Coulomb-driven flow of a dielectric liquid subject to charge injection by a sharp electrode

Abstract

Injection of charge by a sharp electrode into a surrounding dielectric liquid leads to Coulomb forces that set the liquid into motion. An analysis is presented of this motion in a small region around the edge of the electrode, which determines the injected current as a function of the far electric potential seen by this region. By using an injection law appropriate for nonpolar liquids, the analysis predicts an electric current that increases first exponentially and then as the power 7 3 of the harmonic part of the electric potential, sometimes with a range of multiplicity in between