Transient electrohydrodynamics of a liquid drop: The interplay of fluid flow evolution and dynamic response, and the...

Computer simulations are performed to study some of the less explored aspects of the transient electrohydrodynamics of a liquid drop in uniform DC electric fields. The governing equations of the problem are solved using a parallelized front tracking/finite difference method in the framework of Taylor-Melcher's leaky dielectric theory. For density- and viscosity-matched fluid systems, the evolution of the flow field at a high Ohnesorge-squared number Oh^{2}=μ^{2}/γρa is studied. It is shown that the instantaneous flow pattern is the result of superposition of deformation- and hydrodynamic shear-driven vortices, and that depending on the placement of the fluid systems on the deformation-circulation map, there exists two different paths for the development of the velocity field toward steady state. Examination of the steady-state flow patterns shows that the location of the maximum velocity can shift from the (classically known) drop surface to inside the drop along the poles. The effect of Oh^{2} on the dynamic response of the drop and the kinetic energy of the fluid is studied. For high Oh^{2} number flows, the dynamic response is monotonic while the kinetic energy evolves in a nonmonotonic way, achieving a distinct peak before settling to steady state. However, for low Oh^{2} number flows, both the dynamic response and kinetic energy are oscillatory. Inspection of the results show a two-way coupling between the deformation rate and the fluid flow. The effect of the density ratio ρ[over ̃]=ρ_{i}/ρ_{o} (drop to ambient) on the dynamic response and fluid flow strength shows that for high Oh^{2} number flows both parameters remain essentially intact at steady state, while their evolution modes transition from a monotonic response to an oscillatory one at high density ratio. However, for low Oh^{2} number flows, with an increase in ρ[over ̃], the oscillation frequency of both parameters remain intact, while their oscillation amplitudes increase.