Forces acting on water droplets falling in oil under the influence of an electric field: numerical predictions versus experimental observations

Abstract The combination of an electric field and a moderate turbulent flow is a promising technique for separating stable water–oil emulsions. Field-induced charges on the water droplets will cause adjacent droplets to align with the field and attract each other. The present work describes the forces that influence the kinematics of droplets falling in oil when exposed to an electric field. Mathematical models for these forces are presented and discussed with respect to a possible implementation in a multi-droplet Lagrangian framework. The droplet motion is mainly due to buoyancy, drag, film-drainage, and dipole–dipole forces. Attention is paid to internal circulations, non-ideal dipoles, and the effects of surface tension gradients. Experiments are performed to observe the behavior of a droplet falling onto a stationary one. The droplet is exposed to an electric field parallel to the direction of the droplet motion. The behavior of two falling water droplets exposed to an electric field perpendicular to the direction of their motion is also investigated until droplet coalescence. The droplet motion is recorded with a high-speed CMOS camera. The optical observations are compared with the results from numerical simulations where the governing equations for the droplet motion are solved by the RK45 (Runge Kutta) Fehlberg method with step-size control and low tolerances. Results, using different models, are compared and discussed in detail. A framework is otlined to describe the kinematics of both a falling rigid spherical particle and a fluid droplet under the influence of an electric field.

[1]  Robert H. Davis,et al.  The lubrication force between spherical drops, bubbles and rigid particles in a viscous fluid , 1989 .

[2]  A. Nysveen,et al.  Forces and movement of water droplets in oil caused by applied electric field , 2004, The 17th Annual Meeting of the IEEE Lasers and Electro-Optics Society, 2004. LEOS 2004..

[3]  Steve Granick,et al.  No-slip boundary condition switches to partial slip when fluid contains surfactant , 2002 .

[4]  M. H. Davis.  TWO CHARGED SPHERICAL CONDUCTORS IN A UNIFORM ELECTRIC FIELD: FORCES AND FIELD STRENGTH , 1964 .

[5]  Robert H. Davis,et al.  The lubrication force between two viscous drops , 1989 .

[6]  P. Atten,et al.  Electrocoalescence of water droplets in an insulating liquid , 1993 .

[7]  Adel O. Sharif,et al.  Electrostatic enhancement of coalescence of water droplets in oil: a review of the current understanding , 2001 .

[8]  Olga I. Vinogradova,et al.  Drainage of a Thin Liquid Film Confined between Hydrophobic Surfaces , 1995 .

[9]  D. Jordan,et al.  Nonlinear Ordinary Differential Equations: An Introduction for Scientists and Engineers , 1979 .

[10]  L. Lundgaard,et al.  Instability of electrically stressed water droplets in oil , 2002, Proceedings of 2002 IEEE 14th International Conference on Dielectric Liquids. ICDL 2002 (Cat. No.02CH37319).

[11]  J. Happel,et al.  Low Reynolds number hydrodynamics , 1965 .

[12]  G. Bossis,et al.  Many-body electrostatic interactions in electrorheological fluids. , 1993, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[13]  E. Michaelides.  Hydrodynamic Force and Heat/Mass Transfer From Particles, Bubbles, and Drops—The Freeman Scholar Lecture , 2003 .

[14]  K. Yu,et al.  Interparticle force in polydisperse electrorheological fluids , 2000 .

[15]  Motion of a droplet with a newtonian interface , 1981 .

[16]  D. Klingenberg,et al.  The small shear rate response of electrorheological suspensions. II. Extension beyond the point–dipole limit , 1991 .