Abstract
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 , nondimensional mobility , and wave number . It is found that centrally downflowing hexagonal cells, which are characterized by the central region being empty of charge, are preferred in the system.
1 More- Received 3 December 2017
DOI:https://doi.org/10.1103/PhysRevFluids.3.053702
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