The numerical analysis of complete and partial electrocoalescence in the droplet-layer system employing the sharp interface technique for multiphase-medium simulation

In this paper, the coalescence of a drop of water suspended in oil with a layer of water under the influence of a constant electric field is numerically investigated. Unlike most existing studies, the calculations are based on the application of the arbitrary Lagrangian-Eulerian method (ALEM), also called the moving mesh method, which belongs to the class of methods for modeling two-phase liquids with a sharp interface. Using this approach made it possible to avoid a false "escape" of the surface charge from the interface, which often occurs when using methods involving a diffuse interface. Despite the fact that ALEM does not allow describing topology changes by default, a numerical model was implemented in which the calculation is divided into three parts: the convergence of the drop and the layer before the moment of touch; the manual construction of the bridge at the moment of touch; the union of the drop and the layer. The developed model allowed us to obtain three possible modes of this process: complete coalescence, partial coalescence and a mode of stretching which has not practically been considered yet. The dependence of the volume of the separated secondary droplet on the size of the initial droplet and the average intensity of the applied electric field is obtained. The model showed good quantitative agreement with experimental studies. It has been shown that generally, the spots where the bridge and the neck are formed in case of partial coalescence do not coincide. A map of coalescence modes was obtained, i.e., the dependence of the transition threshold from coalescence to partial coalescence and from partial coalescence to stretching regime in a wide range of radii of initial droplets and electric field strengths. It has been shown that there is a maximum field strength at which droplets of any size merge with the layer. This map makes it possible to predict the coalescence regime in electrocoalescer. The proposed modeling technique can be used to calculate electrocoalescence modes at various values of the main parameters, which will help to optimize electrocoalescers at the design stage.