BRAZIL NUT EFFECT MORE COMPLEX THAN THOUGHT PREVIOUSLY

Granular media differ from other materials in their response to stirring or jostling: Unlike two-fluid systems, bi-disperse granular mixtures will "size separate" under external shaking. Large particles rise to the top surface - a phenomenon reported in the 1930's and more recently termed the "Brazil-nut effect" [1, 2]. Explanations, focusing either on infiltration of small particles into voids created underneath larger ones during shaking [1-4] or on granular convection [5, 6] lead to density-independent rise-times for the larger "intruder" particles.

Recently, Shinbrot and Muzzio [7], and Liffman et al. [8] observed an increase in the velocity of a large intruder with increasing intruder density, hypothesizing that the increased inertia of heavier intruders was responsible. Hong et al. in computer simulations [9] found a "reverse Brazil-nut-effect" in which ensembles of larger particles, if sufficiently heavy, segregate to the bottom.

At Chicago, graduate student Matthias Möbius and high-school student Benjamin Lauderdale recently demonstrated [10] that the density of the larger particles on the Brazil Nut effect may be even more complicated: our results show that the speed at which the larger particle rises not only depends on the density of the larger particle, but that it does so in a highly non-monotonic fashion. This means that large particles that are either very heavy or very light move faster toward the surface of a granular mixture than particles of some intermediate weight (keeping size and shape unchanged).

This remarkably complicated density dependence is sensitive to the background air pressure. It diminishes when the air pressure is reduced and it vanishes when the whole system is placed under vacuum. The effect furthermore is most pronounced if the smaller particles surrounding the intruder have diameters below about 1mm; for example, for 0.5mm particles the rise time of the at sizes of 1mm or above the density dependence is reduced to less than 10%. This means that the gas moving back and forth through the intersticies between the grains during shaking plays a key role in the phenomenon (a direct connection between the background gas pressure and the formation of heaps in vibrated granular materials was observed previously by Robert Behringer's group at Duke University [11]).

These new results show that the roles of particle size, particle density and interstitial air are all intricately connected and need to be addressed together in in order to fully understand the Brazil Nut Effect.

For references see the bottom of this page.

For a pdf file of our recent results click here.

 

NUTS in the NEWS

For links to newspaper and journal articles about our recent findings check out the links below:

Daily Telegraph (UK)

BBC (UK)

The Independent (UK)

Rheinische Post (Germany)

Bild der Wissenschaft (Germany)

telepolis magazin der netzkultur (Germany) [this article contains links to nice computer simulations by H. Herrmann's group at the University of Stuttgart]

Science News Online

 

References:

1. Rosato, A., Strandburg, K. J., Prinz, F. & Swendsen, R. H. Why the Brazil Nuts are On Top: Size Segregation of Particulate Matter by Shaking. Physical Review Letters 58, 1038-1040 (1987).

2. Jullien, R. & Meakin, P. A Mechanism for Particle Size Segregation in Three Dimensions. Nature 344, 425-427 (1990); Jullien, R. & Meakin, P. Three-Dimensional Model for Particle-Size Segregation by Shaking. Physical Review Letters 69, 640-643 (1992)

3. Williams, J. C. The Segregation of Particulate Materials. A Review. Powder Technology 15, 245-251 (1976).

4. Duran, J., Rajchenbach, J. & Clement, E. Arching Effect Model for Particle Size Segregation. Physical Review Letters 70, 2431-2434 (1993).

5. Knight, J. B., Jaeger, H. M. & Nagel, S. Vibration-Induced Size Separation in Granular Media: The Convection Connection. Physical Review Letters 70, 3728-3731 (1993); Knight, J. B., Ehrichs, E. E., Kuperman, V. Y., Flint, J. K., Jaeger, H. M. & Nagel, S. R. Experimental Study of Granular Convection. Physical Review E 54, 5726-5738 (1996).

6. Cooke, W., Warr, S., Huntley, J. M. & Ball, R. C. Particle size segregation in a two-dimensional bed undergoing vertical vibration. Physical Review E 53, 2812-2822 (1996).

7. Shinbrot, T. & Muzzio, F. J. Reverse Buoyancy in Shaken Granular Beds. Physical Review Letters 81, 4365-4368 (1998).

8. Liffman, K., Muniandy, K., Rhodes, M., Gutteride, D. & Metcalfe, G. A Segregation Mechanism in a Vertically Shaken Bed. Granular Matter 3, 205-214 (2001).

9. Hong, D. C., Quinn, P. V. & Luding, S. Reverse Brazil Nut problem: Competition between Percolation and Condensation. Physical Review Letters 86, 3423-3426 (2001).

10. Matthias E. Möbius, Benjamin E. Lauderdale, Sidney R. Nagel and Heinrich M. Jaeger, "Size Separation of Granular Particles", Nature 414, 270 (2001). pdf file

11. Pak, H. K., van Doorn, E. & Behringer, R. P. Effects of Ambient Gases on Granular Materials Under Vertical Vibration. Phys. Rev. Lett. 74, 4643-4646 (1995).