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.
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