Electrohydrodynamic instability of dielectric liquid between concentric circular cylinders subjected to unipolar charge injection

In this paper, we demonstrate instability of dielectric liquid subjected to unipolar charge injection from a pair of cylindrical electrodes at high Scmidt and high Peclet numbers. The transport of charge density in the annulus is governed by the Nernst-Planck equation and the electric potential by the Poisson equation. The fluid flow is governed by the Navier-Stokes equation together with the continuity equation. The base solutions composed of the one-dimensional conduction state are obtained numerically and the temporal growth of their perturbations is determined from the normal-mode instability analysis by using numerical simulations. The critical values of the parameter for the onset of 2D convective motion are obtained and compared well with the results of full-2D calculation. At high injection, the system tends to be more unstable for the inner injection case and more stable for the outer injection case, as the radius of the inner cylinder is decreased; this trend is however reversed at low injection. It turns out that the critical angular wave number obtained from the flat-plate case well predicts the one for an annulus for a wide range of the inner cylinder's radius.