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.

  • Article
  • Published:

Coarsening of granular segregation patterns in quasi-two-dimensional tumblers

Nature Physics volume 4, pages 244–248 (2008)Cite this article

Abstract

A fundamental characteristic of granular flows is segregation on the basis of particle size or density. For bidisperse mixtures of particles, revolutions of the order of 10 produce a segregation pattern of several radial streaks in quasi-two-dimensional rotating tumblers with fill fractions between 50% and 70%. By extending the duration of the experiments to the order of 102–103 tumbler revolutions, we have found the first evidence of coarsening of the radial streak pattern to as few as one streak, resulting in an unexpected wedge-shaped segregation pattern. This phenomenon occurs for a wide range of conditions including several fill fractions, particle sizes and mixtures of particles varying in both size and density in circular tumblers as well as for particles varying in size in square tumblers. Coarsening seems to be driven by transport of small (or dense) particles from streak to streak through the semicircular radial core, leading to new questions about the physics of coarsening of granular segregation patterns.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

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

Figure 1: Radial streak coarsening in a bidisperse size-varying mixture.
Figure 2: Evolution of streak coarsening in a size-varying mixture.
Figure 3: Dynamics of coarsening from three streaks to one in a size-varying mixture.
Figure 4: Coarsening for glass and steel particles of different sizes.
Figure 5: Coarsening in a square tumbler.
Figure 6: Pattern periodicity in circular and square tumblers.

Similar content being viewed by others

References

  1. Drahun, J. A. & Bridgwater, J. The mechanisms of free surface segregation. Powder Technol. 36, 39–53 (1983).

    Article  Google Scholar 

  2. Duran, J. Sands, Powders, and Grains: An Introduction to the Physics of Granular Materials (Partially Ordered Systems, Springer, New York, 2000).

    Book  Google Scholar 

  3. Hill, K. M., Khakhar, D. V., Gilchrist, J. F., McCarthy, J. J. & Ottino, J. M. Segregation-driven organization in chaotic granular flows. Proc. Natl Acad. Sci. USA 96, 11701–11706 (1999).

    Article  ADS  Google Scholar 

  4. Khakhar, D. V., McCarthy, J. J. & Ottino, J. M. Radial segregation of granular mixtures in rotating cylinders. Phys. Fluids 9, 3600–3614 (1997).

    Article  ADS  Google Scholar 

  5. Aranson, I. S. & Tsimring, L. S. Patterns and collective behavior in granular media: Theoretical concepts. Rev. Mod. Phys. 78, 641–692 (2006).

    Article  ADS  Google Scholar 

  6. Ottino, J. M. & Khakhar, D. V. Mixing and segregation of granular materials. Ann. Rev. Fluid Mech. 32, 55–91 (2000).

    Article  ADS  MathSciNet  Google Scholar 

  7. Thomas, N. Reverse and intermediate segregation of large beads in dry granular media. Phys. Rev. E 62, 961–974 (2000).

    Article  ADS  Google Scholar 

  8. Oyama, Y. Studies on mixing of solids. Mixing of binary system of two sizes by ball mill motion. 179th Report from Okochi Research Laboratory I.P.C.R. Vol. 37, 17–29 (1939).

  9. Zik, O., Levine, D., Lipson, S. G., Shtrikman, S. & Stavans, J. Rotationally induced segregation of granular materials. Phys. Rev. Lett. 73, 644–647 (1994).

    Article  ADS  Google Scholar 

  10. Frette, V. & Stavans, J. Avalanche-mediated transport in a rotated granular mixture. Phys. Rev. E 56, 6981–6990 (1997).

    Article  ADS  Google Scholar 

  11. Choo, K., Molteno, T. C. A. & Morris, S. W. Traveling granular segregation patterns in a long drum mixer. Phys. Rev. Lett. 79, 2975–2978 (1997).

    Article  ADS  Google Scholar 

  12. Choo, K., Baker, M. W., Molteno, T. C. A. & Morris, S. W. Dynamics of granular segregation patterns in a long drum mixer. Phys. Rev. E 58, 6115–6123 (1998).

    Article  ADS  Google Scholar 

  13. Nakagawa, M. Axial segregation of granular flows in a horizontal rotating cylinder. Chem. Eng. Sci. 49, 2540–2544 (1994).

    Article  Google Scholar 

  14. Nakagawa, M., Altobelli, S. A., Caprihan, A. & Fukushima, E. NMRI study: Axial migration of radially segregated core of granular mixtures in a horizontal rotating cylinder. Chem. Eng. Sci. 52, 4423–4428 (1997).

    Article  Google Scholar 

  15. Hill, K. M., Caprihan, A. & Kakalios, J. Bulk segregation in rotated granular material measured by magnetic resonance imaging. Phys. Rev. Lett. 78, 50–53 (1997).

    Article  ADS  Google Scholar 

  16. Hill, K. M., Caprihan, A. & Kakalios, J. Axial segregation of granular media rotated in a drum mixer: Pattern evolution. Phys. Rev. E 56, 4386–4393 (1997).

    Article  ADS  Google Scholar 

  17. Jain, N., Khakhar, D. V., Lueptow, R. M. & Ottino, J. M. Self-organization in granular slurries. Phys. Rev. Lett. 86, 3771–3774 (2001).

