The structure of electrospray beams in vacuum

Electrospray atomization of liquids in the cone-jet mode generates narrow droplet distributions with average diameters as small as a few nanometres. This ability is important for technologies such as colloid thrusters, nanoparticle generation and ion beam processes, and the optimization of these applications requires an understanding of the physics and structure of the associated beams. This paper presents a detailed experimental characterization of electrosprays in vacuum and formulates an analytical model of the beam. A key feature of our model is the use of a simplified expression for the electric field induced by the space charge. This simplification leads to a time-independent Eulerian formulation compatible with an analytical solution, in contrast to the direct simulation of a multitude of droplets which must be simultaneously tracked to account for Coulombic interactions. We find that the beams open up in an initial region relatively insensitive to the external electrodes, a process dominated by the electric repulsion between droplets and the initial droplet inertia. Although the external electric field modifies the trajectories of the droplets downstream of this initial region, the effect is moderate in our typical electrospray source and the analytical solution in the space charge region explains well the far-field beam structure observed experimentally. We also describe a numerical scheme that implements the full effect of the external electric field and provides a more accurate solution.