The onset of electrospray for droplet impact on hydrophilic/hydrophobic substrate.

This article focuses on the filamentous ejection behavior of droplets impacting solid substrates under a vertical electric field (EF). Through experiments and numerical simulations using OpenFOAM, the study reveals that the threshold electric capillary number (Cae)—which quantifies the ratio of electrostatic to surface tension forces—for filamentous ejection varies nonlinearly with the impact Weber number (We), a dimensionless measure of inertial to surface tension forces. The nonlinear relationship is explained by the interplay between droplet stretching and three-phase line retraction, which depends on substrate properties characterized by advancing (θa) and receding (θr) contact angles. The authors develop physical and geometric models that incorporate substrate wettability, impact dynamics, electrode spacing, and fluid properties to predict the threshold Cae, showing good agreement with experimental data. This work advances understanding of the coupled effects of electric fields, fluid dynamics, and surface characteristics on droplet ejection phenomena relevant to applications such as inkjet printing, microfluidics, and power transmission.