The thermal-expansive growth of prebreakdown steamers in liquids

The growth of electrically conductive, low-density regions has been observed in dielectric breakdown in a variety of liquids. This phenomenon motivates the development of the present theory for coupling thermal effects with fluid mechanical effects in the dynamics of elongated, impulsively driven bubbles. The model describes the time-dependent dimensions of a growing ellipsoidal bubble. The parameters of the model are the external pressure in the liquid, the density of energy which is deposited impulsively in the liquid, and the length over which energy is deposited. Previously, a model was developed for such effects associated with the growth of a bubble about an arc in a liquid. In the case of the prebreakdown streamer, the geometry is not as simple as for an arc and the evolution of the bubble is found in ellipsoidal coordinates. The effect of pressure is to shorten the time scale of the bubble dynamics. Even in the case where the bubble might not be spatially resolved, the time to recollapse can be established from visual data. Calculations based on the model are shown to be consistent with experimental results on the collapse of the streamer