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

Abstract

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 equationsof 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.