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<p>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 <i>n</i>-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.</p>

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

  • 期刊论文

  • 发表日期：

    2025年4月26日

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  • V. H. Phan,
  • V. Monchiet

摘要

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.