Modeling simple-jet mode electrohydrodynamic-atomization droplets' trajectories and spray pattern for a single nozzle system

Abstract Electrohydrodynamic atomization (EHDA), or simply Electrospraying is the process of influencing the breakup of a liquid into droplets by using a strong electric field. There can be different modes of Electrospraying depending, basically, on the created electric field strength and the liquid flowrate, for a specified liquid. Among these modes, the so-called cone-jet mode is the most explored one. This is due to its ability to produce highly charged monodisperse droplets in the nano- to micro-meter size range. Another mode of interest, which can also produce monodisperse droplets is the simple-jet mode. This mode is less explored when compared to the former. Within the papers that were explored by the authors, Agostinho et al. (2012) were the first authors to carefully investigate and characterize this mode. In their work, the authors reported about the influence of the electric field and the liquid flowrate on the droplets' size and spray dispersion. They also pointed out that the charge on these droplets can be expressed as a certain percentage of their Rayleigh limit. So far, there has been no model proposed to describe the droplets' trajectories in the simple-jet mode. This paper describes the design and the implementation of a physical model for determining the droplet trajectories in this mode. The model is done, specifically, for a single nozzle/ring-up configuration. It is a two-dimensional model, which solves the force balance equation for each droplet breaking up from the jet. It takes into consideration; the initial droplet velocity, the force of gravity, the electric field force, the inter-droplet coulombic force and the drag force. The droplets' deformation and reorientation were hypothesized, from observations, to play a major role in initiating the droplets' dispersion. They were simulated by implementing periodic displacements on the droplets' center of charge from its center of mass. The calculated droplets' trajectories' envelope angle was fitted to the experimental envelope angle by adjusting the droplet charge around the values that were reported by Agostinho et al. (2012). The model was validated by comparing the shapes of the theoretical and experimental sprays. The model offers new possibilities of modeling the droplets' trajectories in complex geometries, and of introducing additional forces to manipulate their trajectories in the simple-jet mode.