Steady and transient electrohydrodynamic plumes

Electrohydrodynamic (EHD) plumes arise when sharp metallic contours submerged in non conducting liquids support high electrostatic potential, resulting in charge injection. Self similar solutions exist for steady two-dimensional and axisymmetric EHD plumes. These solutions are the same as those for thermal plumes in the case of very large Prandtl numbers Pr. For two-dimensional plumes the velocity is finite in this limit. For axisymmetric thermal plumes the velocity at the axis becomes infinity for Pr→∞, but in any case this divergence is very weak, since it goes as In √Pr. The inverse of the charged layer cross section plays the role of an effective Prandtl number in EHD plumes. Therefore the velocity of the EHD plumes increases without limit as the thickness of the charged layer decreases. Transient EHD plumes are obtained when applying a step voltage to a metallic point or blade. We present some measurements of the velocity of two-dimensional transient EHD plumes as a function of the applied voltage. Also some theoretical estimations are presented