Space-charge-limited current through conical formations on the surface of a liquid with ionic conductivity

We consider conical structures appearing on the free surface of a liquid with ionic conductivity in an applied electric field. An exact self-similar solution for the electric field distribution near the cone apex is found. It corresponds to the space-charge-limited current mode: the electric current through the liquid cone is limited by both bulk and surface charges of ions with different signs. Dependences of the saturation current and of the potential drops inside and outside the conical formation on the cone half-angle, dielectric constant of liquid, and mobility of anions and cations are determined and analyzed. •The problem concerning conical structures on the free surface of a liquid with ionic conductivity admits an exact solution.•The electric current through the liquid cone is limited by both bulk and surface charges of ions with different signs.•Dependence of space-charge-limited current on the voltage differs from the classical quadratic law.