Hydrodynamic Flows in Electrowetting

In the first part, I will present the hydrodynamic flows generated inside a droplet in electrowetting when an ac voltage is applied. In order to find out the characteristics and origin of the flows, we investigated the flow pattern for a sessile droplet for various conditions. A shape oscillation of a droplet was observed in the low-frequency range by a high-speed camera. The shape oscillation is responsible for the low-frequency flow. The flow at high frequency is caused by some electrohydrodynamic effect. In the second part, an experimental and theoretical work will be presented concerning the shape oscillation of sessile droplet. A set of shape mode equations is derived to describe unsteady motions of a sessile drop actuated by electrowetting. It is revealed that resonance occurs at certain frequencies and the oscillation pattern is significantly dependent on the applied AC frequencies. The domain perturbation method is used to derive the shape mode equations under the assumptions of weak viscous effect and small deformation of drop. The electrical force concentrated on the three-phase contact line is approximated as a delta function, which is decomposed and substituted into each shape mode equation as a forcing term. The theoretical results on the shape and the frequency responses are compared with experimental results, which shows a qualitative agreement. Finally, I will present a novel method to actuate oscillation of a sessile bubble or oil drop in a fluid to produce steady streaming within the fluid. This method is based on time-periodic control of the wettability of the bubble or drop by electrowetting. Jet velocity is proportional to oscillation amplitude and is greatest at natural oscillation frequencies. Analytical and numerical analyses indicate that the jet is produced by steady streaming in the Stokes layer.