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A nonlinear electrohydrodynamic stability analysis of a thermally stabilized plane layer of dielectric liquid

The nonlinear stability of a thermally stabilized horizontal plane layer of dielectric liquid subjected to unipolar charge injection at a voltage near the linear instability threshold is investigated using a normal-mode cascade analysis valid for small perturbation amplitudes. In this first analysis, the primary mode is chosen to be a system of parallel rolls whose amplitude varies aperiodically with time. The branching behaviour at the critical voltage is found to reflect the distinction, apparent in the linear instability problem, between an essentially isothermal space-charge instability and an instability dominated by the effects of an ion mobility varying with temperature. The effect of motion on heat and charge transfer through the system is also considered. Furthermore, in certain cases it appears that overstability is the preferred form of linear instability.