Mathematical modeling of a discontinuous solution of the generalized Poisson-Nernst-Planck problem in a two-phase medium Full article
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Kinetic and Related Models
ISSN: 1937-5093 |
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| Output data | Year: 2018, Volume: 11, Number: 1, Pages: 119-135 Pages count : 17 DOI: 10.3934/krm.2018007 | ||||
| Tags | Energy and entropy estimates; Generalized Poisson-Nernst-Planck model; Interface jump; Mass balance; Nonlinear boundary reaction | ||||
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Abstract:
In this paper a mathematical model generalizing Poisson-Nernst- Planck system is considered. The generalized model presents electrokinetics of species in a two-phase medium consisted of solid particles and a pore space. The governing relations describe cross-diffusion of the charged species together with the overall electrostatic potential. At the interface between the pore and the solid phases nonlinear electro-chemical reactions are taken into account provided by jumps of field variables. The main advantage of the generalized model is that the total mass balance is kept within our setting. As the result of the variational approach, well-posedness properties of a discontinuous solution of the problem are demonstrated and supported by the energy and entropy estimates.
Cite:
Kovtunenko V.A.
, Zubkova A.V.
Mathematical modeling of a discontinuous solution of the generalized Poisson-Nernst-Planck problem in a two-phase medium
Kinetic and Related Models. 2018. V.11. N1. P.119-135. DOI: 10.3934/krm.2018007 WOS Scopus РИНЦ OpenAlex
Mathematical modeling of a discontinuous solution of the generalized Poisson-Nernst-Planck problem in a two-phase medium
Kinetic and Related Models. 2018. V.11. N1. P.119-135. DOI: 10.3934/krm.2018007 WOS Scopus РИНЦ OpenAlex
Identifiers:
| Web of science: | WOS:000436289100007 |
| Scopus: | 2-s2.0-85050717997 |
| Elibrary: | 35788362 |
| OpenAlex: | W2749334197 |