Activity: Talk or presentation › Oral presentation
Coarsening of cellular materials such as foams depends crucially on the geometry of the cells. John von Neumann proved about 50 years ago that the growth rates of polygonal 2-D foam bubbles depend linearly on the number of edges of the polygon. Using a theorem by Minkowski, we derive a three-dimensional Von Neumann law relating the growth rates of polyhedral bubbles to the number of their faces. The analytical, parameter-free expression for the growth rate is non-linear and proves to be in excellent agreement with detailed foam simulations and with experimental data. The model can be refined to incorporate various forms of foam disorder.