Critical strength of an electric field whereby a bubble can adopt a steady shape

Abstract

The electrically induced steady-state solutions of a gas bubble in a dielectric liquid under the action of a steady electric field are considered using the leaky dielectric model. Representing the shape deformation by a sum of spherical harmonics, it is shown that for a given parameter set there exists a critical value of the ratio of the electric to surfaces stresses beyond which no steady states exist, thus implying bubble instability and possible fragmentation. Previous studies imply that bubble instability can only be achieved if either the dielectric constant or the conductivity of the gaseous contents of the bubble is large. We show that on accounting for compressibility of the bubble, no such restriction applies for bubble instability. Below these critical values, multiple steady states are found. It is shown that a more approximate model, which assumes that the bubble is a prolate ellipsoid, can be used to represent the results for weak electric fields, but cannot be used for the prediction of the critical value of the strength of the electric field beyond which no steady-state exists.