Breakup modes of a planar liquid jet in a static electric field

Breakup process of a two-dimensional planar jet is analytically investigated when the jet is placed between two parallel sheath walls on which an external electric field is imposed. In the analysis, we consider the influence of finite relaxation time and convection of surface charges and tangential stress on the jet surfaces due to the parallel electric field. According to the leaky dielectric model and the slender jet approximation, nonlinear evolution equations for the jet are derived when the aerodynamic effect is neglected. The equations are solved numerically under the initial-boundary condition that the jet is emanating from a slit nozzle. It is found that there exist two types of breakup modes for symmetric deformations: (i) the surface tension dominant mode where a tip of the jet grows larger as the jet flows downward and (ii) the electric force dominant mode where the tip of the jet is accelerated and becomes thinner and thinner to the downstream. The existing regions of these two modes are mainly determined by two parameters Pe (=charge relaxation time/time of fluid motion) and Lambda (=electric pressure/fluid inertial). We find critical curves in the Pe-Lambda parameter space, across which the mode is transferred from (i) to (ii) with the increase of. and/or the decrease of Pe. It is also found that antisymmetric deformations of the jet grow to the downward as long as the jet is thick, but the deformations are suppressed and stabilized as the jet becomes sufficiently thin.