The Pursuit of Perfect Packing

Date: 19 January 2011, 06:39

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Foams and bubbles have fascinated scientists of all ages, in all ages. Most have devoted some time to admiration of what Robert Boyle called 'the soap bubbles that boys are wont to play with'. Part of their charm and mystery lies in the colours produced by the interference of light in thin films. Small clusters of bubbles, or the extended ones we call foams, have elegant structures which call for explanation. The poet and philosopher may point to the ephemeral nature of these things as a metaphor for our own mortality or the transience of fame and fortune, but the first interest of the scientist is in making relatively stable foams. This is not difficult with a little ordinary detergent solution shaken in a sealed container. Looking into it, one can see that, though disordered, it shows clear evidence of some principles of equilibrium at work. What are they? When spherical bubbles pack together to form a foam (as when they rise out of a glass of beer) they are forced in! to polyhedral shapes as gravity extracts most of the liquid from their interstices. What began as a sphere packing, in conformity to the rules of previous chapter, now presents a different paradigm for pattern in nature. In this case the density is fixed and surface area is to be minimized.

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