The breakdown of electrical insulation in a plane layer of insulating fluid by electrocapillary instability

Abstract

A theoretical and experimental study is made of the failure of electrical insulation in a layer of dielectric fluid filling a circular hole in a horizontal solid dielectric sheet. A potential difference is applied between conducting fluids which bound the fluid and solid dielectric layer above and below. It is observed that a critical potential difference is reached at which the fluid dielectric becomes statically unstable under the action of surface tension and normal electrical stresses at its interfaces. When this potential is reached the dielectric fluid insulation fails.The critical potential difference is calculated by both an approximate and an exact theory. The approximate theory ignores the changes in the electrostatic field within the solid dielectric by allowing a charge distribution at the curved surface of the hole. Comparison with the results of an exact theory shows that such an approximation introduces only small errors in the calculated points of transition to instability.It is shown that failure may take the form of a symmetric (sausage) mode of displacement, or an antisymmetric (kink) mode, depending on whether the radius of the hole is greater or less than approximately the depth of the layer respectively. The two forms of failure were indicated in the experiments, and the observed critical voltages are in good agreement with those predicted by the theory.