Instabilities of cylindrical bubble clusters

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.