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A Coupled Lattice Boltzmann Method to Solve Nernst–Planck Model for Simulating Electro-osmotic Flows

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Abstract

In this paper, we focus on the nonlinear coupling mechanism of the Nernst–Planck model and propose a coupled lattice Boltzmann method (LBM) to solve it. In this method, a new LBM for the Nernst–Planck equation is developed, a multi-relaxation-time (MRT)-LBM for flow field and an LBM for the Poisson equation are used. And then, we discuss the choice of the model and found that the MRT-LBM is much more stable and accurate than the LBGK model. A reasonable iterative sequence and evolution number for each LBM are proposed by considering the properties of the coupled LBM. The accuracy and stability of the presented coupled LBM are also discussed through simulating electro-osmotic flows (EOF) in micro-channels. Furthermore, to test the applicability of it, the EOF with non-uniform surface potential in micro-channels based on the Nernst–Planck model is simulated. And we investigate the effects of non-uniform surface potential on the pattern of the EOF at different external applied electric fields. Finally, a comparison of the difference between the Nernst–Planck model and the Poisson–Boltzmann model is presented.

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Acknowledgments

We gratefully acknowledge the Prof. Jiankang Wu for his helpful discussions during this work. This work is supported by the National Science Foundation of China (Grant Nos. 51125024, 51006040, 11272132) and China Postdoctoral Science Foundation (Grant No. 2012M521424).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan,  430074, People’s Republic of China

    Xuguang Yang, Baochang Shi & Zhenhua Chai

  2. State Key Laboratory of Coal Combustion, Huazhong University of Science and Technology, Wuhan,  430074, People’s Republic of China

    Zhaoli Guo

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  1. Xuguang Yang
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  2. Baochang Shi
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  3. Zhenhua Chai
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  4. Zhaoli Guo
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Correspondence to Baochang Shi.

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Yang, X., Shi, B., Chai, Z. et al. A Coupled Lattice Boltzmann Method to Solve Nernst–Planck Model for Simulating Electro-osmotic Flows. J Sci Comput 61, 222–238 (2014). https://doi.org/10.1007/s10915-014-9820-6

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  • DOI: https://doi.org/10.1007/s10915-014-9820-6

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