Percolative model of electric breakdown in liquid dielectrics

A percolative approach, useful in modeling liquid dielectric breakdown, is presented. The dielectric is treated as a network of resistors having random values and breakdown characteristics based on a specified statistical distribution. The method is quite general, and lends itself to the inclusion of internal fluctuations and localized heating. It should also be applicable to mixtures and facilitate the inclusion of air bubbles. Despite its simplicity, the model successfully characterizes fractal structure in dielectric breakdown. In particular, the fractal dimension for a two-dimensional (2-D) lattice as given by the exponent of a power law, agrees with the theoretical value. The dependence of critical external voltage on the internal disorder is also investigated. It is shown that the overall breakdown process consists of the successive breakdown of individual elements to finally form a percolation cluster. The clusters have a typical dendrite structure. Also, in keeping with qualitative expectations, it is shown that V_br decreases with the disorder and increases with resistor variance.