Hexagonal convection patterns and their evolutionary scenarios in electroconvection induced by a strong unipolar injection

A regular hexagonal pattern of three-dimensional electroconvective flow induced by unipolar injection in dielectric liquids is numerically observed by solving the fully coupled governing equations using the lattice Boltzmann method. A small-amplitude perturbation in the form of a spatially periodic pattern of hexagonal cells is introduced initially. The transient development of convective cells that undergo a sequence of transitions agrees with the idea of flow seeking an optimal scale. Stable hexagonal convective cells and their subcritical bifurcation together with a hysteresis loop are clearly observed. In addition, the stability of the hexagonal flow pattern is analyzed in a wide range of relevant parameters, including the electric Rayleigh number T, nondimensional mobility M, and wave number k. It is found that centrally downflowing hexagonal cells, which are characterized by the central region being empty of charge, are preferred in the system.