Electrohydrodynamic flow of a dielectric liquid around a blade electrode

Abstract

Injection of charge into a dielectric liquid, and a Coulomb force that sets the liquid into motion, may be obtained by applying a dc voltage to a blade-shaped, metallic electrode immersed in the liquid. An analysis of this motion and its influence on the transport of electric charge is carried out for a simple charge injection law. It is shown that the liquid motion, the electric field, and the charge distribution in a region around the electrode tip of size of the order of the electrode curvature radius determine the injected current as a function of the far electric potential seen by this region. The current increases exponentially with the potential when the contribution of the space charge to the electric field is negligible and algebraically when it is dominant, and presents a range of multiplicity in between. When the inertia of the liquid matters, the region around the electrode tip is also the origin of an electrohydrodynamic plume. An oscillatory current regime is found in which the space charge in the interelectrode space rearranges into many discrete lumps that, under constant voltage bias and small current, induce oscillations of the electric field at the injecting electrode and thus fire new lumps. An order of magnitude analysis and numerical computations for this regime give results in line with known experimental data. In conjunction with the hydrodynamic instability of the plume, this pulse firing mechanism is seen to lead to more complex, nonperiodic oscillations.