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Two-dimensional equations for thin-films of ionic conductors

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Abstract

A theoretical model is developed for predicting both conduction and diffusion in thin-film ionic conductors or cables. With the linearized Poisson-Nernst-Planck (PNP) theory, the two-dimensional (2D) equations for thin ionic conductor films are obtained from the three-dimensional (3D) equations by power series expansions in the film thickness coordinate, retaining the lower-order equations. The thin-film equations for ionic conductors are combined with similar equations for one thin dielectric film to derive the 2D equations of thin sandwich films composed of a dielectric layer and two ionic conductor layers. A sandwich film in the literature, as an ionic cable, is analyzed as an example of the equations obtained in this paper. The numerical results show the effect of diffusion in addition to the conduction treated in the literature. The obtained theoretical model including both conduction and diffusion phenomena can be used to investigate the performance of ionic-conductor devices with any frequency.

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Author information

Authors and Affiliations

  1. Department of Engineering Mechanics, Zhejiang University, Hangzhou, 310027, China

    Shuting Lu, Chunli Zhang, Weiqiu Chen & Jiashi Yang

  2. Soft Matter Research Center, Zhejiang University, Hangzhou, 310027, China

    Chunli Zhang

  3. Key Laboratory of Soft Machines and Smart Devices of Zhejiang Province, Zhejiang University, Hangzhou, 310027, China

    Chunli Zhang

  4. Department of Mechanical and Materials Engineering, University of Nebraska-Lincoln, Lincoln, NE, 68588-0526, U.S.A.

    Jiashi Yang

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  1. Shuting Lu
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  3. Weiqiu Chen
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  4. Jiashi Yang
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Correspondence to Chunli Zhang.

Additional information

Citation: LU, S. T., ZHANG, C. L., CHEN, W. Q., and YANG, J. S. Two-dimensional equations for thin-films of ionic conductors. Applied Mathematics and Mechanics (English Edition), 39(8), 1071–1088 (2018) https://doi.org/10.1007/s10483-018-2354-6

Project supported by the National Natural Science Foundation of China (Nos. 11672265, 11202182, and 11621062), the Fundamental Research Funds for the Central Universities (Nos. 2016QNA4026 and 2016XZZX001-05), and the Open Foundation of Zhejiang Provincial Top Key Discipline of Mechanical Engineering

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Lu, S., Zhang, C., Chen, W. et al. Two-dimensional equations for thin-films of ionic conductors. Appl. Math. Mech.-Engl. Ed. 39, 1071–1088 (2018). https://doi.org/10.1007/s10483-018-2354-6

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  • DOI: https://doi.org/10.1007/s10483-018-2354-6

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