. Kelfoun, T. Druitt, B. van Wyk de Vries, and M.-N. Guilbaud, Bull. Volcanol. 70, 1169 (2008).
  7. K. Kelfoun, P. Samaniego, P. Palacios, and D. Barba, Bull. Volcanol. 71, 1057 (2009).
  8. V. Gueugneau, K. Kelfoun, O. Roche, and L. Chupin, Geophys. Res. Lett. 44, 2194 (2017).
  9. S. Ogburn and E. Calder, Front. Earth Sci. 5, 83 (2017).
  10. D. Salmanidou, S. Guillas, A. Georgiopoulou, and F. Dias, Proc. R. Soc. A 473, 20170026 (2017).
  11. P. Frey and M. Church, Science 325, 1509 (2009).
  12. P. Frey and M. Church, Earth Surf. Process. Landforms 36, 58 (2011).
  13. T. Pähtz, A. Clark, M. Valyrakis, and O. Durán, Rev. Geophys. 58, e2019RG000679 (2020).
  14. A. Bérut, H. Chauvet, V. Legué, B. Moulia, O. Pouliquen, and Y. Forterre, Proc. Natl. Acad. Sci. USA 115, 5123 (2018).
  15. Y. Forterre and O. Pouliquen, C. R. Physique 19, 271 (2018).
  16. P. A. Rühs, J. Bergfreund, P. Bertsch, S. J. Gstöhl, and P. Fischer, Soft Matter 17, 3022 (2021).
  17. B. Andreotti, Y. Forterre, and O. Pouliquen, Granular Media: Between Fluid and Solid (Cambridge University Press, Cambridge, UK, 2013).
  18. L. Staron, P. Lagrée, C. Josserand, and D. Lhuillier, Phys. Fluids 22, 113303 (2010).
  19. E. DeGiuli, J. N. McElwaine, and M. Wyart, Phys. Rev. E 94, 012904 (2016).
  20. E. DeGiuli and M. Wyart, Powders Grains 140, 01003 (2017).
  21. E. DeGiuli and M. Wyart, Proc. Natl. Acad. Sci. USA 114, 9284 (2017).
  22. F. Tapia, O. Pouliquen, and E. Guazzelli, Phys. Rev. Fluids 4, 104302 (2019).
  23. G. D. R. MiDi, Eur. Phys. J. E 14, 341 (2004).
  24. F. da Cruz, S. Emam, M. Prochnow, J.-N. Roux, and F. Chevoir, Phys. Rev. E 72, 021309 (2005).
  25. P. Jop, Y. Forterre, and O. Pouliquen, J. Fluid Mech. 541, 167 (2005).
  26. C. Cassar, M. Nicolas, and O. Pouliquen, Phys. Fluids 17, 103301 (2005).
  27. P. Jop, Y. Forterre, and O. Pouliquen, Nature (London) 441, 727 (2006).
  28. O. Pouliquen, C. Cassar, P. Jop, Y. Forterre, and M. Nicolas, J. Stat. Mech. (2006) P07020.
  29. Y. Forterre and O. Pouliquen, Annu. Rev. Fluid Mech. 40, 1 (2008).
  30. P. E. Peyneau and J. N. Roux, Phys. Rev. E 78, 011307 (2008).
  31. P.-Y. Lagrée, L. Staron, and S. Popinet, J. Fluid Mech. 686, 378 (2011).
  32. M. Tankeo, P. Richard, and E. Canot, Granular Matter 15, 881 (2013).
  33. C. Clavaud, A. Bérut, B. Metzger, and Y. Forterre, Proc. Natl. Acad. Sci. USA 114, 5147 (2017).
  34. L. Fullard, E. Breard, C. Davies, P. Lagrée, S. Popinet, and G. Lube, Powders Grains 140, 11002 (2017).
  35. L. Fullard, D. J. Holland, P. Galvosas, C. Davies, P.-Y. Lagrée, and S. Popinet, Phys. Rev. Fluids 4, 074302 (2019).
