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A n-layered inclusion-based modeling to estimate permeability of multi-phase porous solids.

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Title: A n-layered inclusion-based modeling to estimate permeability of multi-phase porous solids.
Authors: Phan, V. H.1,2 (AUTHOR), Monchiet, V.1,2 (AUTHOR) vincent.monchiet@univ-eiffel.fr
Source: Acta Mechanica. Jun2025, Vol. 236 Issue 6, p3497-3513. 17p.
Subjects: Unit cell, Permeability, Equations
Abstract: This paper concerns the determination of the permeability of multiporous solids in the framework of homogenization considering the Brinkman equation at the microscopic scale. We provide close form solutions for cylindrical and spherical unit cells constituted of n-layered concentric inclusions. Particular attention is paid to the choice of the conditions at the boundary of the unit cell. Specifically, four kind of boundary conditions are used in the literature and are analyzed here in the light of the Hill–Mandel lemma, leading to a hierarchy of the resulting estimate of the macroscopic permeability. Finally, comparisons for two-phase and three-phase porous solids are proposed and the accuracy of the estimates are compared with numerical solutions. [ABSTRACT FROM AUTHOR]
Copyright of Acta Mechanica is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
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  Data: This paper concerns the determination of the permeability of multiporous solids in the framework of homogenization considering the Brinkman equation at the microscopic scale. We provide close form solutions for cylindrical and spherical unit cells constituted of n-layered concentric inclusions. Particular attention is paid to the choice of the conditions at the boundary of the unit cell. Specifically, four kind of boundary conditions are used in the literature and are analyzed here in the light of the Hill–Mandel lemma, leading to a hierarchy of the resulting estimate of the macroscopic permeability. Finally, comparisons for two-phase and three-phase porous solids are proposed and the accuracy of the estimates are compared with numerical solutions. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Acta Mechanica is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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        Value: 10.1007/s00707-025-04331-8
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        Type: general
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              Text: Jun2025
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