FEATURE ARTICLE
Foams and Honeycombs
For centuries, the precise architecture of soap foams has been a source of wonder to children and a challenge to mathematicians
Erica Klarreich
Constructing Real Foams
At this point you may be wondering why one would not simply build a foam out of equal-volume bubbles and look at the configuration it forms. In fact, over the years many have tried the experiment. Until recently, the best known of these efforts were experiments conducted in the 1940s by the physicist Edwin Matzke, who created a foam of 1,900 bubbles one bubble at a time, using a syringe. At the end of this laborious procedure, he examined 600 bubbles at the center of the foam. Matzke found that the average number of sides belonging to each cell was very close to 14 (the number of sides of Kelvin's truncated octahedron), but he did not find a single copy of Kelvin's cell. In fact, he did not discover any ordered pattern at all. In an amusing address in 1950 to the Torrey Botanical Club at Columbia University, he warned of the dangers of leaping from mathematical models to real-world conclusions "in the twinkling of an eye."
For many years, Matzke's experiments appeared to have closed the subject. Weaire and Phelan, however, suspected that his observations were misleading. Matzke's method for creating a foam was so time-consuming that often a full day elapsed between the creation and the measurement of a bubble. This opened the door to serious errors, because as time passes, air tends to leak across foam walls from one bubble to another, altering their size and shape. Weaire and Phelan decided to try the experiment anew, and they built a foam using the time-honored and speedy method of blowing bubbles through a straw. They found several of Kelvin's cells near the surface of the foam and, deeper inside, several small fragments similar to their own structure. Weaire and Phelan observed that "with the benefit of hindsight, it would appear that the subject has suffered in the past from an excess of theorizing and a shortage of experiments." As techniques for building foams are refined, it may be hoped that they will produce clearer and clearer pictures of the structures that nature chooses for its foams.
The overthrow of Kelvin's partition by a less symmetric, more complicated structure came as an intriguing, somewhat disturbing piece of news to scientists who believe that the best configuration should display beautiful symmetry. However, the Weaire-Phelan structure may enjoy only temporary status as the optimal foam structure. We should recall Penrose's dictum: When to us the contest may appear to be between two well-understood possibilities, nature may suddenly pull out of its hat a completely different and infinitely more elegant solution.
© Erica G. Klarreich
