Numerical analysis of electro-convection in dielectric liquids with residual conductivity

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.