Zeroth-order, electrohydrostatic solution for electrospraying in cone-jet mode

Liquid and charge emissions in steady regime from an electrified meniscus take place when its shape develops an almost conical point. A very thin and remarkably stable capillary jet emerging from the conical vertex eventually breaks up into droplets, forming the so-called electrospray. The emission process is an extremely complicated electrohydrodynamic phenomenon which may be solved by performing a perturbation analysis which requires the knowledge of an electrostatic, zeroth-order solution for the shape of the electrified meniscus with a conical tip. In this work, the shape of these tip-ended, axisymmetric, electrified menisci is solved for the first time assuming negligible space charge. The solution of this first-order, electrostatic problem yields not only the backbone result on a further perturbation scheme to solve the liquid and charge emission process, but also the old problem of that value of the potential difference at which the liquid is to be connected in order to achieve a tip-ended shape, necessary to have electrostatic atomization, as a function of the liquid properties and boundary geometry.