A method to determine the onset voltage of single and arrays of electrospray emitters

This paper reports on an accurate and rapid method to compute the onset voltage for a single or for an array of electrospray emitters with complex geometries and on the correlation of the simulation with experimental data. This method permits the exact determination of the onset voltage based only on the surface tension of the sprayed liquid and of the emitter geometry. The approach starts by determining the voltage at which electrostatic forces and surface tension forces are equal for a sharpening conic surface at the tip of a capillary as a function of the apex radius of the liquid. By tracing the curve of this computed equilibrium voltage as a function of apex radius, the onset voltage for a liquid surface with the Taylor half-angle of 49.3{degree sign} or larger can be determined. For smaller cone half-angles the method is only applicable to ionic sprays as an approximate knowledge of the critical field for ion emission is necessary. The combination of analytical models and finite element tools used to compute the necessary parameters are described. The method is validated on a complex MEMS emitter geometry as well as on a linear array of electrospray emitters. Finally an empirical model of the behavior of the electric field near the apex of a conic surface with asymptotes at a fixed half-angle is proposed which allows establishing a simple method for onset voltage determination.