The stability of a planar layer of insulating liquid subjected to charge injection and rotation

Abstract

The problem of the hydrodynamic stability of a plane dielectric liquid layer subjected to unipolar injection and rotation examined here is in many ways analogous to that of rotating horizontal fluid layer heated from below. In both situations instability is likely to arise as steady or oscillatory convection depending on the values of only two parameters. The critical conditions for which instability sets in as a steady convection are determined as functions of both the Taylor number and the level of injection. Because of the mathematical complexity of the problem, the onset of convection as overstability is determined only for the particular case of weak injection. In this case, an analytical treatment is carried out that allows discrimination of regions of steady and oscillatory convective instability.