Two-dimensional equations for thin-films of ionic conductors

doi:10.1007/s10483-018-2354-6

Abstract

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.

Key words: singular perturbation problem, difference scheme, uniform convergence, mixed boundary value condition, semilinear ordinary differential equation, linearized Poisson-Nernst-Planck (PNP) theory, two-dimensional (2D) equation, ionic conductor thin-film, ionic conduction and diffusion

2010 MSC Number:

74F99

Shuting LU, Chunli ZHANG, Weiqiu CHEN, Jiashi YANG. Two-dimensional equations for thin-films of ionic conductors. Applied Mathematics and Mechanics (English Edition), 2018, 39(8): 1071-1088.

TrendMD

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