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An accurate von Neumann's law for three-dimensional foams
S Hilgenfeldt1, A M Kraynik, S A Koehler
1Division of Engineering and Appled Sciences, Harvard University, Cambridge, MA 02138, USA. sascha@tn.utwente.nl
Physical Review Letters
|April 6, 2001
Summary
Scientists derived a new 3D von Neumann
Area of Science:
- Physics
- Materials Science
- Applied Mathematics
Background:
- The diffusive coarsening of 2D soap froths follows von Neumann's law.
- A statistical version for dry 3D foams has been long conjectured but unproven.
Purpose of the Study:
- To derive an explicit analytical von Neumann's law for 3D foams.
- To compare the derived law with experimental and simulation data.
Main Methods:
- Utilized a new derivation based on a theorem by Minkowski.
- Performed detailed simulations and experiments for validation.
Main Results:
- An explicit analytical von Neumann's law in 3D was derived.
- The average bubble growth rate is proportional to F1/2 for large F (number of faces), contradicting the conjectured linear dependence.
- Incorporating foam disorder improved model agreement with data.
Conclusions:
- The new 3D von Neumann's law accurately describes foam coarsening.
- The F1/2 dependence offers a novel understanding of 3D foam dynamics.
- The model provides a robust framework for studying disordered foams.