Skip to main content

Thank you for visiting 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.

  • Letter
  • Published:

Granular materials flow like complex fluids


Granular materials such as sand, powders and foams are ubiquitous in daily life and in industrial and geotechnical applications1,2,3,4. These disordered systems form stable structures when unperturbed, but in the presence of external influences such as tapping or shear they ‘relax’, becoming fluid in nature. It is often assumed that the relaxation dynamics of granular systems is similar to that of thermal glass-forming systems3,5. However, so far it has not been possible to determine experimentally the dynamic properties of three-dimensional granular systems at the particle level. This lack of experimental data, combined with the fact that the motion of granular particles involves friction (whereas the motion of particles in thermal glass-forming systems does not), means that an accurate description of the relaxation dynamics of granular materials is lacking. Here we use X-ray tomography to determine the microscale relaxation dynamics of hard granular ellipsoids subject to an oscillatory shear. We find that the distribution of the displacements of the ellipsoids is well described by a Gumbel law6 (which is similar to a Gaussian distribution for small displacements but has a heavier tail for larger displacements), with a shape parameter that is independent of the amplitude of the shear strain and of the time. Despite this universality, the mean squared displacement of an individual ellipsoid follows a power law as a function of time, with an exponent that does depend on the strain amplitude and time. We argue that these results are related to microscale relaxation mechanisms that involve friction and memory effects (whereby the motion of an ellipsoid at a given point in time depends on its previous motion). Our observations demonstrate that, at the particle level, the dynamic behaviour of granular systems is qualitatively different from that of thermal glass-forming systems, and is instead more similar to that of complex fluids. We conclude that granular materials can relax even when the driving strain is weak.

This is a preview of subscription content, access via your institution

Access options

Buy this article

Prices may be subject to local taxes which are calculated during checkout

Figure 1: Experimental set-up and time dependence of the translational (TMSD) and rotational (RMSD) mean squared displacement for different strain amplitudes (γ), showing the presence of anomalous diffusion.
Figure 2: Time evolution of the self part of the van Hove function Gs(d, t) and probability density function of the translational displacement along the y direction.
Figure 3: Scatter plots of the displacements for two consecutive time intervals and the conditional probability density function of d2, demonstrating the presence of memory effects for large γ.
Figure 4: Memory effect as a function of particle displacement and time.

Similar content being viewed by others


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

    Article  ADS  Google Scholar 

  2. Duran, J. Sands, Powders, and Grains: An Introduction to the Physics of Granular Materials (Springer, 2012)

  3. Coniglio, A ., Fierro, A ., Herrmann, H. J. & Nicodemi, M. Unifying Concepts in Granular Media and Glasses (Elsevier, 2004)

  4. Anthony, J. L. & Marone, C. Influence of particle characteristics on granular friction. J. Geophys. Res. 110, B08409 (2005)

    Article  ADS  Google Scholar 

  5. Binder, K. & Kob, W. Glassy Materials and Disordered Solids: An Introduction to their Statistical Mechanics (World Scientific, 2011)

  6. Bramwell, S. T. The distribution of spatially averaged critical properties. Nat. Phys. 5, 444–447 (2009)

    Article  Google Scholar 

  7. Mueth, D. M. et al. Signatures of granular microstructure in dense shear flows. Nature 406, 385–389 (2000)

    Article  CAS  ADS  Google Scholar 

  8. Dijksman, J. A., Rietz, F., Lorincz, K. A., Van Hecke, M. & Losert, W. Refractive index matched scanning of dense granular materials. Rev. Sci. Instrum. 83, 011301 (2012)

    Article  ADS  Google Scholar 

  9. Panaitescu, A., Reddy, K. A. & Kudrolli, A. Nucleation and crystal growth in sheared granular sphere packings. Phys. Rev. Lett. 108, 108001 (2012)

    Article  ADS  Google Scholar 

  10. Pouliquen, O., Belzons, M. & Nicolas, M. Fluctuating particle motion during shear induced granular compaction. Phys. Rev. Lett. 91, 014301 (2003)

    Article  CAS  ADS  Google Scholar 

  11. Ren, J., Dijksman, J. A. & Behringer, R. P. Reynolds pressure and relaxation in a sheared granular system. Phys. Rev. Lett. 110, 018302 (2013)

