Electrohydrodynamics of a current-carrying semi-insulating jet

Abstract

A quasi-one-dimensional non-linear model is developed for the axisymmetric dynamics. Streaming is coaxial with a cylindrical ‘wall’ supporting a potential having a linear axial dependence. In addition to a tangential field due to an axial current, the stream surface supports charges in proportion to the stream-wall potential difference; hence it is driven by normal and shear electric stresses. Free charge and polarization waves compete with the destabilizing effect of capillarity. With supercritical steady flow (the local jet velocity exceeds the wave velocity), it is found that the stream accelerates or decelerates in accordance with whether an equivalent longitudinal force density is respectively positive or negative. With subcritical flow, the effect of the force is reversed. Experiments demonstrate accelerating and decelerating flow régimes. Model and experiment are in agreement with regard to choking at a critical radius, and the dependence of radius and potential on position. Hysteretic switching between flow régimes is obtained by adjustment of stream and wall potentials, and is explained in terms of the model.