Transient Electrohydrodynamics of a Liquid Jet: Evolution of The Flow Field

Computational studies are performed to explore the underlying physics behind the evolution of the flow field in an around a liquid jet that is immersed in another liquid and is exposed to a uniform electric field. Here the focus is on finite Reynolds and O(1) Ohnesorge number flows. This is achieved by solving the full Navier-Stokes and electric field equations using a front tracking/finite difference technique in the framework of Taylor's leaky dielectric theory. It is shown that the evolution of the flow field is determined by the relative magnitude of the ratio of the electric conductivity R = sigma(i)/sigma(o) and permittivity S = epsilon(i)/epsilon(o), where the subscripts i and o denote the fluid inside and outside of the jet. For fluid systems for which R > S or S > (1/3) (R-2 + R + 1) the flow is established by formation of four vortices inside the jet that gradually grow outward until their growth is limited by the jet interface. On the other hands, for fluid systems for which R < S < (1/ 3) (R-2 + R + 1) the flow evolves through evolution of four vortices that are formed in the ambient fluid and gradually penetrate into the jet until they are confined within the jet. Examination of the electrohydrodynamics of the jets in creeping flows leads to similar observations, and using the closed form analytical solution for these flows the computational and analytical results are justified.