Unified Lattice Boltzmann Method for Electric Field–Space Charge Coupled Problems in Complex Geometries and Its Applications to Annular Electroconvection

A lattice Boltzmann method (LBM) is developed to solve the electric field–space charge coupled problems. Instead of solving the macroscopic charge conservation equation and the Poisson's equation for electric potential, two discrete lattice Boltzmann equations are formulated and solved. A nonequilibrium extrapolation scheme is used to treat the boundary conditions with complex geometry. Our method is validated with several test cases for which analytical solutions and/or reference numerical results exit. An attractive feature of this methodology lies in its natural coupling with the LBM for the fluid flow. As a demonstration and also an application, the unipolar injection induced electroconvection of dielectric liquids in annular geometries is considered. The different flow patterns of the concentric and eccentric configurations are highlighted.