Bubbles in insulating liquids: stability in an electric field

Abstract

It is shown that a bubble of gas or liquid, immersed in a liquid medium and subjected to an electric field between parallel plate electrodes, assumes the shape of a prolate spheroid in the direction of the field. Expressions for interfacial traction between two fluid dielectrics, if derived by taking into account electrostriction (Stratton 1941; Smythe 1950), are shown to be in disagreement with experimental results and must therefore be considered incorrect. Using expressions for interfacial traction not involving electrostrictive terms, equations are derived for the dependence on electric stress of the elongation of compressible (gaseous) and of incompressible (liquid) bubbles immersed in an insulating liquid. These show that as the field strength is increased, conducting bubbles, and also non-conducting bubbles for which the permittivity of the bubble exceeds twenty times the permittivity of the medium, elongate until a critical shape is reached when the bubble becomes unstable. For conducting bubbles the critical shape corresponds to a ratio of the major to the minor semi-axis of 1*85. Bubbles of permittivity ratio lower than 20 have no critical shape, the axial ratio increasing indefinitely with increase of field strength. There is satisfactory agreement between theory and experiment. The implications of these results with regard to electrical breakdown of liquids are discussed.