Electrohydrodynamics of cone-jet flow at high relative dielectric permittivity

In this paper we propose a new solution of the electrohydrodynamic equations describing a novel cone-jet flow structure formed at a conductive liquid meniscus in an electric field. Focusing on the liquids characterized by a high relative dielectric permittivity and using the slender body approximation, the cone-jet transition profiles and their characteristic radii are predicted in relation to the material parameters. The stable value of the cone angle is obtained using the Onsager's principle of maximum entropy production. Three different regimes of the cone-jet flow behavior are identified depending on the relative importance of capillary, viscous and inertial stress contributions. The presented complete analytical solutions for the cone-jet transition zone and the far jet region yield several different laws of algebraic decrease for the radius, surface charge and electric field of the jet.