Three-dimensional electro-convective flows of dielectric liquids between concentric cylinders

Abstract

This study numerically investigates the flow structures and bifurcations of three-dimensional (3D) electro-convection (EC) between concentric cylinders. The flow motion is driven by the volumetric Coulomb force exerting on the free ions introduced by a strong unipolar injection. Three different sets of cases with periodic or symmetric boundary conditions are carried out. The finite volume method is used to numerically resolve the model problem. The co-effect of 2D roll mode and 3D polygon mode at the initial period of the EC flow is identified. The EC flows are made up of different types of regular or irregular centrally downflowing polygonal cells and are characterized by the central charge density cores surrounded by the charge void regions. The symmetry, periodicity, and staggered distribution characteristics of polygonal cells are identified. The cell patterns of EC flow are strongly influenced by the computational domain and the electric Rayleigh number (T). The subcritical bifurcation of linear instability together with a hysteresis loop is observed. In addition, the stability of the triangular flow pattern is analyzed at a large range of T and found that the annular EC flow is more likely to be unstable in three dimensions than in two dimensions.