Analysis of Partial Electrocoalescence by Level-Set and Finite Element Methods

Abstract

The coalescence of a water drop in a dieletric oil phase at a water layer interface in the presence of an electric field is simulated by solving the Navier-Stokes and charge conservation equations with the finite element method. The proprietary software Comsol Multiphysics is used for this purpose. The interface between the oil and water phases is tracked by implementing a Level Set approach. The sensitivity of the model with respect to some input parameters are reported. In particular, the calculations are sensitive to the size of the computational grid elements, interface thickness and reinitialisation parameter. The ratio between the volume of secondary droplets and the initial drop volume is calculated as a function of the initial drop size and compared with experiments available in the literature. A good quantitative agreement can be obtained if the parameters are suitably tuned. The model also predicts a strong role played by the water phase conductivity in the formation of progeny droplets.

Droplet deformation under pulsatile electric fields

“…The Level-Set method is employed to track the boundaries between continuous oil phase and dispersed water phase. The location of interface is obtained by solving the transport equation of the Level-Set function , described by =0.5 [23,32]. The evolution of the boundary is given by Eq.…”

“…We follow the approach of Vivacqua et al [32], coupling Eq. (1) with the Navier Stokes equations for the flow and Laplace equations for the electric field.…”

“…The interface is modelled by an additional transport equation and treated as a material line propagating with the fluid [31]. Vivacqua et al [32] investigated the coalescence of a water drop in a dieletric oil phase at the oil-water interface under a constant electric field by the Level-Set method. They reported the effects of some input parameters, including the mesh size, interface thickness, re-initialization parameter, droplet size and water conductivity, on the model prediction.…”

Electrocoalescence of water droplets in sunflower oil using a novel electrode geometry

“…decreases to 0 exponentially outside and inside the droplet, respectively. We follow the approach of Li et al [20] and Vivacqua et al [36], coupling Eq. 3with the Navier Stokes equations for the flow and Laplace equations for the electric field.…”

“…The water phase in crude oil contains dissolved salts, which influence water conductivity significantly. Vivacqua et al [36] developed a Level-Set approach to model the electrocoalescence and found numerically that as the conductivity was increased, partial coalescence produced larger secondary droplets and the largest was at 10 -3 S m -1 . Moreover, Hamlin et al [37] reported the existence of a critical conductivity, below which the droplets partially coalesced, while above which the droplets bounced off each another.…”