Stability of a plane Poiseuille channel flow of a dielectric liquid subjected to unipolar injection

In this paper, the interaction between a plane Poiseuille channel flow and an electroconvective movement induced by the electric field is investigated. A flow is generated by an inlet parabolic profile in a rectangular duct. Space charges are injected in the flow through a metallic electrode placed on one of the channel walls and brought to a given potential. Transient numerical simulations have been carried out to investigate the structure of the flow. The entire set of the coupled Navier-Stokes and EHD equations are solved using an efficient finite volume technique. The behavior of the flow subjected to an applied voltage between the two electrodes is analyzed and time evolution of the charge density distributions is presented. The interaction between the convective movement induced by space charge injection and electric field and the mainstream flow, emphasizes the appearance of periodic transverse traveling waves convected in the channel. For a given Reynolds number it exists a threshold value of the instability parameters T over which the transverse traveling waves appear or not.