Modeling and simulation of the electrohydrodynamics for dielectric to high-conductivity liquids

Abstract

Electrohydrodynamics investigates the fluid motion driven by electric fields. It provides the theoretical foundation for applications such as high-resolution printing and electrospray. However, existing electrohydrodynamic (EHD) models often suffer from unreal charge diffusion across the mixed fluid–fluid interface. This unreal charge leakage can severely affect numerical convergence and solution accuracy, particularly in systems with extremely large conductivity contrasts between the two phases, where the conductivity ratio exceeds 1013. In this study, a new two-phase EHD model is developed to calculate the EHD phenomena, coupling the flow field, electric field, and phase field. A novel transition function framework is proposed to ensure the smooth and rapid change of electric parameters across the interface, thereby suppressing the unreal charge diffusion. Volume charge transport is resolved using the Poisson–Nernst–Planck-derived charge-transport formulation rather than imposing the leaky-dielectric approximation. Three representative cases are studied, including a parallel-plate capacitor, a suspended droplet, and EHD printing. The model demonstrates superior accuracy in calculating static, electrostatic, and dynamic responses. Additionally, the mechanism of unreal charge leakage is revealed. By using the transition function, the unreal charge leakage is effectively suppressed, even with a large conductivity difference between the two phases. Consequently, the model allows the computable relative conductivity to increase by at least five orders of magnitude to 1018 compared to existing models. This first makes the high-fidelity calculation of EHD systems with high relative conductivity feasible. Overall, the developed model proves to be advantageous, with high fidelity and wide applicability to a range of EHD phenomena.