Numerical simulation of deformation/motion of a drop suspended in viscous liquids under influence of steady electric fields

Abstract

The deformation / motion of a droplet suspended in a viscous liquid under the influence of an applied external electrical field are investigated through numerical simulations. The two-phase flow field of the drop suspension system is simulated using a front tracking / finite volume method for solving the full Navier-Stokes equations. Three different electric field models are applied in order to take into account the effects of the electric field, electric charge, and electrical properties of liquids. Drops with no net charge but finite electrical conductivity are simulated using a leaky dielectric model. Perfect dielectric model is used for the drops of electrically isolating fluid. To take into account the presence of a net charge on drop surface, we proposed a simplified constant surface charge model. In addition, the simulation code using the leaky dielectric model and perfect dielectric model is validated systematically against the results of theoretical analysis, the available experimental data, and the simulations by other researchers. It shows that the proposed numerical method (front tracking / finite volume method coupled with various electric field models) can make reasonable prediction on droplet deformation / motion under externally applied electrical field. Under different combinations of liquid properties, the droplets may deform into either prolate or oblate shape, and induce different inner and outer circulating flow patterns. When a net charge presents on the droplet surface and an electrical field is applied, both droplet deformation and motion can be reasonably predicted by the constant charge model. The simulation results demonstrate that the current numerical method may provide an effective approach to quantitatively analyze the complex electrohydrodynamic problems.

An interface tracking model for droplet electrocoalescence.

“…However, this method is not used to model coalescence or pinch-off, since one weakness of VOF is that it can not distinguish topological changes precisely. The current literature also includes a fronttracking finite volume method that can model electric charge on the droplet surface [18]. In addition, mesoscopic methods such as Lattice Boltzmann methods have been used for simulating drop deformation using electric fields [41,14].…”

Numerical Study on Deformation and Interior Flow of a Droplet Suspended in Viscous Liquid under Steady Electric Fields

“…The results indicated that the interpolation scheme to smoothen the electric properties (conductivity and permittivity) in the interface transition region had a significant influence on the solution in the bulk [17]. Hua et al summarized three different kinds of electric fields: leaky dielectric model, perfect dielectric model, and constant charge model and numerically investigated the deformation of droplet and internal flow inside droplet by employing the interface tracking method where the interface was considered to have a finite thickness of the same order as the mesh size instead of zero thickness [18]. Lin et al proposed the phase field method to study the two-phase electrohydrodynamic flow which was generated by electric field.…”

“…But this method is inaccurate for the calculation of surface tension. Some methods which treated the interface as a finite width region where the physical properties continuously transitioned from one phase to another phase were presented in recent years [16][17][18][19]. Zhang and Kwok investigated the droplet deformation driven by electrohydrodynamics using a multicomponent LBM method that a cosine function was employed to describe such transition interface.…”

Analysis of partial electrocoalescence by Level-Set and finite element methods

“…Explicit approaches, such as boundary integral and front-tracking methods, track discrete points on the interface surface. The motion and deformation of droplets under the presence of an electric field [8][9][10][11][12] [14][15][16][17][18][19][20]. Each implicit technique to represent the interface has its own advantages and drawbacks.…”