  36. R. Delannay, A. Valance, A. Mangeney, O. Roche, and P. Richard, J. Phys. D: Appl. Phys. 50, 053001 (2017).
  37. T. Pähtz, O. Durán, D. N. de Klerk, I. Govender, and M. Trulsson, Phys. Rev. Lett. 123, 048001 (2019).
  38. O. Coquand, M. Sperl, and W. T. Kranz, Phys. Rev. E 102, 032602 (2020).
  39. O. D'Angelo, A. Shetty, M. Sperl, and W. T. Kranz, The manifold rheology of fluidized granular media, arXiv:2309.00413.
  40. S. Courrech du Pont, P. Gondret, B. Perrin, and M. Rabaud, Phys. Rev. Lett. 90, 044301 (2003).
  41. F. Boyer, E. Guazzelli, and O. Pouliquen, Phys. Rev. Lett. 107, 188301 (2011).
  42. E. DeGiuli, G. Düring, E. Lerner, and M. Wyart, Phys. Rev. E 91, 062206 (2015).
  43. E. Guazzelli and O. Pouliquen, J. Fluid Mech. 852, P1 (2018).
  44. K. Suzuki and H. Hayakawa, J. Fluid Mech. 864, 1125 (2019).
  45. W. Götze, Complex Dynamics of Glass-forming Liquids (Oxford University Press, Oxford, UK, 2008).
  46. W. T. Kranz, F. Frahsa, A. Zippelius, M. Fuchs, and M. Sperl, Phys. Rev. Lett. 121, 148002 (2018).
  47. W. T. Kranz, F. Frahsa, A. Zippelius, M. Fuchs, and M. Sperl, Phys. Rev. Fluids 5, 024305 (2020).
  48. G. Vineyard, Phys. Rev. 110, 999 (1958).
  49. M. Fuchs and M. E. Cates, Phys. Rev. Lett. 89, 248304 (2002).
  50. M. Fuchs and M. Cates, J. Rheol. 53, 957 (2009).
  51. J. Hansen and I. McDonald, Theory of Simple Liquids (Elsevier Science, Amsterdam, 2006).
  52. N. Clisby and B. McCoy, J. Stat. Phys. 122, 15 (2006).
  53. M. Fuchs and M. Cates, Faraday Discuss. 123, 267 (2003).
  54. O. Henrich, F. Varnik, and M. Fuchs, J. Phys.: Condens. Matter 17, S3625 (2005).
  55. F. Varnik and O. Henrich, Phys. Rev. B 73, 174209 (2006).
  56. J. Brader, T. Voigtmann, M. Fuchs, R. Larson, and M. Cates, Proc. Natl. Acad. Sci. USA 106, 15186 (2009).
  57. O. Henrich, O. Pfeifroth, and M. Fuchs, J. Phys.: Condens. Matter 19, 205132 (2007).
  58. O. Coquand and M. Sperl, Phys. Rev. E 104, 014604 (2021).
  59. O. Coquand and M. Sperl, Phys. Rev. E 109, 034901 (2024).
  60. W. T. Kranz, M. Sperl, and A. Zippelius, Phys. Rev. Lett. 104, 225701 (2010).
  61. W. T. Kranz, M. Sperl, and A. Zippelius, Phys. Rev. E 87, 022207 (2013).
  62. R. Bagnold, Proc. R. Soc. Lond. A 225, 49 (1954).
  63. P. Haff, J. Fluid Mech. 134, 401 (1983).
  64. N. Petford, Mineral. Mag. 73, 167 (2009).
  65. O. D'Angelo, M. Sperl, and W. T. Kranz, Phys. Rev. Lett. 134, 148202 (2025).

Outline

Information

Phys. Rev. E 112, 035405– Published 2 September, 2025
  • Received 27 March 2025
  • Accepted 11 August 2025
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation