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.

Spontaneous chaotic granular mixing

Nature volume 397, pages 675–678 (1999)Cite this article

Abstract

There are several types of instabilities in fluid mechanics that lead to spontaneous chaotic mixing and intricate patterns. Classical examples include the Kelvin–Helmholtz instability1,2 in shear layers, the instability of Taylor–Couette flow between rotating cylinders3,4 and the Rayleigh-Bénard instability in thermal convection5. More recently, a variety of two- and three-dimensional chaotic mixing phenomena have been observed in other geometries6,7,8,9. Mixing in granular flows10,11, unlike that in stirred fluids, is thought to be diffusive—although periodic forcing has been used to enhance granular mixing12,13, spontaneous chaotic granular mixing has not previously been reported. Here we report the observation of chaotic granular mixing patterns in simple cylindrical tumblers partially filled with fine grains. The patterns form spontaneously when sufficiently fine grains (≲300 µm diameter) are blended. We identify the mechanism by which the chaotic patterns are produced: a periodic stick–slip behaviour occurs in the shear layer separating static and flowing regions of grains. This causes weakly cohesive grains to mix at rates overwhelmingly exceeding those achievable for previously studied11,14 freely flowing grains.

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

Learn more

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

Figure 1: Comparison between experiments (a) and simulation (b) of mixing in rotating cylindrical tumblers one-third filled with identical red and green particles.
Figure 3: Stretching of experimental and numerical interfaces versus the number of tumbler revolutions.
Figure 2: The continuum model.

Similar content being viewed by others

References

  1. Thorpe, S. A. Experiments on the instability of stratified shear flows: miscible fluids. J. Fluid Mech. 46, 299–319 (1971).

    Article  ADS  Google Scholar 

  2. Van Dyke, M. (ed.) An Album of Fluid Motion (Parabolic, Stanford, California, 1982).

    Book  Google Scholar 

  3. 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 

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

    Article  ADS  Google Scholar 

  5. Solomon, T. H. & Gollub, J. P. Chaotic particle transport in time-dependent Rayleigh-Bénard convection. Phys. Rev. A 38, 6280–6284 (1988).

    Article  ADS  CAS  Google Scholar 

  6. Aref, H. Stirring by chaotic advection. J. Fluid Mech. 143, 1–21 (1984).

    Article  ADS  MathSciNet  Google Scholar 

  7. Alvarez, M. M., Muzzio, F. J., Cerbelli, S., Androver, A. & Giona, M. Self-similar spatio-temporal structure of material filaments in chaotic flows. Phys. Rev. Lett. 81, 3395–3398 (1998).

    Article  ADS  CAS  Google Scholar 

  8. Lamberto, D. J. & Muzzio, FJ. Experimental and computational investigaiton of the laminar flow structure in a stirred tank. Chem. Eng. Sci. (in the press).

  9. Hobbs, D. M., Alvarez, M. M. & Muzzio, F. J. Mixing in globally chaotic flows: a self-similar process. Fractals 5, 395–428 (1997).

    Article  MathSciNet  CAS  Google Scholar 

  10. Choo, K., Molteno, T. C. A. & Morris, S. W. Traveling granular segregation patterns in a long drum mixer. Phys. Rev. Lett. 79, 2975–2977 (1997).

    Article  ADS  CAS  Google Scholar 

  11. Metcalf, G., Shinbrot, T., McCarthy, J. J. & Ottino, J. M. Avalanche mixing of granular solids. Nature 374, 39–41 (1995).

    Article  ADS  Google Scholar 

  12. Wightman, C., Mort, P. R., Muzzio, F. J., Riman, R. E. & Gleason, E. K. The structure of mixtures of particles generated by time-dependent flows. Powder Technol. 84, 231–240 (1995).

    Article  CAS  Google Scholar 

  13. Brone, D. et al. Using flow perturbations to enhance mixing of dry powders in V-blenders. Powder Technol. 91, 165–172 (1997).

    Article  CAS  Google Scholar 

  14. Khakhar, D. V., McCarthy, J. J., Shinbrot, T. & Ottino, J. M. Transverse flow and mixing of granular materials in a rotating cylinder. Phys. Fluids 9, 31–43 (1997).

    Article  ADS  CAS  Google Scholar 

  15. Van Cleef, J. Powder technology. Am. Sci. 79, 304–315 (1991).

    ADS  Google Scholar 

  16. Gupta, S. D., Khakhar, D. V. & Bhatia, S. K. Axial segregation of particles in a horizontal rotating cylinder. Chem. Eng. Sci. 46, 1513–1525 (1991).

    Article  Google Scholar 

  17. 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  CAS  Google Scholar 

  18. Pouliquen, O., Delour, J. & Savage, S. B. Fingering in granular flows. Nature 386, 816–817 (1997).

    Article  ADS  CAS  Google Scholar 

  19. Nakagawa, M., Altobelli, S. A., Caprihan, A., Fukushima, E. & Jeong, E. K. Non-invasive measurements of granular flows by magnetic resonance imaging. Exp. Fluids 16, 54–60 (1993).

    Article  Google Scholar 

  20. Campbell, H. & Bauer, W. C. Cause and cure of demixing in solid-solid mixers. Chem. Eng. 179–185 (1966).

  21. Chester, A. W. et al. Mixing dynamics in catalyst impregnation in twin-cone blenders. Powder Technol. (in the press).

  22. Moakher, M., Shinbrot, T. & Muzzio, F. J. Experimentally validated computations of flow, mixing and segregation of non-cohesive grains in 3D tumbling blenders. (preprint, Rutgers Univ., Piscataway, New Jersey 08854 USA, 1998).

  23. Nasono, S., Kudrolli, A. & Gollub, J. P. Friction in granular layers: hysteresis and precursors. Phys. Rev. Lett. 79, 949–952 (1997).

    Article  ADS  Google Scholar 

  24. Alvarez, M. M., Muzzio, F. J., Cerbelli, S., Adrover, A. & Giona, M. Self-similar spatiotemporal structure of intermaterial boundaries in chaotic flows. Phys. Rev. Lett. 81, 3395–3398 (1998).

    Article  ADS  CAS  Google Scholar 

  25. Rudolph, M., Shinbrot, T. & Lueptow, R. M. Amodel of mixing and transport in wavy Taylor-Couette flow. Physica D 121, 163–174 (1998).

    Article  ADS  CAS  Google Scholar 

  26. Shinbrot, M. Fixed-point theorems. Sci. Am. 214, 105–110 (1966).

    Article  ADS  Google Scholar 

  27. 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 

  28. Pöschel, T. & Buchholtz, V. Complex flow of granular material in a rotating cylinder. Chaos Solitons Fractals 5, 1901–1912 (1995).

    Article  ADS  Google Scholar 

  29. Wolf, A., Swift, J. B., Swinney, H. L. & Vastano, J. A. Determining Lyapunov exponents from a time series. Physica D 16, 285–317 (1985).

    Article  ADS  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by the International Fine Powder Research Institute, the NSF, the New Jersey Commission on Science and Technology, and Pfizer Pharmaceuticals. We thank A. Abad for tehnical assistance.

Author information

Authors and Affiliations

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

    Troy Shinbrot, Albert Alexander & Fernando J. Muzzio

Authors
  1. Troy Shinbrot
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Albert Alexander
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Fernando J. Muzzio
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Fernando J. Muzzio.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Shinbrot, T., Alexander, A. & Muzzio, F. Spontaneous chaotic granular mixing. Nature 397, 675–678 (1999). https://doi.org/10.1038/17760

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/17760

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