Two-dimensional numerical analysis of electroconvection in a dielectric liquid subjected to strong unipolar injection

Abstract

Two-dimensional numerical simulations are carried out to examine the problem of transient electroconvection stability of dielectric liquids subjected to unipolar injection. The entire set of electrohydrodynamics equations associated with the electroconvective phenomena that occur in a layer of a dielectric liquid between two parallel electrodes subjected to a potential difference are solved numerically. We first validate the numerical simulation by comparing our linear stability electroconvection criteria with those obtained by other authors with a stability approach. In this paper, we restrict the study to the strong injection case, which corresponds to values of the non-dimensional injection parameter C greater than or equal to 10. The numerical solution of the electroconvective problem is then presented for rigid lateral boundary conditions. A detailed analysis of the scenario that occurs for different characteristic values of the stability parameter T is provided. The flow structure and its behaviour highlight the existence of different regimes, from laminar to chaotic. The development of charged plumes has been observed in particular. We compute the electrical Nusselt number for different values of the stability parameter and ion mobility. The electrical Nusselt number saturates with increasing T, a fact that it is in agreement with available experimental data. Finally, a spectral analysis is conducted for different aspect ratios of the computational domain. The spectral analysis gives an insight into the physical origin of the velocity and current oscillations.