Threshold electric field for pulsed electrodeformation and electrocoalescence of conducting droplets: A dimensionless approach to the low-to-high frequency transition

This study investigates the behavior of water droplets suspended in oil under pulsed electric fields, focusing on the electrodeformation of a single droplet and the electrocoalescence of a droplet pair. Numerical simulations were performed using the arbitrary Lagrangian–Eulerian (ALE) method, which allows for accurate tracking of sharp interfaces between the droplet and the surrounding medium. A key objective was to determine the threshold electric field required for irreversible droplet deformation and coalescence across a range of frequencies, droplet sizes, viscosities, and interfacial tensions. The main contribution of this work is the introduction of a dimensionless time-scale parameter that effectively captures the transition from low-to high-frequency regimes. The parameter is defined in terms of the pulse frequency f , the natural oscillation period t 1 , and the Ohnesorge number O h as P t y = f t 1 O h − 0.7 . This parameter allows for the collapse of threshold–frequency curves for different system properties, providing a unified framework for predicting the frequency-dependent behavior of droplets under pulsed electric fields. Regarding the dependence of the threshold field on frequency, single-droplet electrodeformation occurs in a quasi-static regime for P t y < 0.01 , in a high-frequency regime for P t y > 1 , and in a transitional region between these values. For the electrocoalescence of two droplets, analogous boundaries may be taken as P t y = 0.01 and P t y = 10 . The proposed parameter also offers a practical tool for interpreting experimental observations and planning further studies in electrohydrodynamic processes. • Droplet electrodeformation and electrocoalescence in pulsed fields are studied. • Breakup threshold increases with frequency for both deformation and coalescence. • The transition from low to high frequencies depends on droplet size and fluid properties. • A new time-scale parameter , Pty , links oscillation time and the Ohnesorge number. • The parameter Pty helps unify data and guide future studies.