Hamburg 2001 – wissenschaftliches Programm
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DY: Dynamik und Statistische Physik
DY 13: Statistische Physik (Allgemein) II
DY 13.3: Vortrag
Montag, 26. März 2001, 11:00–11:15, S 7
Foam geometry and foam coarsening: A three-dimensional Von Neumann law — •Sascha Hilgenfeldt1,2, Andrew Kraynik3, Stephan Koehler2, and Howard Stone2 — 1Applied Physics, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands — 2DEAS, Harvard University, Pierce Hall, Cambridge, MA 02138 — 3Engineering Sciences Center, Sandia National Laboratories, Albuquerque, NM 87185
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.