The complex structure of electrohydrodynamic flows arising in a two-phase liquid with weakly conducting dispersion medium and unequal ions mobilities

The study numerically investigates the electrohydrodynamics of conducting droplets in leaky dielectric dispersion medium under high electric fields, with focus on how electrophysical properties of the dispersion medium (ion mobility, electrical conductivity) govern droplet dynamics and their pair interactions in cases of unequal ion mobilities. Using the arbitrary Lagrangian–Eulerian method with sharp interface resolution, the qualitative and quantitative effects of these parameters on space charge formation, Coulomb forces, and electrohydrodynamic flows were analyzed. The results reveal that asymmetric ion transport in most cases results in rapid translational motion of droplets along the force lines of the external electric field, while strong asymmetry (mobilities differ five times) may lead to intense reverse flows in droplet traces, which under specific conductivity and mobility ranges prevent droplet collision despite dipole–dipole attraction. Dimensionless analysis reduces 11 physical parameters of the system to 7 dimensionless ones, which simplifies the prediction of emulsion dynamics. The paper contains a large amount of simulation results for various system parameters and recommendations for scaling epy problem to optimize emulsion analysis.