Homogenization of the generalized Poisson–Nernst–Planck problem in a two-phase medium: correctors and estimates Full article
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Applicable Analysis
ISSN: 0003-6811 |
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| Output data | Year: 2021, Volume: 100, Number: 2, Pages: 253-274 Pages count : 22 DOI: 10.1080/00036811.2019.1600676 | ||||
| Tags | 35B27; 35M10; 82C24; Andrey Piatnitski; Generalized Poisson–Nernst–Planck model; homogenization; periodic unfolding method; residual error estimate; two-phase interface condition | ||||
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Abstract:
The paper provides a rigorous homogenization of the Poisson–Nernst–Planck problem stated in an inhomogeneous domain composed of two, solid and pore, phases. The generalized PNP model is constituted of the Fickian cross-diffusion law coupled with electrostatic and quasi-Fermi electrochemical potentials, and Darcy's flow model. At the interface between two phases inhomogeneous boundary conditions describing electrochemical reactions are considered. The resulting doubly non-linear problem admits discontinuous solutions caused by jumps of field variables. Using an averaged problem and first-order asymptotic correctors, the homogenization procedure gives us an asymptotic expansion of the solution which is justified by residual error estimates.
Cite:
Kovtunenko V.A.
, Zubkova A.V.
Homogenization of the generalized Poisson–Nernst–Planck problem in a two-phase medium: correctors and estimates
Applicable Analysis. 2021. V.100. N2. P.253-274. DOI: 10.1080/00036811.2019.1600676 WOS Scopus РИНЦ OpenAlex
Homogenization of the generalized Poisson–Nernst–Planck problem in a two-phase medium: correctors and estimates
Applicable Analysis. 2021. V.100. N2. P.253-274. DOI: 10.1080/00036811.2019.1600676 WOS Scopus РИНЦ OpenAlex
Identifiers:
| Web of science: | WOS:000609611600002 |
| Scopus: | 2-s2.0-85063928817 |
| Elibrary: | 45550161 |
| OpenAlex: | W2940006616 |