Stability Analysis of a Drop in a Pin-to-Plate Electrohydrostatic System(Fluids Engineering)

Stability of a drop in a pin-to-plate electrohydrostatic system was examined both theoretically and experimentally. With this static model, the mechanism of electrostatic ink jetting process was estimated. The basic equations are the augmented Young-Laplace equation for drop shape and the Laplace equation for electric field. These coupled equations were solved by the Finite Element Method. By the initial condition of its shape, a drop could be deformed into anomalous shapes, such as "nipple" and "dog bone," as well as conical shape, often referred as Taylor cone with the increment of non-dimensional electric field. The concentration of electric field around the corner of a nozzle was the cause of these anomalous shapes. By this stability analysis, it was demonstrated that the electrostatic ink jetting modes, dripping mode and the onset of cone-jet mode, were governed by the force balance between forces from surface tension, pressure and electrostatic field.