Eur. Phys. J. E 9, 453-460 (2002)
DOI: 10.1140/epje/i2002-10103-4

Instabilities of cylindrical bubble clusters

K.A. Brakke¹ and F. Morgan<sup>2

1</sup>  Mathematics Department, Susquehanna University, Selinsgrove, PA 17870, USA
²  Department of Mathematics and Statistics, Williams College, Williamstown, MA 01267, USA

brakke@susqu.edu
frank.morgan@williams.edu

(Received 22 September 2002 / Published online: 4 February 2003)

Abstract
Small bubbles in an experimental two-dimensional foam between glass plates regularly undergo a three-dimensional instability as the small bubbles shrink under diffusion or equivalently as the plate separation increases, and end up on one of the plates. The most recent experiments of Cox, Weaire, and Vaz are accompanied by Surface Evolver computer simulations and rough theoretical calculations. We show how a recent second variation formula may be used to perform exact theoretical calculations for infinitesimal perturbations for such a system, and verify results with Surface Evolver simulations.

PACS
82.70.Rr - Aerosols and foams.
47.20.Dr - Surface-tension-driven instability.

© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2002