Posted on behalf of Philip Ball.
Physicists working at Trinity College in Dublin, Ireland, have finally made the perfect foam. Whereas most Dubliners might consider that to be the head on a pint of Guinness, Denis Weaire and his colleagues have a more sophisticated answer.
‘Perfect’ here means the lowest-energy configuration of packed bubbles of equal size. This is a compromise between the surface area of the bubbles and the stability of the many interlocking faces of the polyhedral bubbles in the foam. The Belgian scientist J. A. P. Plateau calculated in the nineteenth century that three soaps films are mechanically stable when they meet at angles of 120 degrees, whereas four films meet at the tetrahedral angle of about 109.5 degrees.
So what bubble shape minimizes the total surface area while (more or less) satisfying Plateau’s rules? That’s essentially the same as asking what shape balloons, or any squashy spheres, will adopt when squeezed together. Scientists including the French zoologist Georges Buffon have pondered that question, using lead shot and garden peas, for centuries. The Irish scientist Lord Kelvin thought he had the answer in 1887: the ‘perfect foam’ is one in which the cells are truncated octahedra, with eight hexagonal faces and six square ones — provided that the faces are a little curved to better fit Plateau’s rules.
Kelvin’s solution was thought to be optimal for a long time, but there was no formal proof. Then, in 1994, Weaire and his colleague Robert Phelan found a better way. It wasn’t so elegant — the structure had a repeating unit of 8 polyhedra, 6 of them with 14 faces and 2 with 12, all with hexagons and imperfect pentagons and, again, slightly curved (pictured, top). This has 0.3% less surface area than Kelvin’s foam.
But does it really exist? The duo found no definitive evidence of their ideal foam in experiments (conducted with washing-up liquid). Now there is. The key was finding the right container. Normal containers have flat walls, which the Weaire-Phelan (WP) foam won’t sit comfortably against. But physicist Ruggero Gabbrielli from the University of Trento in Italy figured that a container with walls shaped to fit the WP foam might encourage it to form. He has collaborated with Weaire and his colleagues, along with mathematician Kenneth Brakke at Susquehanna University in Selinsgrove, Pennsylvania, to design and make one out of plastic.
When Gabbrielli filled this container with equal-sized bubbles, he found that the 6 layers of about 1,500 bubbles were ordered into the WP structure (pictured below). The researchers describe their results in a paper to be published in Philosophical Magazine Letters.
This isn’t actually the first time that the WP foam has been made. But the previous example was built by hand, one cell at a time, from girders and plastic sheets, to comprise the walls of the iconic Olympic Swimming Stadium in Beijing (pictured below).
Image credits: 1 – Philip Ball. 2 – Ruggero Gabbrielli 3 – Philip Ball.