Published online 23 March 2001 | Nature | doi:10.1038/news010329-1


Shaking up is hard to do

A new theory should help you work out when to reach for the muesli packet.

A balanced bowl of breakfast is hard to come by.A balanced bowl of breakfast is hard to come by.

Whoever starts the muesli packet often gets a bowl of Brazil nuts. For she who finishes it, breakfast can be a bowl of oaty dust. The 'Brazil nut' problem, which has so far defeated cereal manufacturers, is that the different sized grains separate out when the packets are shaken in transit, leaving the biggest on top. Now, a team of physicists finds that the reverse can happen too -- leaving the last-comer all the nuts1.

Daniel Hong of Lehigh University in Pennsylvania and colleagues looked at fairly equal mixtures of big and small particles. They found a mechanism for producing segregation that can work either way round.

The key to this mechanism is the fact that a collection of gently agitated grains can behave as a fluid or a solid, depending on how hard you shake it. Shaking is analogous to temperature: if it is gentle enough, the grains condense to a solid, just as water molecules in random, jostling motion turn to ice if the temperature is low enough.

Grains of different sizes may have quite different 'freezing' points. One type might solidify into a densely packed layer while the other remains fluid, dividing the two. Hong's team simulated this system on the computer, for the case in which the large grains condense first.

If large grains are not too heavy, they can form a kind of porous plug in the vessel, through which the small grains filter down to form a layer on the bottom. This is the normal Brazil nut effect, with large grains on top.

But if the big grains are either heavier, or closer in size to the small grains, they tend to sink when they condense, forming a dense, closely packed layer on the bottom while the smaller grains dance above: reverse Brazil nut effect. At the breakfast table this would pull all the dust to the top of the packet.

The Brazil nut effect -- known to chemical engineers since at least the 1960s -- is one of the many ways in which grainy substances behave strangely. Many explanations have been put forward for the segregation of different-sized particles.

Some researchers have pointed to a sieving effect, whereby small grains fall through the gaps between larger ones. Others have shown how the voids created below large grains when the whole system is shaken vertically can quickly fill up with small grains, moving the large ones steadily upwards.

And still others have identified a kind of convection effect that causes grains to move up in the centre and down at the sides of a shaken vessel. The large grains get trapped at the top, because they are too large to fit within the narrow descending stream. It seems that all of these phenomena may be involved, under different circumstances, in segregating the big grains to the top of the heap.

Hong and colleagues believe that the reverse effect was overlooked because most earlier studies focused on the case of just one or a few big grains mixed with many small ones, rather than the more equal mixtures in their simulations. 

  • References

    1. Hong,D.C.,Quinn, P.V.& Luding, S. Reverse Brazil nut problem: competition between percolation and condensation. Physical Review Letters (in the press).