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Spontaneous chaotic granular mixing


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.

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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.

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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.

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Correspondence to Fernando J. Muzzio.

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Shinbrot, T., Alexander, A. & Muzzio, F. Spontaneous chaotic granular mixing. Nature 397, 675–678 (1999).

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