A comprehensive study of interpolation methods in electrohydrodynamic cone-jet across diverse liquid conductivities

Accurate modeling of electrohydrodynamic atomization (EHDA) in the cone-jet regime requires reliable interpolation of fluid properties—such as permittivity, conductivity, and viscosity—across the liquid–gas interface. While the weighted arithmetic mean (WAM) is widely used in two-phase simulations due to its simplicity and stability, it may introduce significant inaccuracies in electrohydrodynamic (EHD) applications by over-smoothing critical property gradients. This study presents a comprehensive comparative analysis of five mean interpolation methods—weighted arithmetic mean (WAM), weighted harmonic mean (WHM), geometric mean (GM), modified geometric mean (mGM), and power-law mean (PLM)—for modeling electrohydrodynamic atomization (EHDA) processes under varying conductivity regimes. By evaluating their performance on key EHD metrics such as surface charge distribution, cone-jet dynamics, droplet size, jet breakup, and beam current, we reveal the strengths and limitations of each method. Numerical results were validated against experimental data and established scaling laws. For low-conductivity fluids, WAM demonstrated superior accuracy in predicting droplet sizes and beam currents due to its balanced interpolation and numerical robustness, while WHM offered stronger charge retention at the expense of stability. GM, mGM, and PLM provided improved physical accuracy under conditions of assured numerical stability. In the medium-conductivity regime, WHM emerged as the most effective method for capturing interfacial charge dynamics and droplet formation, although WAM excelled in predicting geometric features such as jet length and Taylor-cone height. For high-conductivity fluids, all five interpolation schemes yielded comparable results, accurately estimating droplet sizes and beam currents within a 5% margin of experimental values. The findings underscore the importance of selecting appropriate interpolation methods based on fluid conductivity, with WAM favored for low-conductivity fluids, WHM for medium-conductivity systems, and flexibility among all schemes for high-conductivity scenarios. These findings provide practical guidance for selecting or tuning interpolation methods in two-phase EHD simulations and establish a robust framework for improving numerical reliability in multiphase electrohydrodynamic modeling.