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The two-dimensional (2D) electro-convection (EC) flow of dielectric liquids between two concentric cylindrical electrodes driven by unipolar injection of ions is investigated numerically. The finite volume method is used to resolve the spatiotemporal distributions of the flow field, electric field, and charge density. The flow transition routes from steady laminar to chaotic flow states are studied in various scenarios where the mobility parameter M of the dielectric liquids varies from 5 to 200. The dynamic characteristics and bifurcation routes of the EC flow depend on the electric Rayleigh number T, a ratio of the electric force to viscous force, and the mobility parameter M. For increasing T, three different transition routes from a convective steady-state to chaos via different intermediate states are observed. The flow states have been quantified by the power spectral density distribution and phase space trajectory of the velocity. The fractal dimensions and Lyapunov exponents are calculated to identify the chaotic flow. The increase in the mobility parameter M leads to a shorter and more direct route with fewer intermediate states when bifurcating to chaos. In addition, the power scale of charge transport that is defined by the electric Nusselt number Ne and T is discussed when the EC flow develops into electro-turbulence.

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Injection-induced electro-convection (EC) of dielectric liquids is a fundamental problem in electrohydrodynamics. However, most previous studies with this type of EC assume that the liquid is perfectly insulating. By perfectly insulating, we mean an ideal liquid with zero conductivity, and in this situation, the free charges in the bulk liquid originate entirely from the injection of ions. In this study, we perform a numerical analysis with the EC of dielectric liquids with a certain residual conductivity based on a dissociation–injection model. The spatiotemporal distributions of the flow field, electric field, and positive/negative charge density in the parallel plate configuration are solved utilizing the finite volume method. It is found that the residual conductivity inhibits the onset of EC flow, as well as the strength of the flow field. The flow features and bifurcations are studied in various scenarios with three different injection strengths in the strong, medium, and weak regimes. Three distinct bifurcation sequences with abundant features are observed by continually increasing or decreasing the electric Reynolds number. The present study shows that the residual conductivity significantly affects the bifurcation process and the corresponding critical point of EC flows.