A three-dimensional level set method for two-phase electrohydrodynamics with finite electric Reynolds number

The electrohydrodynamics (EHD) of droplets under electric fields underpins technologies from ink-jet printing and electrosprays to droplet sorting and microfluidics, yet accurate prediction remains challenging because most existing studies are confined to two-dimensional or axisymmetric models and often neglect surface-charge convection, a mechanism that strongly modifies interfacial stresses and breakup. To address this gap, we develop a fully three-dimensional (3D) level-set computational framework for leaky–dielectric two-phase flows that resolves bulk charge conservation, interfacial surface-charge convection, and topology change over a wide range of electric Reynolds numbers R e E (the ratio of charge-relaxation to convection time) and electric capillary numbers C a E (the ratio of electric stress to surface tension). Unlike existing three-dimensional studies that either neglect surface-charge convection or are restricted to small deformations without breakup, our framework provides a comprehensive 3D treatment of finite- R e E charge convection, topology change, and breakup mapping. The method is carefully verified (mass conservation error < 0 . 5 % ) and validated against Taylor’s small-deformation theory and silicone–castor oil experiments, confirming quantitative accuracy. Our simulations demonstrate that surface-charge convection redistributes interfacial charges, weakens EHD circulation, suppresses oblate deformation, and enhances prolate deformation; three-dimensional charge maps and two-dimensional cross-sectional contours quantify these effects in detail. For prolate drops, we capture and classify breakup transitions in full 3D — from end-pinching to conic cusping and ultimately tip streaming — and construct a comprehensive ( C a E , R e E ) phase diagram. By integrating finite- R e E effects, 3D surface-charge diagnostics, and breakup mapping in a validated computational method, this study establishes a novel predictive framework for electric-field-driven droplet technologies. • A fully three-dimensional level-set method is developed for two-phase electrohydrodynamics based on the leaky–dielectric model. The method has been validated against Taylor’s small-deformation theory and silicone–castor oil experiments which confirms accuracy and reliability. • The method incorporates finite electric Reynolds numbers ( R e E = 1 –20), resolving surface-charge convection and topology change. • Charge convection mechanisms are quantified using 3D isosurfaces and 2D contours, showing suppression of oblate and enhancement of prolate deformation. • Breakup modes including end-pinching, conic cusping, and tip-streaming are captured in full 3D with mechanistic explanation. • A comprehensive ( C a E , R e E ) phase diagram is established, mapping stable, end-pinching, cusping, and tip-streaming regimes.