    Article  ADS  Google Scholar 

  18. Fiedor, S. J. & Ottino, J. M. Dynamics of axial segregation and coarsening of dry granular materials and slurries in circular and square tubes. Phys. Rev. Lett. 91, 244301 (2003).

    Article  ADS  Google Scholar 

  19. Arndt, T., Siegmann-Hegerfeld, T., Fiedor, S. J., Ottino, J. M. & Lueptow, R. M. Dynamics of granular band formation: Long-term behavior in slurries, parameter space, and tilted cylinders. Phys. Rev. E 71, 011306 (2005).

    Article  ADS  Google Scholar 

  20. Finger, T. et al. Coarsening of axial segregation patterns of slurries in a horizontally rotating drum. Phys. Rev. E 74, 031312 (2006).

    Article  ADS  Google Scholar 

  21. Taberlet, N., Newey, M., Richard, P. & Losert, W. On axial segregation in a tumbler: An experimental and numerical study. J. Stat. Mech. Theory Exp. P07013 (2006).

  22. Fiedor, S. J. & Ottino, J. M. Mixing and segregation of granular matter: Multi-lobe formation in time-periodic flows. J. Fluid Mech. 533, 223–236 (2005).

    Article  ADS  Google Scholar 

  23. Cisar, S. E., Umbanhowar, P. B. & Ottino, J. M. Radial granular segregation under chaotic flow in two-dimensional tumblers. Phys. Rev. E 74, 051305 (2006).

    Article  ADS  Google Scholar 

  24. Meier, S. W., Cisar, S. E., Lueptow, R. M. & Ottino, J. M. Capturing patterns and symmetries in chaotic granular flow. Phys. Rev. E 74, 031310 (2006).

    Article  ADS  Google Scholar 

  25. Rajchenbach, J. Flow in powders: From discrete avalanches to continuous regime. Phys. Rev. Lett. 65, 2221–2224 (1990).

    Article  ADS  Google Scholar 

  26. Hill, K. M., Gioia, G. & Amaravadi, D. Radial segregation patterns in rotating granular mixtures: Waviness selection. Phys. Rev. Lett. 93, 224301 (2004).

    Article  ADS  Google Scholar 

  27. Hill, K. M., Gioia, G., Amaravadi, D. & Winter, C. Moon patterns, sun patterns, and wave breaking in rotating granular mixtures. Complexity 10, 79–86 (2005).

    Article  Google Scholar 

  28. Khakhar, D. V., Orpe, A. V. & Ottino, J. M. Continuum model of mixing and size segregation in a rotating cylinder: Concentration-flow coupling and streak formation. Powder Technol. 116, 232–245 (2001).

    Article  Google Scholar 

  29. Jain, N., Ottino, J. M. & Lueptow, R. M. Combined size and density segregation and mixing in noncircular tumblers. Phys. Rev. E 71, 051301 (2005).

    Article  ADS  Google Scholar 

  30. Jain, N., Ottino, J. M. & Lueptow, R. M. Regimes of segregation and mixing in combined size and density granular systems: An experimental study. Granular Matter 7, 69–81 (2005).

    Article  Google Scholar 

  31. Zuriguel, I., Gray, J. M. N. T., Peixinho, J. & Mullin, T. Pattern selection by a granular wave in a rotating drum. Phys. Rev. E 73, 061302 (2006).

    Article  ADS  Google Scholar 

  32. Jain, N., Ottino, J. M. & Lueptow, R. M. Effect of interstitial fluid on a granular flowing layer. J. Fluid Mech. 508, 23–44 (2004).

    Article  ADS  Google Scholar 

  33. Jain, N., Ottino, J. M. & Lueptow, R. M. An experimental study of the flowing granular layer in a rotating tumbler. Phys. Fluids 14, 572–582 (2002).

    Article  ADS  Google Scholar 

Download references

Acknowledgements

This work was supported in part by the Office of Basic Energy Sciences of the Department of Energy (Grant No. DE-FG02-95ER14534). S.W.M. and D.A.M.B. acknowledge support from the National Science Foundation.

Author information

Authors and Affiliations

  1. Department of Chemical and Biological Engineering, Northwestern University, 2145 Sheridan Rd, Evanston, Illinois 60208, USA

    Steven W. Meier & Julio M. Ottino

  2. Department of Mechanical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, Massachusetts 02139, USA

    Diego A. Melani Barreiro

  3. Department of Mechanical Engineering, Northwestern University, 2145 Sheridan Rd, Evanston, Illinois 60208, USA

    Julio M. Ottino & Richard M. Lueptow

  4. Northwestern Institute on Complex Systems (NICO), Northwestern University, Chambers Hall, 600 Foster St, Evanston, Illinois 60208, USA

    Julio M. Ottino

Authors
  1. Steven W. Meier
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Diego A. Melani Barreiro
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Julio M. Ottino
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Richard M. Lueptow
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

S.W.M. conceived the experiments. S.W.M. and D.A.M.B. carried out the experimental work. All authors analysed the results and co-wrote the paper.

Corresponding author

Correspondence to Richard M. Lueptow.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Meier, S., Melani Barreiro, D., Ottino, J. et al. Coarsening of granular segregation patterns in quasi-two-dimensional tumblers. Nature Phys 4, 244–248 (2008). https://doi.org/10.1038/nphys881

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nphys881

This article is cited by

Search

Advanced 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