    Article  ADS  Google Scholar 

  12. Paulsen, J. D., Keim, N. C. & Nagel, S. R. Multiple transient memories in experiments on sheared non-Brownian suspensions. Phys. Rev. Lett. 113, 068301 (2014)

    Article  ADS  Google Scholar 

  13. Dauchot, O., Marty, G. & Biroli, G. Dynamical heterogeneity close to the jamming transition in a sheared granular material. Phys. Rev. Lett. 95, 265701 (2005)

    Article  CAS  ADS  Google Scholar 

  14. Slotterback, S. et al. Onset of irreversibility in cyclic shear of granular packings. Phys. Rev. E 85, 021309 (2012)

    Article  ADS  Google Scholar 

  15. Radjai, F. & Roux, S. Turbulent-like fluctuations in quasistatic flow of granular media. Phys. Rev. Lett. 89, 064302 (2002)

    Article  ADS  Google Scholar 

  16. Bi, D., Zhang, J., Chakraborty, B. & Behringer, R. P. Jamming by shear. Nature 480, 355–358 (2011)

    Article  CAS  ADS  Google Scholar 

  17. Royer, J. R. & Chaikin, P. M. Precisely cyclic sand: self-organization of periodically sheared frictional grains. Proc. Natl Acad. Sci. USA 112, 49–53 (2015)

    Article  CAS  ADS  Google Scholar 

  18. GDR MiDi . On dense granular flows. Eur. Phys. J. E 14, 341–365 (2004)

    Article  CAS  Google Scholar 

  19. Xia, C. et al. The structural origin of the hard-sphere glass transition in granular packing. Nat. Commun. 6, 8409 (2015)

    Article  CAS  ADS  Google Scholar 

  20. Mailman, M., Harrington, M., Girvan, M. & Losert, W. Consequences of anomalous diffusion in disordered systems under cyclic forcing. Phys. Rev. Lett. 112, 228001 (2014)

    Article  ADS  Google Scholar 

  21. Bouchaud, J. P. & Georges, A. Anomalous diffusion in disordered media: statistical mechanisms, models and physical applications. Phys. Rep. 195, 127–293 (1990)

    Article  ADS  MathSciNet  Google Scholar 

  22. Singh, A., Magnanimo, V., Saitoh, K. & Luding, S. The role of gravity or pressure and contact stiffness in granular rheology. New J. Phys. 17, 043028 (2015)

    Article  ADS  Google Scholar 

  23. Kumar, N. & Luding, S. Memory of jamming—multiscale models for soft and granular matter. Granul. Matter 18, 58 (2016)

    Article  Google Scholar 

  24. Henann, D. L. & Kamrin, K. Continuum modeling of secondary rheology in dense granular materials. Phys. Rev. Lett. 113, 178001 (2014)

    Article  ADS  Google Scholar 

  25. Caballero-Robledo, G. A., Goldenberg, C. & Clement, E. Local dynamics and synchronization in a granular glass. Granul. Matter 14, 239–245 (2012)

    Article  Google Scholar 

  26. Kob, W. & Andersen, H. C. Testing mode-coupling theory for a supercooled binary Lennard–Jones mixture I: the van Hove correlation function. Phys. Rev. E 51, 4626–4641 (1995)

    Article  CAS  ADS  Google Scholar 

  27. Doliwa, B. & Heuer, A. The origin of anomalous diffusion and non-Gaussian effects for hard spheres: analysis of three-time correlations. J. Phys. Condens. Matter 11, A277–A283 (1999)

    Article  CAS  ADS  Google Scholar 

  28. Larson, R. G. The Structure and Rheology of Complex Fluids (Oxford Univ. Press, 1999)

  29. Kamrin, K. & Koval, G. Nonlocal constitutive relation for steady granular flow. Phys. Rev. Lett. 108, 178301 (2012)

    Article  ADS  Google Scholar 

  30. Donev, A. et al. Improving the density of jammed disordered packings using ellipsoids. Science 303, 990–993 (2004)

    Article  CAS  ADS  Google Scholar 

  31. Titow, M. PVC Technology 1189–1191 (Springer, 1984)

  32. Johnson, K. L. & Johnson, K. L. Contact Mechanics 92–95 (Cambridge Univ. Press, 1987)

  33. Hansen, J. P. & McDonald, I. R. Theory of Simple Liquids (Elsevier, 1990)

  34. Chaudhuri, P., Berthier, L. & Kob, W. Universal nature of particle displacements close to glass and jamming transitions. Phys. Rev. Lett. 99, 060604 (2007)

