Mathematics, Vol. 11, Pages 1188: Electro-Thermo-Convection of a Dielectric Liquid in the External DC and AC Electric Fields

Mathematics, Vol. 11, Pages 1188: Electro-Thermo-Convection of a Dielectric Liquid in the External DC and AC Electric Fields

Mathematics doi: 10.3390/math11051188

Authors: Oleg Nekrasov Boris Smorodin

The electro-thermo-convection of a dielectric liquid in a horizontal capacitor is investigated under the autonomous charge injection from the cathode and heating from above. In the case of a DC electric field, the linear stability analysis is carried out, and the thresholds of monotonic and oscillatory instability are determined. The finite difference method is used for the numerical simulation of the nonlinear behavior of electro-thermo-convective patterns: stationary convection and traveling waves. In the case of AC, electric field transient and permanent oscillations are analyzed. Two types of stable solutions are found. The modulated traveling waves are characterized by the quasiperiodic oscillations of convective characteristics. Another solution is modulated electroconvection (MEC). The patterns of MEC oscillate around some average flow synchronously with the external AC field and do not move laterally. The average intensity of convective mixing in modulated traveling waves is several times less than in modulated electroconvection. The spatiotemporal evolution of the stream function, temperature, and charge distributions for different types of transient and permanent solutions are analyzed.