Ruggero Gabbrielli from the University of Bath has spent a short period at Swansea's School of Engineering as a Leverhulme Trust Research Fellow.
His work addresses the Kelvin Problem, posed by Scottish mathematical physicist and engineer, Lord Kelvin, in 1887. The problem asked how space could be partitioned into cells of equal volume with the least area of surface between them, i.e., what was the most efficient soap bubble foam?
Lord Kelvin's bitruncated cubic honeycomb foam became known as the Kelvin structure. The convex uniform honeycomb formed by the truncated octahedron, (a 14-sided space-filling polyhedron (a tetrakaidecahedron), with 6 square sides and 8 hexagonal sides) was believed to solve the Kelvin problem.
It was not until 1993 that Denis Weaire and Robert Phelan, two physicists based at Trinity College Dublin, challenged the Kelvin structure, establishing the Weaire-Phelan structure, a complex 3-dimensional structure which in computer simulations of foam was found to be a better solution to the Kelvin problem. The Weaire-Phelan structure uses two kinds of cells of equal volume; an irregular pentagonal dodecahedron and a tetrakaidecahedron with 2 hexagons and 12 pentagons and has a surface area 0.3% less than the Kelvin structure, quite a significant difference in this context.
However, Ruggero Gabbrielli has devised a new way to mathematically model foam while studying the structure for his PhD in mechanical engineering. Whereas the Weaire-Phelan model used two shapes, Ruggero's honeycomb-like model is composed of four different shapes that fit together and has a surface area of 0.2% more than the Weaire-Phelan model, and 0.1% less than Kelvin structure.
Ruggero explained: "The method uses a partial differential equation, well-known in two-dimensional pattern formation. The novelty is that I've applied it to a three-dimensional problem to model the shape of foams."
The structure has been observed to be much like the foams found in nature and could lead to medical advances in creating hip replacements and replacement bone tissue for bone cancer patients.
For more information about research within the School of Engineering at Swansea University, visit: www.swan.ac.uk/engineering
