Mechanism of electrohydrodynamic instability with collinear conductivity gradient and electric field

We describe the physical mechanism responsible for electrohydrodynamic (EHD) instability of a fluid layer with collinear conductivity gradient and electric field. In particular, we resolve the ambiguity in literature regarding the cause for switching between stationary and oscillatory modes of EHD instability. Using linear stability analysis, we show that a small perturbation in conductivity field perturbs the local electric field and also induces a perturbation charge. The coupling of base-state electric field with the perturbation charge leads to a force which causes overstability. Whereas, the coupling of base-state free charge with perturbation electric field leads to a force which causes EHD instability via a stationary mode. The proposed mechanism correctly explains the existence of stationary and oscillatory modes for varying conductivity gradients and wave number of disturbances, depending upon the relative magnitude of these two forces.