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Fluctuation-Dissipation Theorems for Multiphase Flow in Porous Media
A thermodynamic description of porous media must handle the size- and shape-dependence of media properties, in particular on the nano-scale. Such dependencies are typically due to the presence of immiscible phases, contact areas and contact lines. We propose a way to obtain average densities suitabl...
Autores principales: | , |
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Formato: | Online Artículo Texto |
Lenguaje: | English |
Publicado: |
MDPI
2021
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Materias: | |
Acceso en línea: | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8774567/ https://www.ncbi.nlm.nih.gov/pubmed/35052072 http://dx.doi.org/10.3390/e24010046 |
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author | Bedeaux, Dick Kjelstrup, Signe |
author_facet | Bedeaux, Dick Kjelstrup, Signe |
author_sort | Bedeaux, Dick |
collection | PubMed |
description | A thermodynamic description of porous media must handle the size- and shape-dependence of media properties, in particular on the nano-scale. Such dependencies are typically due to the presence of immiscible phases, contact areas and contact lines. We propose a way to obtain average densities suitable for integration on the course-grained scale, by applying Hill’s thermodynamics of small systems to the subsystems of the medium. We argue that the average densities of the porous medium, when defined in a proper way, obey the Gibbs equation. All contributions are additive or weakly coupled. From the Gibbs equation and the balance equations, we then derive the entropy production in the standard way, for transport of multi-phase fluids in a non-deformable, porous medium exposed to differences in boundary pressures, temperatures, and chemical potentials. Linear relations between thermodynamic fluxes and forces follow for the control volume. Fluctuation-dissipation theorems are formulated for the first time, for the fluctuating contributions to fluxes in the porous medium. These give an added possibility for determination of the Onsager conductivity matrix for transport through porous media. Practical possibilities are discussed. |
format | Online Article Text |
id | pubmed-8774567 |
institution | National Center for Biotechnology Information |
language | English |
publishDate | 2021 |
publisher | MDPI |
record_format | MEDLINE/PubMed |
spelling | pubmed-87745672022-01-21 Fluctuation-Dissipation Theorems for Multiphase Flow in Porous Media Bedeaux, Dick Kjelstrup, Signe Entropy (Basel) Article A thermodynamic description of porous media must handle the size- and shape-dependence of media properties, in particular on the nano-scale. Such dependencies are typically due to the presence of immiscible phases, contact areas and contact lines. We propose a way to obtain average densities suitable for integration on the course-grained scale, by applying Hill’s thermodynamics of small systems to the subsystems of the medium. We argue that the average densities of the porous medium, when defined in a proper way, obey the Gibbs equation. All contributions are additive or weakly coupled. From the Gibbs equation and the balance equations, we then derive the entropy production in the standard way, for transport of multi-phase fluids in a non-deformable, porous medium exposed to differences in boundary pressures, temperatures, and chemical potentials. Linear relations between thermodynamic fluxes and forces follow for the control volume. Fluctuation-dissipation theorems are formulated for the first time, for the fluctuating contributions to fluxes in the porous medium. These give an added possibility for determination of the Onsager conductivity matrix for transport through porous media. Practical possibilities are discussed. MDPI 2021-12-27 /pmc/articles/PMC8774567/ /pubmed/35052072 http://dx.doi.org/10.3390/e24010046 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/). |
spellingShingle | Article Bedeaux, Dick Kjelstrup, Signe Fluctuation-Dissipation Theorems for Multiphase Flow in Porous Media |
title | Fluctuation-Dissipation Theorems for Multiphase Flow in Porous Media |
title_full | Fluctuation-Dissipation Theorems for Multiphase Flow in Porous Media |
title_fullStr | Fluctuation-Dissipation Theorems for Multiphase Flow in Porous Media |
title_full_unstemmed | Fluctuation-Dissipation Theorems for Multiphase Flow in Porous Media |
title_short | Fluctuation-Dissipation Theorems for Multiphase Flow in Porous Media |
title_sort | fluctuation-dissipation theorems for multiphase flow in porous media |
topic | Article |
url | https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8774567/ https://www.ncbi.nlm.nih.gov/pubmed/35052072 http://dx.doi.org/10.3390/e24010046 |
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