Accurate boundary treatments for lattice Boltzmann simulations of electric fields and electro-kinetic applications

In this paper a novel boundary method is proposed for lattice Boltzmann simulations of electric potential fields with complex boundary shapes and conditions. A shifted boundary from the physical surface location is employed in simulations to achieve a better finite-difference approximation of the potential gradient at the physical surface. Simulations are presented to demonstrate the accuracy and capability of this method in dealing with complex surface situations. An example simulation of the electrical double layer and electro-osmotic flow around a three-dimensional spherical particle is also presented. These simulated results are compared with analytical predictions and are found to be in excellent agreement. This method could be useful for electro-kinetic and colloidal simulations with complex boundaries, and can also be readily extended to other phenomena and processes, such as heat transfer and convection-diffusion systems. (paper)