Numerical investigation of electroconvection induced by strong unipolar injection between two rotating coaxial cylinders

In this paper, the interaction between a Couette shear flow and an electroconvective motion induced by an unipolar injection between two-coaxial cylinders is numerically investigated. A flow is generated by two counter-rotating coaxial cylinders inducing a shear flow. Space charges are injected in the flow through a metallic electrode placed on the inner cylinder and brought to a given potential. Transient numerical simulations have been carried out to investigate the structure of the induced flow. The entire set of the coupled Navier-Stokes and EHD equations is solved using an efficient finite volume technique. The behaviour 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 motion induced by space charge injection and the mainstream flow, emphasizes the appearance of periodic counter-rotating electroconvective cells. The electroconvective cells are convected in the annular space by the azimuthal fluid velocity. From the stability point of view the bifurcation diagram is very similar to the one obtained in the case when Re = 0. We observe a threshold value Tc of the instability parameters T above which the electroconvective instability initiates. A non-linear criterion Tf under which the electro-convective motion is suppressed is also found. When increasing the Reynolds number the flow induced by the two rotating cylinders has a sweeping effect on the charge density distribution. Consequently the instability parameter T must be drastically increased to allow the electroconvective instability to develop. For Re = 10 a subcritical instability characterized by an hysteresis loop and therefore a linear and non-linear criteria, Tc and Tf respectively, are determined. While for Re = 0, Tc = 122.42 and Tf = 86.5, for Re = 10 we numerically found that Tc = 802 and Tf = 722. The magnitude of the linear and non-linear criteria are directly linked to the value of the Reynolds number.