Stationary coaxial electrified jet of a dielectric liquid surrounded by a conductive liquid

Abstract

The electrohydrodynamic problem describing the evolution of a coaxial jet of two immiscible Newtonian liquids injected through concentric orifices into a region of uniform electric field is formulated in the framework of the leaky dielectric model, and the dimensionless parameters governing the flow are identified. A simplified model is proposed combining a quasi-uni-directional approximation for the flow and the transport of electric charge with a fully numerical evaluation of the electric field. Results of this model are compared with boundary element solutions of the full governing equations for viscosity-dominated flows. The current/flow rate characteristic of a coaxial viscosity-dominated jet is computed and the ranges of flow rates in which a stationary axisymmetric jet is realized are discussed in the case of an outer liquid of finite electrical conductivity surrounding a dielectric liquid, in which the electric shear that stretches the jet is concentrated at its outer surface. The dependence of the flow on the applied electric field and the flow rates of the liquids, as well as the effects of the viscosity and electrical conductivity of the inner liquid, and of the surface tension of the inner surface, are discussed.