Numerical investigation of a conducting drop’s interaction with a conducting liquid pool under an external electric field

Abstract

A charged conducting drop suspended in an insulating medium shows non-coalescence with an interface under high strength of an externally applied electric field. We perform numerical simulations of the non-coalescence phenomenon to understand the underlying physical mechanisms and the effect of electric field strength and fluid conductivity on the coalescence behavior of a conducting drop with a conducting liquid pool under highly viscous conditions. We show that two factors primarily govern the coalescence or non-coalescence of the drop with the interface. First, the magnitude of the charge transfer time scale (which governs the rate of charge transfer during contact between the drop and the pool) relative to the time scale of the capillary waves. Second, the strength of the electric forces compared to the viscous forces. We further show that for the case of macro drops (D∼2 mm), charge transfer by fluid convection dominates charge conduction at lower electric conductivities (σ∼10−8 S/m) only. Finally, we explain the non-dependence of secondary droplet’s size and charge on the fluid’s electric conductivity as observed in the experiments.