Estimation of hydrophobicity of insulating surfaces by studying sessile water drops

Abstract: Today, the traditional insulator materials for high voltage powerlines, i.e. glass and porcelain, are gradually being replaced with new materials, most notably silicone rubber. One of the properties that make composite insulators based on silicone rubber attractive is their hydrophobicity, which in the laboratory can be estimated by measuring contact angles of sessile water drops. The hydrophobic surface gives composite insulators better electrical flashover characteristics than hydrophilic insulators when being wet or polluted. However, the hydrophobicity of insulators in service is degraded by many factors such as pollution deposits, surface arcing and ageing, and should therefore be checked regularly. In this thesis, image analysis of water drop patterns on an inclined flat polymeric insulator surface has been performed in order to find a simple mathematical function that indicates the level of hydrophobicity of the insulator surface. The result, given the name of "Average of Normalised Entropies", ANE, seems to correlate well with hydrophobicity as defined by the classification of the Swedish Transmission Research Institute. This function is a composition of three other functions, viz. the standard deviation, the Shannon entropy and the "fraction of small differences". All these are in turn based on the histogram of horizontal nearest-neighbour pixel differences for a given digital greyscale image of a water drop pattern. ANE is fairly independent of illumination intensity (exposure), electronic gain and offset, and also of limited changes in the surface inclination. It is known that the shape of water drops can enhance the local electric field and influence the initiation of electrical discharges on the insulator surface. In this thesis, a particularly simple form of the Young-Laplace equation governing the shape of a sessile drop is derived and augmented with measures that facilitate efficient numerical computation. This mathematical representation will be useful for simulating axisymmetric drops in a vertical electric field as well as for contact angle measurement methods based on fitting theoretical drop shapes to sessile drops in digital images.