Single and Multiple Cusp Formation in an Electrified and Curved Film of Liquid Metal

Above a critical value of the electric field strength, an electrified film of perfecting conducting fluid can overcome capillary leveling to form a cusp-like protrusion known as a dynamic Taylor cone. The accelerating flow generates large electric field strengths at the moving tip, ultimately causing ion emission. This physical process is the basis of focused ion beam systems utilizing a single component liquid metal or eutectic alloy. Here we describe results of extensive numerical simulations prior to ion emission to uncover how initial state variables including liquid film curvature induce formation and growth of single and multiple cusps in an electrified film. Explicating the complexities of this electrohydrodynamic flow necessitates high resolution spatial and temporal tracking of rapidly accelerating protrusions under operating conditions and system geometry designed to replicate actual systems. Our results reveal the existence of several flow regimes exhibiting different behavior depending on choice of initial state variables. For the case of multiple cusp formations, we compare and contrast protrusion growth rate and wavelength selection against results of a comparable electrohydrodynamic (EHD) instability known to occur in a flat liquid layer.