Electrohydrodynamic plumes in point-plane geometry

We examine the flow organization induced by charge injection from a needle of small radius of curvature into an insulating dielectric liquid. Experimental results are presented for the electrical current as a function of the point-plane distance and of the applied voltage. Schlieren visualization reveals the existence of very thin plumes which are slightly vacillating. An approximate analysis of the laminar plume is developed which takes into account the finite but very thin axial region where charge is confined. A classical type of asymptotic treatment results in a set of ordinary differential equations, provided the current and the field distribution are known. A new expression for the order of magnitude of the liquid velocity is proposed which leads to estimates of the radius a of the charge core and the typical radial scale δ of the velocity profile. For a gap spacing d, these estimates are of the order of 10^-3 d and 10^-2 d which confirm the thinness of such charge plumes