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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-12-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/24/1/46 |
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| author | Dick Bedeaux Signe Kjelstrup |
| author_facet | Dick Bedeaux Signe Kjelstrup |
| author_sort | Dick Bedeaux |
| collection | DOAJ |
| 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. |
| first_indexed | 2024-03-10T01:31:16Z |
| format | Article |
| id | doaj.art-05cffcffe5274fd8830e4c6352259bbd |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T01:31:16Z |
| publishDate | 2021-12-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-05cffcffe5274fd8830e4c6352259bbd2023-11-23T13:41:01ZengMDPI AGEntropy1099-43002021-12-012414610.3390/e24010046Fluctuation-Dissipation Theorems for Multiphase Flow in Porous MediaDick Bedeaux0Signe Kjelstrup1PoreLab, Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, NorwayPoreLab, Department of Chemistry, Norwegian University of Science and Technology, NO-7491 Trondheim, NorwayA 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.https://www.mdpi.com/1099-4300/24/1/46fluctuation-dissipation theoremsnonequilibrium thermodynamicsflux-force relationsporous media |
| spellingShingle | Dick Bedeaux Signe Kjelstrup Fluctuation-Dissipation Theorems for Multiphase Flow in Porous Media Entropy fluctuation-dissipation theorems nonequilibrium thermodynamics flux-force relations 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 | fluctuation-dissipation theorems nonequilibrium thermodynamics flux-force relations porous media |
| url | https://www.mdpi.com/1099-4300/24/1/46 |
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