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:

A Taylor vortex analogy in granular flows

Nature volume 431, pages 433–437 (2004)Cite this article

Abstract

Fluids sheared between concentric rotating cylinders undergo a series of three-dimensional instabilities. Since Taylor's archetypal 1923 study1, these have proved pivotal to understanding how fluid flows become unstable and eventually undergo transitions to chaotic or turbulent states2,3,4,5. In contrast, predicting the dynamics of granular systems—from nano-sized particles to debris flows—is far less reliable. Under shear these materials resemble fluids, but solid-like responses, non-equilibrium structures and segregation patterns develop unexpectedly6,7,8,9. As a result, the analysis of geophysical events10 and the performance of largely empirical particle technologies might suffer11,12. Here, using gas fluidization to overcome jamming6,13, we show experimentally that granular materials develop vortices consistent with the primary Taylor instability in fluids. However, the vortices observed in our fluidized granular bed are unlike those in fluids in that they are accompanied by novel mixing–segregation transitions. The vortices seem to alleviate increased strain by spawning new vortices, directly modifying the scale of kinetic interactions. Our observations provide insights into the mechanisms of shear transmission by particles and their consequent convective mixing.

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: Fluidized granular bed imaged through a transparent outer cylinder alongside vertical composition profiles.
Figure 2: Shear response of fluidized granular bed.
Figure 3: Evidence of Taylor vortices.

Similar content being viewed by others

References

  1. Taylor, G. I. Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. Lond. A 223, 289–343 (1923)

    Article  ADS  Google Scholar 

  2. Andereck, D., Liu, S. S. & Swinney, H. L. Flow regimes in a circular Couette system with independently rotating cylinders. J. Fluid Mech. 164, 155–183 (1986)

    Article  ADS  Google Scholar 

  3. Mullin, T. & Benjamin, T. B. Transition to oscillatory motion in the Taylor experiment. Nature 288, 567–569 (1980)

    Article  ADS  Google Scholar 

  4. Mullin, T. Mutations of steady cellular flows in the Taylor experiment. J. Fluid Mech. 121, 207–218 (1982)

    Article  ADS  Google Scholar 

  5. Abshagen, J., Meincke, O., Pfister, G., Cliffe, K. A. & Mullin, T. Transient dynamics at the onset of Taylor vortices. J. Fluid Mech. 476, 335–343 (2003)

    Article  ADS  MathSciNet  Google Scholar 

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

    Article  ADS  CAS  Google Scholar 

  7. Forterre, Y. & Pouliquen, O. Longitudinal vortices in granular flows. Phys. Rev. Lett. 86, 5886–5889 (2001)

    Article  ADS  CAS  Google Scholar 

  8. Mobius, M. E., Lauderdale, B. E., Nagel, S. R. & Jaeger, H. M. Size separation of granular particles. Nature 414, 270 (2001)

    Article  ADS  CAS  Google Scholar 

  9. Burtally, N., King, P. J. & Swift, N. R. Spontaneous air-driven separation in vertically vibrated fine granular mixtures. Science 295, 1877–1879 (2002)

    Article  ADS  CAS  Google Scholar 

  10. Scott, D. R. Seismicity and stress rotation in a granular model of the brittle crust. Nature 381, 592–595 (1996)

    Article  ADS  CAS  Google Scholar 

  11. Bridgwater, J. The dynamics of granular materials - towards grasping the fundamentals. Granular Matter 4, 175–181 (2003)

    Article  Google Scholar 

  12. Michaels, J. N. Toward rational design of powder processes. Powder Technol. 138, 1–6 (2003)

    Article  CAS  Google Scholar 

  13. Savage, S. B. & Sayed, M. Stresses developed by dry cohesionless granular materials sheared in an annular shear cell. J. Fluid Mech. 142, 391–430 (1984)

    Article  ADS  Google Scholar 

  14. Wereley, S. T. & Lueptow, R. M. Spatio-temporal character of non-wavy and wavy Taylor–Couette flow. J. Fluid Mech. 364, 59–80 (1998)

    Article  ADS  MathSciNet  Google Scholar 

  15. Losert, W., Bocquet, L., Lubensky, T. & Gollub, J. Particle dynamics in sheared granular matter. Phys. Rev. Lett. 85, 1428–1431 (2000)

