Q: Shaking a packet of cornflakes causes the contents to pack down rather than merely redistribute. What physical principles apply? (continued)
A: Your answers in The Last Word (13 May) describe special cases of the shake 鈥榥鈥� pack effect without touching upon the fundamental principle involved. The effect, which is well known to geologists and civil engineers, does not depend on a mixture of particles of different sizes. It works just as well with an accumulation of spheres of uniform size.
Depending on how gently these are poured into the container, in theory their packing will vary from the loosest, so-called cubic packing, with intergranular porosity forming 48 per cent of the total volume, to the tightest, rhombohedral packing, with a greatly reduced porosity of 26 per cent. Loose packing is stabilised by friction between particles. Shaking reduces this friction and allows particles to rotate and slide into denser packing.
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Earthquakes shake sediments on the sea floor, causing a sudden change to denser packing with simultaneous release of the surplus pore-water which then acts as a lubricant. The result maybe a submarine landslide and tidal wave.
A: Previous explanations do not explain why packing down occurs in a container full of similar objects. Fill an empty jam jar with sugar cubes until adding one more would prevent you from closing the lid. Gently shake the jar for 15 seconds and you will find you can add more cubes and still close the lid.
The potential energy of an arrangement of sugar cubes is proportional to the height of its centre of gravity. Initially the cubes are in a relatively unpacked state with a high potential energy. Tapping the jar injects a small amount of kinetic energy which can make the cubes jump up. They can then either stick where they are, drop back into the original arrangement, or fall into an arrangement with better packing and lower potential energy.
Optimal arrangements can be achieved by annealing: tapping vigorously at first and then progressively more gently This principle is exploited by blacksmiths aligning metal crystals.