Upscaling the Poisson-Nernst-Planck equations for ion transport in weakly heterogeneous charged porous media

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F23%3A00364751" target="_blank" >RIV/68407700:21340/23:00364751 - isvavai.cz</a>

Result on the web

<a href="https://doi.org/10.1016/j.aml.2022.108482" target="_blank" >https://doi.org/10.1016/j.aml.2022.108482</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1016/j.aml.2022.108482" target="_blank" >10.1016/j.aml.2022.108482</a>

Result language

angličtina

Original language name

Upscaling the Poisson-Nernst-Planck equations for ion transport in weakly heterogeneous charged porous media

Original language description

The Poisson-Nernst-Planck (PNP) equations govern the continuum level descrip-tion of ions in electrolytes and especially the impact of charged surfaces. In numerous applications such surfaces are complex, varying on a small lengthscale compared to the overall scale of the system, often prohibiting the direct prediction of the osmotic swelling pressures induced by ion behaviours in Debye layers near surfaces. With periodicity, upscaling techniques can be readily used to determine the behaviour of the swelling pressure on large lengthscales without solving the PNP equations on the complex domain, though generalising to cases where the periodicity is only approximate is more challenging. Here, we generalise a method by Bruna and Chapman (2015) for upscaling a non-periodic diffusion equation to the PNP equations. After upscaling, we find a rational derivation of the swelling pressure closely resembling the classical, though phenomenological, use of Donnan membrane theory predictions for the swelling pressure in cartilage, together with a novel contribution driven by heterogeneous fixed (surface) charges. The resulting macroscale model is also shown to be thermodynamically consistent, though its comparison with a recent upscaled models for swelling pressure in cartilage mechanics emphasises the need to understand how macroscale models depend on differing upscaling techniques, especially in the absence of perfect periodicity.(c) 2022 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).

Czech name

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Czech description

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Type

J_imp - Article in a specialist periodical, which is included in the Web of Science database

CEP classification

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OECD FORD branch

10102 - Applied mathematics

Project

<a href="/en/project/GA20-22092S" target="_blank" >GA20-22092S: Multiscale thermodynamics: boundary conditions, integration and applications</a><br>

Continuities

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year

2023

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Applied Mathematics Letters

ISSN

0893-9659

e-ISSN

1873-5452

Volume of the periodical

137

Issue of the periodical within the volume

108482

Country of publishing house

NL - THE KINGDOM OF THE NETHERLANDS

Number of pages

8

Pages from-to

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UT code for WoS article

000927084700011

EID of the result in the Scopus database

2-s2.0-85141751757