Conical structures on the surface of a liquid with surface ionic conductivity: the space charge effect

Conical structures arising on the surface of a liquid with surface conductivity in an electric field are considered taking into account the influence of space charge of particles emanating from the cone apex. It is demonstrated that the field distribution problem admits an exact self-similar solution corresponding to the Taylor scaling law. This solution allows us to determine the relation between the total electric current flowing through the cone and the cone and space-charge region half-angles. The structure of this relation is quite sophisticated; it changes essentially with changing the permittivity of a liquid and the mobility of carriers.