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.