Abstract
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.
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