    Article  ADS  Google Scholar 

  35. Umarov, S., Tsallis, C. & Steinberg, S. On a q-central limit theorem consistent with nonextensive statistical mechanics. Milan J. Math. 76, 307–328 (2008)

    Article  MathSciNet  Google Scholar 

  36. Picoli, S., Mendes, R. S., Malacarne, L. C. & Santos, R. P. B. q-Distributions in complex systems: a brief review. Braz. J. Phys. 39, 468–474 (2009)

    Article  ADS  Google Scholar 

Download references


Some of the preliminary experiments were carried out at BL13W1 beamline of Shanghai Synchrotron Radiation Facility. The work is supported by the National Natural Science Foundation of China (numbers 11175121, 11675110 and U1432111), Specialized Research Fund for the Doctoral Program of Higher Education of China (grant number 20110073120073) and ANR-15-CE30-0003-02. W.K. is member of the Institut Universitaire de France.

Author information

Authors and Affiliations



Y.W. and W.K. designed the research. B.K., Y.C., J.L., C.X., Z.L., H.D., A.Z., J.Z. and Y.W. performed the experiment. B.K., W.K. and Y.W. analysed the data and wrote the paper.

Corresponding authors

Correspondence to Walter Kob or Yujie Wang.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Additional information

Reviewer Information Nature thanks R. Behringer and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Publisher's note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Figure 1 Trajectories of 20 particles in the central region of the sample.

The strain amplitude is γ = 0.26 and the length of the trajectory is 615 cycles, the total length of the experiment for this γ. Time is represented by the colour scale. The short axis of the particles is 2b.

Extended Data Figure 2 The static structure factor S(q) (equation (3)) of the system in steady state, for different γ.

Extended Data Figure 3 Evolution of the volume fraction Φ of the system during the cyclic shear measurements at different γ.

For γ = 0.10 we have two curves that stem from two completely independent measurements. The fact that the corresponding packing fractions are compatible shows that sample-to-sample fluctuations are small.

Extended Data Figure 4 The normalized local number density ρi/〈ρi〉 in the system as a function of i, for i {x, y, z}, for different γ.

The vertical dashed lines denote the boundaries of the central region that we chose for the subsequent analysis.

Extended Data Figure 5 Time dependence of the self (Fs(q, t); large open symbols) and collective (F(q, t); small closed symbols) intermediate scattering functions (equation (4)), for different γ.

a, q = 3.49b−1. b, q = 4.46b−1. The correlators decay without any sign of a two-step relaxation, thus showing that in this system the particles are not caged.

Extended Data Figure 6 PDF in the y direction for γ = 0.26.

a, Comparison of the fits with the Gumbel distribution (black line) and the q-Gaussian distribution (pink line) for the whole accessible range in the displacement. b, An enlarged view of the area indicated by the blue rectangle in a. c, d, The ratio between the logarithm of the PDF for the data (ln(P(dy))) and for the Gumbel distribution (ln(Pg); c), and for the data and the q-Gaussian distribution (ln(Pq); d).

Extended Data Table 1 Experimental protocol used to prepare the system and to measure its properties

Supplementary information

The dynamics of the particles during the cycling experiment (γ=0.26): Top view.

The video shows a view of the system from the top. It shows a horizontal cut through the middle of the sample and only the particles in the lower half of the central region of the box are displayed. The value of γ is 0.26 and the video covers the 615 cycles of the measurement with the CT scanner. Note that on the time scale considered, most of the particles move less than their long axis (see Fig. 1b of the main text) (MOV 6585 kb)

The dynamics of the particles during the cycling experiment (γ=0.26): Side view.

The video shows a side view of the same system of Supplementary Video 1. We made a vertical cut through the middle of the sample and show only the particles in the sector with large x. Note that the system shows no evident signature for convective motion. (MOV 3672 kb)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kou, B., Cao, Y., Li, J. et al. Granular materials flow like complex fluids. Nature 551, 360–363 (2017).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


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.


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