Effective permeabilities for flow through anisotropic microscopic geometries

TL;DR

This paper presents a computational and theoretical framework for accurately determining anisotropic effective permeabilities in fibrous microstructures, improving flow modeling in biomedical and engineering applications like aneurysm treatment.

Contribution

It introduces a systematic methodology to capture directional permeability variations due to fiber orientation, validated through homogenisation theory and simulations.

Findings

Anisotropic permeability significantly affects flow direction and magnitude.

Permeability tensors improve the accuracy of flow simulations.

The framework is applicable to various fibrous porous microstructures.

Abstract

This work develops a computational and theoretical framework for determining effective permeabilities in anisotropic microscopic geometries containing dense, fibre-like obstacles, motivated by the need to model flow in coiled aneurysm domains accurately. Building on homogenisation theory and fully resolved simulations in Representative Elementary Volumes (REVs), we validate the permeability model introduced in [C. Boutin, Study of permeability by periodic and self-consistent homogenisation. Eur. J. Mech. A Solids, 19(4):603-632, 2000] and propose a systematic methodology for capturing the directional variations induced by fibre orientation. The resulting permeability tensors are incorporated into macroscopic flow simulations based on the Darcy equation, enabling direct comparison of anisotropic and isotropic permeability models across several benchmark configurations. Our findings show that anisotropy has a significant impact on local flow direction and magnitude, generating directional permeability contrasts which cannot be reproduced by classical isotropic approximations. By integrating coil-induced microstructural effects into continuum-scale hemodynamic models, the proposed approach enables more realistic assessment of post-treatment aneurysm flow behaviour. Beyond this clinical application, the framework is broadly applicable to other biomedical and engineering systems involving fibrous or filamentous porous microstructures.