Electrically induced bubble deformation, translation and collapse

In this work, the behaviour of a gas bubble in a low-Mach-number, weakly viscous, dielectric liquid under the action of a spatially uniform electric field is considered. Using domain perturbation analysis and assuming any shape deformation of the bubble or induced translation to be small, but placing no such restriction on the volume oscillations, appropriate equations to second order in the small-interaction terms are derived. Steady and time-dependent solutions are presented. The results indicate that only even shape modes and odd components of the interfacial charge density are excited starting from an initially stationary and uncharged spherical bubble. In order for the bubble to be set into motion it must either be initially deformed in terms of an odd shape mode or acquire an even charge density component. Situations are examined wherein all modes are excited and the presence of an instability that arises due to a coupling between an even mode of the charge density and bubble translation is demonstrated. The instability manifests itself via the sudden acceleration of the bubble and growth of its radius; this leads ultimately to conditions beyond the reach of the present theory.