Electrohydrodynamics of a liquid jet in transverse AC electric fields

Abstract

The behavior of a liquid jet in a transverse AC electric field is investigated. The governing electrohydrodynamic equations are solved analytically for Newtonian and immiscible fluids in the framework of leaky-dielectric model and in the limit of small electric field and fluid inertia. It is shown that ratios of electric conductivity and permittivity of the constituting fluids along with a nondimensional frequency (i.e., the time scale of the electric field oscillation over the time scale of charge relaxation from the bulk of the ambient fluid to the jet surface) are the key parameters that determine the mean and the time-periodic behavior of the jet, and that on the basis of these parameters the fluids can be categorized into three different classes in terms of their impact on the mean behavior of the jet. In the first class, the jet elongates in the direction of or perpendicular to the field, becoming a prolate or an oblate ellipse, respectively, depending on the field frequency, and the mean deformation increases with an increase in the frequency of the field. In the second class, the jet deforms to a prolate and the mean deformation increases with an increase in the frequency. In the third class, the jet deforms to a prolate and the mean deformation decreases with an increase in the frequency. It is shown that for the first class of the fluids a critical frequency exists at which the jet remains circular regardless of the strength of the electric field. Concerning the time-periodic behavior, it is shown that the jet surface oscillates with a frequency that is twice that of the imposed electric field, and the time-periodic deformation has a time lag with respect to the imposed electric field. The evolution of the flow field with time is studied and it is shows that the flow structure is determined by the interplay of the net interfacial tangential and normal electric forces, and that depending on the relative importance of these two parameters the flow will consist of closed vortices or open-ended streamlines (open vortices). The frequency of oscillation of the flow field is twice that of the external electric field, and it has a time lag with respect to the imposed electric field.