Electrohydrodynamic Simulations of Self-Similar Cuspidal Formations Relevant to Liquid Metal Ion Sources

Liquid metal ion sources, used in applications ranging from metal deposition or ion doping to space propulsion, rely on spontaneous emission in liquids subject to strong electric fields. The liquid source, placed in close proximity to a counter electrode with a circular aperture, is typically either a small droplet at the tip of a capillary tube or a thin film made to coat the rounded tip and length of a solid needle. While the latter geometry affords certain advantages, it introduces significant complexity in the spatiotemporal response of the film prior to emission, behavior which can only be explored by high fidelity electrohydrodynamic simulations. In this talk, we present results based on finite element modeling of electrified films coating a solid needle which reveal formation of liquid conformations not previously reported. The accelerating cuspidal shapes, pressure and velocity field values at the apical tip evolve by a self-similar process terminating in blowup, which can be characterized by various exponents. We discuss parameter ranges and factors controlling film response by presenting a novel “phase diagram” delineating those configurations so far observed.