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.

  • Letter
  • Published:

High-speed tracking of rupture and clustering in freely falling granular streams

Abstract

Thin streams of liquid commonly break up into characteristic droplet patterns owing to the surface-tension-driven Plateau–Rayleigh instability1,2,3. Very similar patterns are observed when initially uniform streams of dry granular material break up into clusters of grains4,5,6, even though flows of macroscopic particles are considered to lack surface tension7,8. Recent studies on freely falling granular streams tracked fluctuations in the stream profile9, but the clustering mechanism remained unresolved because the full evolution of the instability could not be observed. Here we demonstrate that the cluster formation is driven by minute, nanoNewton cohesive forces that arise from a combination of van der Waals interactions and capillary bridges between nanometre-scale surface asperities. Our experiments involve high-speed video imaging of the granular stream in the co-moving frame, control over the properties of the grain surfaces and the use of atomic force microscopy to measure grain–grain interactions. The cohesive forces that we measure correspond to an equivalent surface tension five orders of magnitude below that of ordinary liquids. We find that the shapes of these weakly cohesive, non-thermal clusters of macroscopic particles closely resemble droplets resulting from thermally induced rupture of liquid nanojets10,11,12.

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

Access options

Rent or buy this article

Prices vary by article type

from$1.95

to$39.95

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

Figure 1: Break-up of a granular stream.
Figure 2: Controlling clustering by altering cohesion.
Figure 3: Clustering dynamics.

Similar content being viewed by others

References

  1. Shi, X. D., Brenner, M. P. & Nagel, S. R. A cascade of structure in a drop falling from a faucet. Science 265, 219–222 (1994)

    Article  ADS  MathSciNet  CAS  Google Scholar 

  2. Eggers, J. & Villermaux, E. Physics of liquid jets. Rep. Prog. Phys. 71, 036601, (2008)

  3. Doshi, P. et al. Persistence of memory in drop breakup: the breakdown of universality. Science 302, 1185–1188 (2003)

    Article  ADS  CAS  Google Scholar 

  4. Lohse, D. et al. Impact on soft sand: void collapse and jet formation. Phys. Rev. Lett. 93, 198003 (2004)

    Article  ADS  Google Scholar 

  5. Royer, J. R. et al. Formation of granular jets observed by high-speed X-ray radiography. Nature Phys. 1, 164–167 (2005)

    Article  ADS  CAS  Google Scholar 

  6. Möbius, M. E. Clustering instability in a freely falling granular jet. Phys. Rev. E 74, 051304 (2006)

    Article  ADS  Google Scholar 

  7. Cheng, X., Xu, L., Patterson, A., Jaeger, H. M. & Nagel, S. R. Towards the zero-surface-tension limit in granular fingering instability. Nature Phys. 4, 234–237 (2008)

    Article  ADS  CAS  Google Scholar 

  8. Cheng, X., Varas, G., Citron, D., Jaeger, H. M. & Nagel, S. R. Collective behavior in a granular jet: emergence of a liquid with zero surface tension. Phys. Rev. Lett. 99, 188001 (2007)

    Article  ADS  Google Scholar 

  9. Amarouchene, Y., Boudet, J.-F. & Kellay, H. Capillarylike fluctuations at the interface of falling granular jets. Phys. Rev. Lett. 100, 218001 (2008)

    Article  ADS  Google Scholar 

  10. Koplik, J. & Banavar, J. R. Molecular dynamics of interface rupture. Phys. Fluids A 5, 521–536 (1993)

    Article  ADS  CAS  Google Scholar 

  11. Moseler, M. & Landman, U. Formation, stability, and breakup of nanojets. Science 289, 1165–1169 (2000)

    Article  ADS  CAS  Google Scholar 

  12. Kawano, S. Molecular dynamics of rupture phenomena in a liquid thread. Phys. Rev. E 58, 4468–4472 (1998)

    Article  ADS  CAS  Google Scholar 

  13. Khamontoff, N. Application of photography to the study of the structure of trickles of fluid and dry materials. J. Russ. Phys-Chem. Soc. 22, 281–284 (1890)

    Google Scholar 

  14. Goldhirsch, I. Rapid granular flows. Annu. Rev. Fluid Mech. 35, 267–293 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  15. Brilliantov, N. V. & Pöschel, T. Kinetic Theory of Granular Gases (Oxford University Press, 2004)

    Book  Google Scholar 

  16. Efrati, E., Livne, E. & Meerson, B. Hydrodynamic singularities and clustering in a freely cooling inelastic gas. Phys. Rev. Lett. 94, 088001 (2005)

