Bubble dynamics and transition into streamers in liquid dielectrics under a high divergent electric field

The paper deals with the dynamics of a bubble initiated in the vicinity of a sharp electrode in a liquid dielectric gap submitted to an electric field, and to the conditions leading to the generation of a streamer at the bubble-liquid interface. By taking into account the different stresses acting at any point of the surface of the bubble, we establish a mathematical expression describing the shape of the bubble and allowing us to analyse its deformation and instability. The frequency of the disturbances at the interface is studied and the zone at which the local electric field is the highest is determined. It is shown that depending on this frequency and therefore on the value of the local electric field, different streamer patterns can be generated. Some examples of the topology of the disturbed interface are given and discussed.