Von Neumann law
The Von Neumann's law describes the change in the size of two-dimensional cell foam .
Due to the pressure differences between neighboring foam cells and the resulting diffusion , the surface area of the individual two-dimensional foam cells also changes over time. In 1952, John von Neumann found the law named after him
where indicates the change in the area of a cell with N corners over time. k> 0 is a growth coefficient with unity . It is interesting that the change in area only depends on the number of sides of the foam cell, but not on the neighbors or the area of the cell. An equilibrium is thus established when an area consists entirely of hexagonal cells.
4-corner | Cell is shrinking | |
5-corner | Cell is shrinking | |
6-corner | Area constant | |
7-corner | Cell grows | |
Octagon | Cell grows |
Von Neumann's law only applies to two-dimensional foam. A corresponding law for three-dimensional foam was published by Sascha Hilgenfeldt et al. and Robert D. MacPherson & David J. Srolovitz.
literature
- Denis Weaire, Stefan Hutzler: The Physics of Foams . Clarendon Press, Oxford 1999, ISBN 0-19-851097-7 .
Individual evidence
- ^ J. von Neumann: Metal Interfaces . American Society for Metals, Cleveland 1992.
- ^ Sascha Hilgenfeldt: An Accurate von Neumann's Law for Three-Dimensional Foams . In: Physical Review Letters . No. 86 , 2001, doi : 10.1103 / PhysRevLett.86.2685 .
- ^ Robert D. MacPherson, David J. Srolovitz: The von Neumann relation generalized to coarsening of three-dimensional microstructures . In: Nature . tape 446 , no. 7139 , April 26, 2007, p. 1053-1055 , doi : 10.1038 / nature05745 ( nature.com [accessed April 10, 2016]).