Transient electrohydrodynamics of a liquid drop in AC electric fields

The transient behavior of a leaky dielectric liquid drop under a uniform AC electric field of small strength is investigated, using a closed form analytical solution. The drop settles to a quasi-steady state in a relaxation time that is set by the viscosities of the drop and the ambient fluid and the surface tension, and oscillates around a mean deformation with a frequency that is twice the electric field frequency. The mode of instantaneous deformation remains the same (oblate or prolate) or switches between oblate and prolate, depending on the relative importance of the time-periodic component of the deformation compared to that of the time-exponential. The structure of the flow field and its evolution is studied for representative fluid systems at a high and a low electric field frequency. The individual contribution of the net tangential and normal electric stresses, which are the driving forces of the problem, on the flow structure and drop deformation is characterized. On the basis of the mean (time-independent) and time-periodic components of the driving forces, the flow field is represented as the superposition of three different flow patterns. It is shown that the interplay of these flow patterns leads to formation and destruction of toroidal vortices, and that the residence time of these vortices correlates inversely with the field frequency.