Conical structures on the surface of a liquid with ion current in the space-charge limited mode

Conical structures arising on the surface of a liquid with ionic conductivity in an electric field are considered taking into account the influence of both bulk and surface charges. It is demonstrated that the field distribution problem admits an exact analytical solution corresponding to the space-charge-limited current mode. The dependence of the saturation current through the conical formation on the cone apex angle, on the dielectric constant of the liquid, and on the mobilities of positive and negative ions is found. The current vanishes at zero and Taylor’s (49.3°) cone half-angles, and reaches the maximum value between them. The maximum current is shifted to higher angles with increasing dielectric constant of the medium.