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

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## Abstract

**:**

**2012**, 231, 4295–4303] is extended to handle the electrokinetic flows with complex boundary shapes and conditions. Several numerical simulations are performed to validate the electric boundary treatment. Simulations are presented to demonstrate the accuracy and capability of this method in dealing with complex surface potential situations, and simulated results are compared with analytical predictions with excellent agreement. This method could be useful for electrokinetic simulations with complex boundaries, and can also be readily extended to other phenomena and processes.

## 1. Introduction

## 2. Macroscopic Governing Equations for EOF

## 3. Numerical Method

#### 3.1. Lattice Boltzmann Model for the NS Equations

#### 3.2. Lattice Boltzmann Model for Poisson–Boltzmann Equation

#### 3.3. Boundary Conditions

## 4. Validation and Discussions

#### 4.1. Electric Potential with Flat Surface

**Figure 2.**Electric potential distributions from our LBM simulation (symbols) and the analytical solution (black lines) with different height between two identically charged plates in an electrolyte solution.

**Figure 3.**Electric potential distributions from present treatment, classical Bounce-Back treatment and the analytical solution with different offset (red symbol $\Delta \text{=}0.5$; blue symbol $\Delta \text{=}0.7$; green symbol $\Delta \text{=}0.2$).

**Figure 4.**The error for electric potential between two identically charged plates in an electrolyte solution.

#### 4.2. Electric Potential with Complex Geometry

#### 4.3. Application in Electro-Osmotic Flows

**Figure 6.**The electric potential distribution (

**a**) and (

**b**) and electro-osmotic flow (

**c**) and (

**d**) around the spherical particle in the $\text{y}={y}_{c}$ plane.

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

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**MDPI and ACS Style**

Chen, Q.; Zhou, H.; Jiang, X.; Xu, L.; Li, Q.; Ru, Y.
Extension of the Improved Bounce-Back Scheme for Electrokinetic Flow in the Lattice Boltzmann Method. *Entropy* **2015**, *17*, 7406-7419.
https://doi.org/10.3390/e17117406

**AMA Style**

Chen Q, Zhou H, Jiang X, Xu L, Li Q, Ru Y.
Extension of the Improved Bounce-Back Scheme for Electrokinetic Flow in the Lattice Boltzmann Method. *Entropy*. 2015; 17(11):7406-7419.
https://doi.org/10.3390/e17117406

**Chicago/Turabian Style**

Chen, Qing, Hongping Zhou, Xuesong Jiang, Linyun Xu, Qing Li, and Yu Ru.
2015. "Extension of the Improved Bounce-Back Scheme for Electrokinetic Flow in the Lattice Boltzmann Method" *Entropy* 17, no. 11: 7406-7419.
https://doi.org/10.3390/e17117406