Deformation of Platonic foam cells: Effect on growth rate

Evans M, Zirkelbach J, Schröder-Turk G, Kraynik AM, Mecke K (2012)

Publication Status: Published

Publication Type: Journal article

Publication year: 2012

Journal

Publisher: AMER PHYSICAL SOC

Book Volume: 85

Journal Issue: 6

DOI: 10.1103/PhysRevE.85.061401

Abstract

The diffusive growth rate of a polyhedral cell in dry three-dimensional foams depends on details of shape beyond cell topology, in contrast to the situation in two dimensions, where, by von Neumann's law, the growth rate depends only on the number of cell edges. We analyze the dependence of the instantaneous growth rate on the shape of single foam cells surrounded by uniform pressure; this is accomplished by supporting the cell with films connected to a wire frame and inducing cell distortions by deforming the wire frame. We consider three foam cells with a very simple topology; these are the Platonic foam cells, which satisfy Plateau's laws and are based on the trivalent Platonic solids (tetrahedron, cube, and dodecahedron). The Surface Evolver is used to model cell deformations induced through extension, compression, shear, and torsion of the wire frames. The growth rate depends on the deformation mode and frame size and can increase or decrease with increasing cell distortion. The cells have negative growth rates, in general, but dodecahedral cells subjected to torsion in small wire frames can have positive growth rates. The deformation of cubic cells is demonstrated experimentally.

Authors with CRIS profile

Additional Organisation(s)

Involved external institutions

University of Manchester United Kingdom (GB)

How to cite

APA:

Evans, M., Zirkelbach, J., Schröder-Turk, G., Kraynik, A.M., & Mecke, K. (2012). Deformation of Platonic foam cells: Effect on growth rate. Physical Review E, 85(6). https://doi.org/10.1103/PhysRevE.85.061401

MLA:

Evans, Myfanwy, et al. "Deformation of Platonic foam cells: Effect on growth rate." Physical Review E 85.6 (2012).

BibTeX: Download