We study theoretically the axisymmetric nonlinear dynamics of viscous conducting liquid jets or threads under the action of a radial electric field. The field is generated by a potential difference between the jet surface and a concentrically placed electrode of given radius. We develop a long wave nonlinear model that is used to predict the dynamics of the system and, in particular, to address the effect of the radial electric field on jet breakup. Two canonical regimes are identified that depend on the size of the gap between the outer electrode and the unperturbed jet surface. For relatively large gap sizes, long waves are stabilized for sufficiently strong electric fields but remain unstable as in the nonelectrified case for electric field strengths below a critical value. For relatively small gaps, an electric field of any strength enhances the instability of long waves as compared to the nonelectrified case. We carry out numerical simulations based on our nonlinear models to describe the nonlinear evolution and terminal states in these two regimes. We find that jet pinching does not occur irrespective of the parameters. We identify regimes where capillary instability leads to the formation of stable quasistatic microthreads (connected to large main drops) whose radius decreases with the strength of the electric field. The generic ultimate singular event described by our models is the attraction of the jet surface toward the enclosing electrode and its contact with the electrode in finite time. A self-similar closed form solution is found that describes this event with the interface near touchdown having locally a cusp geometry. The theory is compared to the time-dependent simulations with excellent agreement.

The effect of an electric field on a periodic array of two-dimensional liquid drops suspended in simple shear flow is studied numerically. The shear is produced by moving the parallel walls of the channel containing the fluids at equal speeds but in opposite directions and an electric field is generated by imposing a constant voltage difference across the channel walls. The level set method is adapted to electrohydrodynamics problems that include a background flow in order to compute the effects of permittivity and conductivity differences between the two phases on the dynamics and drop configurations. The electric field introduces additional interfacial stresses at the drop interface and we perform extensive computations to assess the combined effects of electric fields, surface tension and inertia. Our computations for perfect dielectric systems indicate that the electric field increases the drop deformation to generate elongated drops at steady state, and at the same time alters the drop orientation by increasing alignment with the vertical, which is the direction of the underlying electric field. These phenomena are observed for a range of values of Reynolds and capillary numbers. Computations using the leaky dielectric model also indicate that for certain combinations of electric properties the drop can undergo enhanced alignment with the vertical or the horizontal, as compared to perfect dielectric systems. For cases of enhanced elongation and alignment with the vertical, the flow positions the droplets closer to the channel walls where they cause larger wall shear stresses. We also establish that a sufficiently strong electric field can be used to destabilize the flow in the sense that steady-state droplets that can exist in its absence for a set of physical parameters, become increasingly and indefinitely elongated until additional mechanisms can lead to rupture. It is suggested that electric fields can be used to enhance such phenomena.

The dynamics of a plane interface separating two sheared, density and viscosity matched fluids in the vertical gap between parallel plate electrodes are studied computationally. A Couette profile is imposed onto the fluids by moving the rigid plates at equal speeds in opposite directions. In addition, a vertical electric field is applied dielectrics the vertical electric field was found to enhance interfacial motion irrespective of the permittivity ratio, while in leaky dielectrics the electric field can either stabilize or destabilize the interface, depending on the conductivity and permittivity ratio between the fluids.

No abstract