On the parametric excitation of electrothermal instability in a dielectric liquid layer using an alternating electric field

The onset of electrothermal convective instability of a liquid dielectric subjected to an unsteady electric field is studied in the EHD approximation, when charge formation is produced only due to dielectrophoresis. Convective thresholds are found in two different cases: (i) instability of the liquid equilibrium in a horizontal layer, and (ii) instability of the liquid flow in a vertical layer. The stability boundaries are obtained when there is interaction of dielectrophoretic and gravitational forces. Stability plots of electrical Rayleigh number versus thermal Rayleigh number are given. We show that only synchronous response to variations of the external electric field of finite frequency exists when heating a horizontal layer from above. Quasiperiodic response to the external alternating action is possible in the case of a vertical layer. The influence of the Prandtl number on the stability thresholds is also examined. The asymptotic behavior of the critical parameters in the limiting case of low-frequency modulation is studied using the Wentzel–Kramers–Brillouin method.