    Article  ADS  CAS  Google Scholar 

  16. Medlin, J., Wong, H.-W. & Jackson, R. Fluid mechanical description of fluidized beds: Convective instabilities in bounded beds. Indust. Eng. Chem. Fundam. 13, 247–259 (1974)

    Article  CAS  Google Scholar 

  17. Apicella, E., D'Amore, M., Tardos, G. & Mauri, R. Onset of instability in sheared gas fluidized beds. AIChE J. 43, 1362–1373 (1997)

    Article  CAS  Google Scholar 

  18. Wightman, C., Muzzio, F. J. & Wilder, J. A quantitative image analysis method for characterizing mixtures of granular materials. Powder Technol. 89, 165–176 (1996)

    Article  CAS  Google Scholar 

  19. Wilkes, J. O. Fluid Mechanics for Chemical Engineers (Prentice-Hall, Upper Saddle River, 1999)

    Google Scholar 

  20. Silva, S. R. D., Dyrøy, A. & Enstad, G. G. in IUTAM Symposium on Segregation in Granular Flows (eds Rosato, A. D. & Blackmore, D. L.) 11–30 (Kluwer Academic, Dordrecht, 1999)

    Google Scholar 

  21. Djeridi, H., Fave, J.-F., Billard, J.-Y. & Fruman, D. H. Bubble capture and migration in Couette–Taylor flow. Expts Fluids 26, 233–239 (1999)

    Article  ADS  Google Scholar 

  22. Khosropour, R., Zirinsky, J., Pak, H. K. & Behringer, R. P. Convection and size segregation in a Couette flow of granular material. Phys. Rev. E 56, 4467–4473 (1997)

    Article  ADS  CAS  Google Scholar 

  23. Hirschfield, D. & Rapaport, D. C. Molecular dynamics simulation of Taylor–Couette vortex formation. Phys. Rev. Lett. 80, 5337–5341 (1998)

    Article  ADS  Google Scholar 

  24. Conway, S. & Glasser, B. Density waves and coherent structures in granular Couette flows. Phys. Fluids 16, 509–529 (2004)

    Article  ADS  MathSciNet  CAS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  26. Bridgewater, J. Fundamental powder mixing mechanisms. Powder Technol. 15, 215–236 (1976)

    Article  Google Scholar 

  27. Joseph, D. D., Wang, J., Bai, R., Yang, B. H. & Hu, H. H. Particle motion in a liquid film rimming the inside of a partially filled rotating cylinder. J. Fluid Mech. 496, 139–163 (2003)

    Article  ADS  MathSciNet  Google Scholar 

  28. Matson, W. R., Ackerson, B. J. & Tong, P. Pattern formation in a rotating suspension of non-Brownian settling particles. Phys. Rev. E 67, 050301 (2003)

    Article  ADS  CAS  Google Scholar 

  29. Shinbrot, T. & Muzzio, F. Nonequilibrium patterns in granular mixing and segregation. Physics Today 53, 25–30 (2000)

    Article  Google Scholar 

Download references

Acknowledgements

We thank K. LaMarche, D. Brain, S. Shah, M. Ozbas, M. Clark, A. Alexander and D. Trinkle for assistance. This work was partly supported by NSF, ACS-PRF and NASA. S.L.C. thanks Merck & Co. for financial support during an educational leave of absence.

Author information

Author notes

  1. Stephen L. Conway

    Present address: Merck & Co., Inc., Whitehouse Station, New Jersey, 08889, USA

Authors and Affiliations

  1. Department of Chemical and Biochemical Engineering, Rutgers, The State University of New Jersey, Piscataway, New Jersey, 08854, USA

    Stephen L. Conway & Benjamin J. Glasser

  2. Department of Biomedical Engineering, Rutgers, The State University of New Jersey, Piscataway, New Jersey, 08854, USA

    Troy Shinbrot

Authors
  1. Stephen L. Conway
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Troy Shinbrot
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Benjamin J. Glasser
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Benjamin J. Glasser.

Ethics declarations

Competing interests

The authors declare that they have no competing financial interests.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Conway, S., Shinbrot, T. & Glasser, B. A Taylor vortex analogy in granular flows. Nature 431, 433–437 (2004). https://doi.org/10.1038/nature02901

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nature02901

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

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