The charging level of a ligament-droplet system atomized in a uniform electric field

In this paper, a numerical algorithm has been formulated for calculating the charge magnitude on a spherical droplet created by break-up of a cylindrical ligament in an external electric field. The algorithm is based on the Finite Element Method and it determines the droplet charge as a function of the droplet radius and ligament length. It has been found that the droplet charge is a function of particle radius to some exponent, which is equal to 2 when the droplet is in direct contact with the atomizer and decreases dramatically to approach 1.1, as the ligament length increases. The effect of the ligament radius on the charging level has been found to be significant and increases with the ligament length. It was determined that the charging level is affected by the presence of adjacent ligaments and previously ejected droplets. To investigate the dynamics of the droplet atomization, the Navier-Stokes equations, describing the fluid motion, as well as the level-set equation for tracking the interfaces between the air and liquid have been solved. A comparison between the charging level of the dynamically formed droplets and an assumed spherical one has been presented. It has been found that the predicted charging level of the spherical droplet is lower than the one of the actual shape in a range of 15-26%.