Letter | Published:

Granular materials flow like complex fluids

Nature volume 551, pages 360363 (16 November 2017) | Download Citation


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.

Access optionsAccess options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.


  1. 1.

    , & Granular solids, liquids, and gases. Rev. Mod. Phys. 68, 1259–1273 (1996)

  2. 2.

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

  3. 3.

    ., ., & Unifying Concepts in Granular Media and Glasses (Elsevier, 2004)

  4. 4.

    & Influence of particle characteristics on granular friction. J. Geophys. Res. 110, B08409 (2005)

  5. 5.

    & Glassy Materials and Disordered Solids: An Introduction to their Statistical Mechanics (World Scientific, 2011)

  6. 6.

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

  7. 7.

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

  8. 8.

    , , , & Refractive index matched scanning of dense granular materials. Rev. Sci. Instrum. 83, 011301 (2012)

  9. 9.

    , & Nucleation and crystal growth in sheared granular sphere packings. Phys. Rev. Lett. 108, 108001 (2012)

  10. 10.

    , & Fluctuating particle motion during shear induced granular compaction. Phys. Rev. Lett. 91, 014301 (2003)

  11. 11.

    , & Reynolds pressure and relaxation in a sheared granular system. Phys. Rev. Lett. 110, 018302 (2013)

  12. 12.

    , & Multiple transient memories in experiments on sheared non-Brownian suspensions. Phys. Rev. Lett. 113, 068301 (2014)

  13. 13.

    , & Dynamical heterogeneity close to the jamming transition in a sheared granular material. Phys. Rev. Lett. 95, 265701 (2005)

  14. 14.

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

  15. 15.

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

  16. 16.

    , , & Jamming by shear. Nature 480, 355–358 (2011)

  17. 17.

    & Precisely cyclic sand: self-organization of periodically sheared frictional grains. Proc. Natl Acad. Sci. USA 112, 49–53 (2015)

  18. 18.

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

  19. 19.

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

  20. 20.

    , , & Consequences of anomalous diffusion in disordered systems under cyclic forcing. Phys. Rev. Lett. 112, 228001 (2014)

  21. 21.

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

  22. 22.

    , , & The role of gravity or pressure and contact stiffness in granular rheology. New J. Phys. 17, 043028 (2015)

  23. 23.

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

  24. 24.

    & Continuum modeling of secondary rheology in dense granular materials. Phys. Rev. Lett. 113, 178001 (2014)

  25. 25.

    , & Local dynamics and synchronization in a granular glass. Granul. Matter 14, 239–245 (2012)

  26. 26.

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

  27. 27.

    & 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)

  28. 28.

    The Structure and Rheology of Complex Fluids (Oxford Univ. Press, 1999)

  29. 29.

    & Nonlocal constitutive relation for steady granular flow. Phys. Rev. Lett. 108, 178301 (2012)

  30. 30.

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

  31. 31.

    PVC Technology 1189–1191 (Springer, 1984)

  32. 32.

    & Contact Mechanics 92–95 (Cambridge Univ. Press, 1987)

  33. 33.

    & Theory of Simple Liquids (Elsevier, 1990)

  34. 34.

    , & Universal nature of particle displacements close to glass and jamming transitions. Phys. Rev. Lett. 99, 060604 (2007)

  35. 35.

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

  36. 36.

    , , & q-Distributions in complex systems: a brief review. Braz. J. Phys. 39, 468–474 (2009)

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


  1. School of Physics and Astronomy, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai 200240, China

    • Binquan Kou
    • , Yixin Cao
    • , Jindong Li
    • , Chengjie Xia
    • , Zhifeng Li
    • , Jie Zhang
    •  & Yujie Wang
  2. Department of Radiology, Ruijin Hospital, Shanghai Jiao Tong University School of Medicine, Shanghai 200025, China

    • Haipeng Dong
    •  & Ang Zhang
  3. Institute of Natural Sciences, Shanghai Jiao Tong University, Shanghai 200240, China

    • Jie Zhang
  4. Laboratoire Charles Coulomb, University of Montpellier and CNRS, UMR 5221, 34095 Montpellier, France

    • Walter Kob
  5. Materials Genome Initiative Center, Shanghai Jiao Tong University, 800 Dong Chuan Road, Shanghai 200240, China

    • Yujie Wang
  6. Collaborative Innovation Center of Advanced Microstructures, Nanjing University, Nanjing, 210093, China

    • Yujie Wang


  1. Search for Binquan Kou in:

  2. Search for Yixin Cao in:

  3. Search for Jindong Li in:

  4. Search for Chengjie Xia in:

  5. Search for Zhifeng Li in:

  6. Search for Haipeng Dong in:

  7. Search for Ang Zhang in:

  8. Search for Jie Zhang in:

  9. Search for Walter Kob in:

  10. Search for Yujie Wang in:


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.

Competing interests

The authors declare no competing financial interests.

Corresponding authors

Correspondence to Walter Kob or Yujie Wang.

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

Supplementary information


  1. 1.

    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)

  2. 2.

    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.

About this article

Publication history






Further reading


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.