Granular convection

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Brazil nuts ride on top of other assorted nuts

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Brazil nut with shell

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Mixed nuts

Granular convection is a phenomenon where granular material subjected to shaking or vibration will exhibit circulation patterns similar to types of fluid convection. It is sometimes described as the Brazil nut effect when the largest particles end up on the surface of a granular material containing a mixture of variously sized objects; this derives from the example of a typical container of mixed nuts, where the largest will be Brazil nuts. The phenomenon is also known as the muesli effect since it is seen in packets of breakfast cereal containing particles of different sizes but similar density, such as muesli mix.

Under experimental conditions, granular convection of variously-sized particles has been observed forming convection cells similar to fluid motion. However, in general the convection of granular flows is not a well-understood phenomenon.

Explanation

It may be counter-intuitive to find that the largest and (presumably) heaviest particles rise to the top, but there are several possible explanations:

• Smaller particles can fall into the spaces underneath a larger particle after each shake. Over time, the larger particle rises in the mixture. In other words: The center of mass of the whole system (containing the mixed nuts) in an arbitrary state is not optimal (because of the space close to the Brazil nuts); it has the tendency to be higher due to gravity. When the nuts are shaken, gravity will make sure the center of mass of the system moves down and this can only be done by moving the Brazil nuts up. Gravity will also make sure they stay up.
• When shaken, the particles move in vibration-induced convection flow: individual particles move up through the middle, across the surface, and down the sides. If a large particle is involved, it will be moved up to the top by convection flow. Once at the top, the large particle will stay there because the convection currents are too narrow to sweep it down along the wall.
• Including the effects of air in spaces between particles, larger particles may become buoyant or sink.
• The phenomenon is related to Parrondo's paradox inasmuch as the Brazil nuts move to the top of the mixed nuts against the gravitational gradient when subjected to random shaking.

Granular convection has been probed by the use of MRI imaging where convection rolls similar to those in fluids (Bénard cells) can be visualized.

Applications

Manufacturing

The effect is of serious interest for some manufacturing operations; once a heterogeneous mixture of granular materials has been produced, it is usually undesirable for the different particle types to segregate. Several factors determine the severity of the Brazil nut effect, including the sizes and densities of the particles, the pressure of any gas between the particles, and the shape of the container. A rectangular box (such as a box of breakfast cereal) or cylinder (such as a can of nuts) works well to counter the effect, while a cone-shaped container results in what is known as the reverse Brazil nut effect.

Astronomy

In astronomy, it is also seen in some low density, or rubble pile asteroids, for example the asteroid 25143 Itokawa.

Geology

In geology, this phenomenon is one of the causes of inverse grading which can be observed in many situations including soil liquefaction during earthquakes or mudslides.

See also

• Cheerios effect

External links

• Beads in a Box at YouTube
• Convection rolls in almost densely filled rotating containers, University of Magdeburg
• PhysicsWeb: The Brazil Nut Effect
• 
• The Brazil Nut Effect: Numerical Simulation Example of the numerical simulation of the Brazil Nut Effect.
• "Why brazils always end up on top", BBC News, 15 November 2001
• "Why does shaking a can of coffee cause the larger grains to move to the surface?", Scientific American, 9 May 2005
• "Of airbags, Avalungs and avalanche safety", Toronto Star, 13 January 2008
• Sixty Symbols: Brazil Nut Effect, The University of Nottinghamcs:Efekt paraořechu

zh:巴西果效应