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

Abstract

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.

Counter-extrapolation method for conjugate interfaces in computational heat and mass transfer

“…We label the intersecting position as x int . Inspired by our recent work on Neumann and mixed Robin boundary conditions [18,19], we draw a line at point x int perpendicular to the interface. On this line we find points x 1 and x 1 in domain 1 and points x 2 and x 2 in domain 2 .…”

“…[7] at locations where the interface is parallel or perpendicular to the underlying lattice grid lines. With a properly selected extrapolation interval δ (δ = 1.5δx in this study) [19], all the extrapolation control points x 1 , x 1 , x 2 , and x 2 are well defined in their respective domains; unless the local curvature radius is very small (for example, a circular interface with a radius R < 2δx), and such a situation should be avoided anyway for the low spatial resolution. With the scalar value φ int at the interface from Eq.…”

“…However, the mathematical formulation is relatively complicated even for the simplest D2Q5 (two-dimensional, five lattice velocities) lattice model (see Eqs. (19)- (21) and Table 1 in Ref. [7]).…”

“…Moreover, the general algorithm (Eq. (19) in Ref. [7]) cannot be applied at a location where the interface is approximately parallel or perpendicular to the underlying lattice grid lines, since in such situations the transverse intersection points (x ss and x ff there) may belong to a same domain.…”

Extension of the Improved Bounce-Back Scheme for Electrokinetic Flow in the Lattice Boltzmann Method

“…EDL theory [40] related the electrostatic potential and the ion distribution in the bulk solution can be well approximated by the Poisson equation as follows: …”