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
Subscribe to this journal
Receive 51 print issues and online access
$199.00 per year
only $3.90 per issue
Rent or buy this article
Prices vary by article type
Prices may be subject to local taxes which are calculated during checkout
Similar content being viewed by others
Thorpe, S. A. Experiments on the instability of stratified shear flows: miscible fluids. J. Fluid Mech. 46, 299–319 (1971).
Van Dyke, M. (ed.) An Album of Fluid Motion (Parabolic, Stanford, California, 1982).
Taylor, G. I. Stability of a viscous liquid contained between two rotating cylinders. Phil. Trans. R. Soc. Lond. A 223, 289–343 (1923).
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).
Solomon, T. H. & Gollub, J. P. Chaotic particle transport in time-dependent Rayleigh-Bénard convection. Phys. Rev. A 38, 6280–6284 (1988).
Aref, H. Stirring by chaotic advection. J. Fluid Mech. 143, 1–21 (1984).
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).
Lamberto, D. J. & Muzzio, FJ. Experimental and computational investigaiton of the laminar flow structure in a stirred tank. Chem. Eng. Sci. (in the press).
Hobbs, D. M., Alvarez, M. M. & Muzzio, F. J. Mixing in globally chaotic flows: a self-similar process. Fractals 5, 395–428 (1997).
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).
Metcalf, G., Shinbrot, T., McCarthy, J. J. & Ottino, J. M. Avalanche mixing of granular solids. Nature 374, 39–41 (1995).
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).
Brone, D. et al. Using flow perturbations to enhance mixing of dry powders in V-blenders. Powder Technol. 91, 165–172 (1997).
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).
Van Cleef, J. Powder technology. Am. Sci. 79, 304–315 (1991).
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).
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).
Pouliquen, O., Delour, J. & Savage, S. B. Fingering in granular flows. Nature 386, 816–817 (1997).
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).
Campbell, H. & Bauer, W. C. Cause and cure of demixing in solid-solid mixers. Chem. Eng. 179–185 (1966).
Chester, A. W. et al. Mixing dynamics in catalyst impregnation in twin-cone blenders. Powder Technol. (in the press).
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).
Nasono, S., Kudrolli, A. & Gollub, J. P. Friction in granular layers: hysteresis and precursors. Phys. Rev. Lett. 79, 949–952 (1997).
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).
Rudolph, M., Shinbrot, T. & Lueptow, R. M. Amodel of mixing and transport in wavy Taylor-Couette flow. Physica D 121, 163–174 (1998).
Shinbrot, M. Fixed-point theorems. Sci. Am. 214, 105–110 (1966).
Scott, D. R. Seismicity and stress rotation in a granular model of the brittle crust. Nature 381, 592–595 (1996).
Pöschel, T. & Buchholtz, V. Complex flow of granular material in a rotating cylinder. Chaos Solitons Fractals 5, 1901–1912 (1995).
Wolf, A., Swift, J. B., Swinney, H. L. & Vastano, J. A. Determining Lyapunov exponents from a time series. Physica D 16, 285–317 (1985).
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.
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
This article is cited by
Effects of segregation in binary granular mixture avalanches down inclined chutes impinging on defending structures
Environmental Earth Sciences (2016)
Granular Matter (2010)
Chinese Science Bulletin (2007)
Large phreatomagmatic vent complex at Coombs Hills, Antarctica: Wet, explosive initiation of flood basalt volcanism in the Ferrar-Karoo LIP
Bulletin of Volcanology (2006)