Fractal analysis of creeping discharge patterns propagating at solid/liquid interfaces: influence of the nature and geometry of solid insulators

The paper is aimed at the fractal analysis of the creeping discharge patterns propagating over different solid insulators immersed in mineral oil, under negative impulse voltage using a point-plane electrode arrangement. The considered solid insulators are circular samples of different thickness made of polycarbonate, phenoplast resin (Bakelite) and glass. Two methods are used to estimate the fractal dimension, namely the box counting method and the fractal measure relations method. It is shown that the creeping discharges propagate radially; the shape and the length of these discharges depend on the types of solid insulators and their thicknesses. By using the box counting method, we show that the discharge patterns present a fractal dimension D which depend on the thickness of the solid samples (e) and the type of insulator. D decreases when e increases. This suggests the possible implication of capacitive effects on the propagation phenomena of creeping discharges. So D increases with the dielectric constant of the insulator; it is the highest for glass and the lowest for polycarbonate; D is in between for phenoplast resin. This dependency of D on the solid insulators and their thicknesses reveals the existence of a relation between the fractal dimension and the physical parameters. The fractal measure relations method gives a fractal dimension equal to the Euclidian dimension (D = 2) due to the fact that the density of branches ρ(r) remains constant whatever the radius r of the circular domain within which ρ(r) is determined. ρ(r) depends on the thickness and the nature of solid insulating material. The value of the density of branches increases when the thickness of the solid insulating material decreases.