Electrohydrodynamic flow of a dielectric liquid due to autonomous injection of charge by a needle electrode

An analysis is presented of the creeping axisymmetric flow induced by Coulomb's force in a dielectric liquid subject to autonomous unipolar injection of electric charge through a paraboloidal metallic electrode. A stationary flow and a I proportional toV(3) current-voltage characteristic are found when the constant voltage applied between the injecting electrode and another, collecting electrode is well above the injection threshold but below a certain critical value. For larger voltages the flow and the electric current become time dependent, owing to the instability of a charged layer that surrounds the injecting electrode. Qualitative order of magnitude estimates are presented for both regimes. (C) 2002 American Institute of Physics.