Induced coulomb-driven electroconvection between two rotating coaxial cylinders

Abstract

In this paper, the interaction between a Taylor-Couette flow between two-coaxial cylinders and an electroconvective motion induced by an unipolar injection from the inner cylinder 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 flow. The entire set of the coupled Navier-Stokes and EHD equations is 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 counter-rotating electroconvective cells convected in the space annulus. For a given Reynolds number it may exists a threshold value Tc of the instability parameters T above which the electroconvective instability initiates. The Reynolds number 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, is observed. While for Re=0, Tc =122.42 and Tf =86.5, for Re=10 we numerically found that Tc =802 and Tf =722. The magnitudes of the linear and non-linear criteria are directly linked to the value of the Reynolds number.