Critical Modes of Thermoelectric Convection Instabilities in a Vertical Slot

Investigation of the natural convection in a dielectric fluid confined inside a vertical slot subject to a constant horizontal temperature gradient and a high-frequency electric field was revisited. The thermoelectric coupling produces a dielectrophoretic force which contains a term called electric buoyancy associated with an electric gravity. Similar to the Archimedean buoyancy, this force can induce thermo-electro-convective instability in a stable fluid flow. Including the feedback effect of the electric field on the flow, a three-dimensional linear stability analysis is performed to characterize the instability induced by this force. Different critical modes are found depending on the intensity of the electric field: stationary hydrodynamic modes, oscillatory thermal modes and stationary electric modes. The threshold of the electric modes is independent of the Prandtl number in contrast with the threshold of the hydrodynamic and thermal modes. The obtained results are compared with those of previous studies.