Numerical Simulation of Electric Field-Induced Noncoalescence of Conductive Droplets of Different Sizes Dispersed in a Dielectric Liquid

!This study investigates the coalescence behavior of two water droplets of different sizes dispersed in oil under a constant electric field, using numerical simulations based on the arbitrary Lagrangian–Eulerian (ALE) method. The analysis considered droplet pairs with varying sizes: for a 1 mm reference droplet, the second droplet ranged from 0.2 to 2.4 mm; for a 0.3 mm droplet, from 0.05 to 1.2 mm. A regime of partial coalescence was identified, in which the larger droplet accumulates volume while the smaller one loses it, and secondary droplets may detach from the smaller one. The range of electric field strengths where partial coalescence occurs widens as the droplet size ratio increases: for a radius ratio of 2.4, the electric Weber number range is 0.15–0.35; for 1.2, it is 0.22–0.30; and for equal-sized droplets, it is limited to 0.20. The threshold electric field for complete coalescence decreases with increasing size asymmetry—for example, for a fixed 1 mm droplet, the threshold drops from 2.5 kV/cm (when the second droplet is also 1 mm) to 2.0 kV/cm (when the second is 0.2 mm). For practical applications, an empirical estimate is proposed: if the droplet radius ratio does not exceed 1.5, the coalescence threshold can be approximated by that of two equal-sized droplets with a radius equal to the larger one, with an error below 5%. The ALE-based model used in this work, due to its sensitivity to topological changes, allows precise determination of coalescence thresholds and can be employed to generate data for multiparticle models such as Direct Element Method or Population Balance Equation.