Applied Mathematics and Mechanics >
Two-dimensional equations for thin-films of ionic conductors
Received date: 2017-10-08
Revised date: 2018-02-20
Online published: 2018-08-01
Supported by
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
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.
Shuting LU, Chunli ZHANG, Weiqiu CHEN, Jiashi YANG . Two-dimensional equations for thin-films of ionic conductors[J]. Applied Mathematics and Mechanics, 2018 , 39(8) : 1071 -1088 . DOI: 10.1007/s10483-018-2354-6
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