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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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/).

Název v anglickém jazyce

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

Popis výsledku anglicky

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/).

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/GA20-22092S" target="_blank" >GA20-22092S: Víceškálová termodynamika: okrajové podmínky, integrace a aplikace</a><br>

Návaznosti

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

Rok uplatnění

2023

Kód důvěrnosti údajů

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

Název periodika

Applied Mathematics Letters

ISSN

0893-9659

e-ISSN

1873-5452

Svazek periodika

137

Číslo periodika v rámci svazku

108482

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

8

Strana od-do

—

Kód UT WoS článku

000927084700011

EID výsledku v databázi Scopus

2-s2.0-85141751757