The effects of electrostatic forces on the distribution of drops in a channel flow: Two-dimensional oblate drops

Abstract

Numerical simulations are used to examine the effect of an electrostatic field on an emulsion of drops in a channel. The leaky-dielectric theory of Taylor is used to find the electric field, the charge distribution on the drop surface, and the resulting forces. The Navier-Stokes equations are solved using a front-tracking/finite-volume technique. Depending on the ratios of conductivity and permittivity of the drop fluid and the suspending fluid the drops can become oblate or prolate. In addition to normal forces that deform the drops, tangential forces can induce a fluid motion either from the poles of the drops to their equator or from the equator to the poles. In this paper we focus on oblate drops, where both the dielectrophoretic and the electrohydrodynamic interactions of the drops work together to "fibrate" the emulsion by lining the drops up into columns parallel to the electric field. When the flow through the channel is slow, the fibers can extend from one wall to the other. As the flow rate is increased the fibers are broken up and drops accumulate at the channel walls. For high enough flow rate, when the drop interactions are dominated by the fluid shear, the drops remain in suspension. Only two-dimensional systems are examined here, but the method can be used for fully three-dimensional systems as well.

Critical Angle for Electrically Driven Coalescence of Two Conical Droplets

“…Similarly, drop pairs also deform in an electric field. The dynamics of a pair of drops aligned with an electric field have been investigated for both inviscid [15][16][17][18] and viscous responses [19][20][21]. Each drop enhances the deformation of the other, and below a critical separation distance, the drops become unstable and rapidly converge.…”

Rhythmic motion of a droplet under a dc electric field

“…deformation and breakup of a single droplet [1][2][3], formation of a fiber-like chain of droplets [4], return motion [2] and so on.…”

Direct simulation of film boiling including electrohydrodynamic forces

“…Juric and Tryggvason 15 used source terms in the continuity and energy equations on an Eulerian grid to simulate horizontal film boiling in which vapor bubbles were released from the vapor film. More advanced simulations were provided by Fernandez et al 32 who implemented the Taylor-Melcher leaky dielectric model and the method of Tryggvason et al 33 in simulations of multiple drops interacting in channel flow. Welch and Wilson 17 modified the volume-of-fluid ͑VOF͒ method to simulate two-dimensional boiling flows and their approach was used in subsequent work in simulating film boiling including conjugate heat transfer with a solid wall 18 and in simulating film boiling including the temperature dependence of fluid properties near the critical point.…”