Nonlinear evolution of the interface between immiscible fluids in a micro channel subjected to an electric field
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The long wave analysis of the interface between two leaky dielectric fluids flowing in a micro channel subjected to an electric field is performed. The electric field is applied normal to the flat interface. The evolution equations for the interface position and the surface charge density are derived. The results show that the base flow prevents the interface from reaching the channel walls for the values of the parameters considered. When the strength of the base flow is diminished, it is possible to asymptotically approach the stationary base flat interface solution. At early times of instability, interface deflections for different strengths of base flow share a common shape as suggested by the linear theory, which states that the base pressure-driven flow does not affect the linear stability point. The base flow breaks the symmetry of the interface profile yielding an asymmetric pattern at steady-state. It is also found that, the amplitude of the interface deflections is decreased and the symmetry is lost when the depth ratio changes in such a way that the maximum speed at the base flow does not occur at the flat interface between the two fluids.
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