Modeling and Simulation of \Sub-Microsecond Electrical Breakdown in Liquids with Application to Water

In this dissertation, the inherent physics and sub-microsecond electrical breakdown of water stressed to high voltages is analyzed, and several relevant models are constructed for quantitative analysis. A bubble-based, drift-diffusion (DD) model proposed here includes almost all the important physical process of the system, and successfully explains many important features routinely observed in sub-microsecond water electrical breakdown. Here many physical properties and response characteristics typical for high-field stressing of liquid water have been analyzed through numerical calculations. The internal temperature profile in the water system has been calculated by Finite Difference Time Domain (FDTD) method to probe possible heating and vaporization effects. Results show temperature increases of less than 7° Kelvin, precluding possibilities for localized evaporation. Second, it is shown through Monte-Carlo simulations that electrons in liquid water cannot contribute to impact ionization and electron multiplication at normal liquid water densities. Instead, it is shown that electrons emitted within pre-existing microbubbles within the liquid could contribute to electron multiplication and initiate the electric breakdown process. Third, it is demonstrated here through microscopic Monte-Carlo calculations that the dielectric constant of water would be a monotonically decreasing function of the electrical field, with strong reductions beyond 3 MV/cm. It is also shown that this field-dependent behavior, coupled with electric field enhancements across dielectric discontinuities such as the water-bubble interface, can potentially contribute to electrical breakdown. Finally, the most important contribution of this dissertation is the development of a bubble-based, drift-diffusion (DD) model that includes the field-dependent effects. Simulation results based on this model show strong agreement with many features of experimentally observed features. The features include: (i) streamer branching for the positive polarity due to internal micro-bubbles; (ii) negative streamers normally having a higher breakdown voltage requirement; (iii) negative streamers having a thicker root and larger cross-sectional radii as compared to positive streamers; (iv) increasing hold-on voltage with system over-pressure; and (v) faster breakdown times for positive polarity, point-plane geometries. The model is quite general, and applicable to other liquids