Abstract: The paper is devoted to the existence and rigorous homogenisation of the generalised Poisson-Nernst-Planck problem describing the transport of charged species in a two-phase domain. By this, inhomogeneous conditions are supposed at the interface between the pore and solid phases. The solution of the doubly non-linear cross-diffusion model is discontinuous and allows a jump across the phase interface. To prove an averaged problem, the two-scale convergence method over periodic cells is applied and formulated simultaneously in the two phases and at the interface. In the limit, we obtain a non-linear system of equations with averaged matrices of the coefficients, which are based on cell problems due to diffusivity, permittivity and interface electric flux. The first-order corrector due to the inhomogeneous interface condition is derived as the solution to a non-local problem.

Cite: KOVTUNENKO V.A. , ZUBKOVA A.V.
Existence and two-scale convergence of the generalised Poisson–Nernst–Planck problem with non-linear interface conditions
European Journal of Applied Mathematics. 2021. V.32. N4. P.683-710. DOI: 10.1017/s095679252000025x WOS Scopus РИНЦ OpenAlex

Identifiers:

Web of science:	WOS:000754606800004
Scopus:	2-s2.0-85094179821
Elibrary:	45194992
OpenAlex:	W3047094906

Citing:

DB	Citing
Scopus	2
OpenAlex	6
Elibrary	3
Web of science	3

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