Modelling the onset of instability for charged droplets in an external electric field

Injecting fuel as a dispersion of charged droplets and applying electric fields has been proposed as a mechanism to improve the fuel flexibility of aviation engines. Modelling such systems requires computationally efficient methods that can predict when droplet instability occurs due to electrical forces overcoming surface tension. Therefore, two methods are developed to provide the maximum charge a droplet can hold before instability. Taylor’s approach of assuming prolate spheroidal droplet shapes up until instability is generalised to charged linear dielectric droplets in an insulating linear dielectric fluid and subject to a uniform electric field. Additionally, an analytical charge limit expression is derived by considering a spherical droplet and analysing the stresses acting at the point of maximum surface charge density. Both methods predict that the charge limit increasingly falls below the Rayleigh limit as the electric field intensity is increased, with the electric field effect increasing with increasing droplet diameter and permittivity. Taylor’s generalised method provides accurate electric field limits for uncharged dielectric droplets, while the analytical expression overestimates these limits. For conducting droplets in reasonably strong electric fields, the generalised method underestimates the charge limits by overestimating droplet elongation, while the analytical expression provides more accurate charge limits. The analytical expression is also expected to provide accurate charge limits when the droplet diameter, droplet permittivity, and/or electric field intensity are not large. Ultimately, the derived methods provide a computationally efficient approach for simulating the fragmentation of charged droplets in electric fields.