Three dimensional numerical simulation of drops suspended in a channel under uniform electric field

Abstract

Abstract In this paper, numerical study of emulsion of drops in a channel under uniform electric field is investigated. The electric field is created by imposing an electric potential difference across the channel walls. The leaky dielectric model developed by Taylor is used to compute the electric force. The electric conductivity ratio σ r = σ i σ o and electric permittivity ratio e r = e i e o are used to study oblate and prolate drops The interaction of drop-to-wall and drop-to-drop are investigated by changing the dimensionless numbers. Oblate drops and prolate drops with σ r e r , are always attracted to the walls, but prolate drops with σ r > e r , are attracted by or repelled from the walls depending on the initial distance and electric properties. Drop-to-drop interaction depends on the initial configuration of drops. Drop pairs that are placed at an angle relative to the direction of the electric field, are always attracted towards each other. If they have an initial separation distance in the direction of the electric field, they are attracted to the walls or towards each other depending on their separation distance. Prolate drops with σ r > e r , obtain a different configuration in their final state. They may stick together or have a small separation distance, depending on their electric properties. Increasing the electric capillary number, changes the vertical and horizontal separation distance of drop pairs at steady state configuration. It also decreases the time required to reach steady state configuration. The behavior of emulsion of drops is studied by considering oblate drops, prolate drops with σ r e r and prolate drops with σ r > e r . All drops form fiber chains in the direction of the electric field that will break in stronger Poiseuille flow. Oblate drops either settle on the walls or migrate to the channel center line, but prolate drops form chains of fibers that sometimes extend between the walls. Presence of drops will change the well-known parabolic velocity profile especially for prolate drops that are suspended in the channel. The channel flow rate is also studied for different emulsion of drops and electric field. At a constant electric field and pressure gradient, the channel flow rate for oblate emulsion is higher than prolate ones. As the electric field strength increases, the channel flow rate will also increase for oblate emulsions.