Weaire-Phelan structure
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The Weaire-Phelan structure is a complex 3-dimensional structure discovered in 1993 by Denis Weaire and Robert Phelan, 2 physicists based at Trinity College Dublin, using computer simulations of foam. It is proposed to be the optimal solution of the Kelvin problem.
In 1887, Lord Kelvin asked how could space be partitioned into cells of equal volume with the least area of surface between them, i.e. the most efficient soap bubble foam.
He proposed a 14-sided space-filling polyhedron (a tetrakaidecahedron) with 6 square sides and 8 hexagonal sides (or truncated octahedron) with slightly curved faces because of Plateau's laws which govern the structures of foams. The Kelvin structure was believed to be the optimal solution for more than 100 years.
The Weaire-Phelan structure uses two kinds of cells of equal volume; a dodecahedron and a tetrakaidecahedron with 2 hexagons and 12 pentagons with slightly curved faces. The surface area is 0.3% less than the Kelvin structure, quite a large difference in this context. It has not been proved that the Weaire-Phelan structure is optimal, but it is generally believed to be likely.
The structure is also found in chemistry where it is usually known as the Type I clathrate structure.
It is the inspiration for the design of the aquatic centre for the 2008 Olympics in Beijing in China.
See also
External links
- [Weaire-Phelan structure unfolded dodecahedron and tetrakaidecahedron in .pdf / .dxf formats]
- [Weaire-Phelan structure three-dimensional model in .dxf format]
- [An image of the Weaire-Phelan structure]
- ['The Water Cube', National Swimming Centre, Beijing, China]
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