    Article  ADS  Google Scholar 

  17. Kuwabara, G. & Kono, K. Restitution coefficient in a collision between two spheres. Jpn. J. Appl. Phys. 26, 1230–1233 (1987)

    Article  ADS  Google Scholar 

  18. Foerster, S. F., Louge, M. Y., Chang, H. & Allia, K. Measurements of the collision properties of small spheres. Phys. Fluids 6, 1108–1115 (1994)

    Article  ADS  CAS  Google Scholar 

  19. Israelachvili, J. N. Intermolecular and Surface Forces 2nd edn (Academic Press, 1992)

    Google Scholar 

  20. Podczeck, F. Particle-Particle Adhesion in Pharmaceutical Powder Handling (Imperial College Press, 1998)

    Book  Google Scholar 

  21. Visser, J. Van der Waals and other cohesive forces affecting powder fluidization. Powder Technol. 58, 1–10 (1989)

    Article  CAS  Google Scholar 

  22. Jones, R. From single particle AFM studies of adhesion and friction to bulk flow: forging the links. Granular Matter 4, 191–204 (2003)

    Article  ADS  CAS  Google Scholar 

  23. Schaefer, D. M. et al. in Fundamentals of Adhesion and Interfaces (eds Rimai, D. S., Demejo, L. P. & Mittal, K. L.) 35–48 (VSP, 1995)

    Google Scholar 

  24. Halsey, T. C. & Levine, A. J. How sandcastles fall. Phys. Rev. Lett. 80, 3141–3144 (1998)

    Article  ADS  CAS  Google Scholar 

  25. Bocquet, L., Charlaix, E., Ciliberto, S. & Crassous, J. Moisture-induced ageing in granular media and the kinetics of capillary condensation. Nature 396, 735–737 (1998)

    Article  ADS  CAS  Google Scholar 

  26. Brilliantov, N. V., Albers, N., Spahn, F. & Pöschel, T. Collision dynamics of granular particles with adhesion. Phys. Rev. E 76, 051302 (2007)

    Article  ADS  Google Scholar 

  27. Sorace, C. M., Louge, M. Y., Crozier, M. D. & Law, V. H. C. High apparent adhesion energy in the breakdown of normal restitution for binary impacts of small spheres at low speed. Mech. Res. Commun. 36, 364–368 (2009)

    Article  Google Scholar 

  28. Rowlinson, J. S. & Widom, B. Molecular Theory of Capillarity (Clarendon Press, 1982)

    Google Scholar 

  29. Hennequin, Y. et al. Drop formation by thermal fluctuations at an ultralow surface tension. Phys. Rev. Lett. 97, 244502 (2006)

    Article  ADS  CAS  Google Scholar 

  30. Eggers, J. Dynamics of liquid nanojets. Phys. Rev. Lett. 89, 084502 (2002)

    Article  ADS  Google Scholar 

Download references

Acknowledgements

We thank X. Cheng, R. Cocco, E. Corwin, R. Karri, N. Keim, T. Knowlton, S. Nagel, T. Witten and W. Zhang for discussions and J. Jureller for AFM training and assistance. This work was supported by NSF through its MRSEC programme and the Inter-American Materials Collaboration Chicago-Chile, and by the Keck Initiative for Ultrafast Imaging at the University of Chicago.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to John R. Royer.

Supplementary information

Supplementary Information

This file contains Supplementary Notes and Data, Supplementary Figures 1-4 with Legends and Supplementary References. (PDF 1966 kb)

Supplementary Movie 1

This file shows a high-speed movie of the break up of a granular stream. The camera falls with the stream to capture the break up of a stream of d = (107 ± 19) μm diameter glass grains falling out of a D0 = 4.0 mm nozzle. The nozzle and reservoir of grains are housed in a 2.5 m tall acrylic tube, which is sealed and evacuated to 0.03 kPa (gas mean free path ~ 200 μm) to reduce air drag. (MOV 3598 kb)

Supplementary Movie 2

This file shows a high-speed movie of a stream of d = (130 ± 30) μm diameter copper grains. Conditions are otherwise identical to those in Supplementary Movie 1. (MOV 2376 kb)

PowerPoint slides

Rights and permissions

Reprints and permissions

About this article

Cite this article

Royer, J., Evans, D., Oyarte, L. et al. High-speed tracking of rupture and clustering in freely falling granular streams. Nature 459, 1110–1113 (2009). https://doi.org/10.1038/nature08115

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature08115

This article is cited by

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

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