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A major challenge in flow through porous media is to better understand the link between microstructure and macroscale flow and transport. For idealised microstructures, the mathematical framework of homogenisation theory can be used for…

Fractured porous media or double porosity media are common in nature. At the same time, accurate modeling remains a significant challenge due to bi-modal pore size distribution, anisotropy, multi-field coupling, and various flow patterns.…

Geophysics · Physics 2024-06-13 Qi Zhang , Xia Yan , Jianli Shao

This study introduces an open-source computational framework for the generation and permeability evaluation of synthetic porous media. The proposed methodology integrates crystallographic and meshing tools to construct controlled…

Tissues and Organs · Quantitative Biology 2025-02-21 Thomas Lavigne , Camilo Andrés Suarez Afanador , Anas Obeidat , Stéphane Urcun

Porous materials are ubiquitous in various engineering and geological applications, where their permeability plays a critical role in viscous fluid flow and transport phenomena. Understanding and characterizing the microscale properties,…

Fluid Dynamics · Physics 2025-03-11 David Krach , Matthias Ruf , Holger Steeb

When modelling fluid flow in fractured reservoirs, it is common to represent the fracturesas lower-dimensional inclusions embedded in the host medium. Existing discretizationsof flow in porous media with thin inclusions assume that the…

Numerical Analysis · Mathematics 2021-01-22 Michele Starnoni , Inga Berre , Eirik Keilegavlen , Jan M. Nordbotten

In the field of nanoconfined fluids, there are striking examples of deformation/transport coupling in which mechanical solicitation of the confining host and dynamics of the confined fluid impact each other. While this intriguing behavior…

Computational Physics · Physics 2024-04-01 Alexander Schlaich , Matthieu Vandamme , Marie Plazanet , Benoit Coasne

Porous membranes are thin solid structures that allow the flow to pass through their tiny openings, called pores. Flow inertia may play a significant role in several filtration flows of natural and engineering interest. Here, we develop a…

We provide an analytical solution to examine the impact of steady and pulsatile flow in a symmetric wavy channel filled with an anisotropic porous medium. The flow inside the wavy channel with a porous substrate is governed by the…

Fluid Dynamics · Physics 2025-10-13 Sanchita Pramanik , Timir Karmakar

We propose a suite of technologies for analyzing the interaction between anisotropic arterial walls and blood flow for subject-specific geometries. Utilizing an established lumen modeling strategy, we present a comprehensive pipeline for…

Medical Physics · Physics 2024-06-21 Yujie Sun , Jiayi Huang , Qingshuang Lu , Xinhai Yue , Xuanming Huang , Wei He , Yun Shi , Ju Liu

The work is devoted to the development and computational implementation of the homogenization method for modeling unsteady flows of a viscous incompressible fluid in periodic porous media taking into account memory effects. At the…

Numerical Analysis · Mathematics 2026-04-29 P. N. Vabishchevich

Hypothesis Control of capillary flow through porous media has broad practical implications. However, achieving accurate and reliable control of such processes by tuning the pore size or by modification of interface wettability remains…

Fluid Dynamics · Physics 2021-06-08 MingchaoLiu , Si Suo , Jian Wu , Yixiang Gan , DorianAH HanaorcC. Q. Chen

We report and discuss, by means of pore-scale numerical simulations, the possibility of achieving a directional-dependent two-phase flow behaviour during the process of invasion of a viscous fluid into anisotropic porous media with…

Fluid Dynamics · Physics 2021-10-27 Dario Maggiolo , Francesco Picano , Federico Toschi

Despite the ubiquity of fluid flows interacting with porous and elastic materials, we lack a validated non-empirical macroscale method for characterizing the flow over and through a poroelastic medium. We propose a computational tool to…

Fluid Dynamics · Physics 2017-03-24 Uǧis Lācis , Giuseppe Antonio Zampogna , Shervin Bagheri

The paper presents a new type of weakly nonlinear two-scale model of controllable periodic porous piezoelectric structures saturated by Newtonian fluids. The flow is propelled by peristaltic deformation of microchannels which is induced due…

Analysis of PDEs · Mathematics 2024-07-18 Eduard Rohan , Vladimír Lukeš

When a fluid carrying a passive solute flows quickly through porous media, three key macroscale transport mechanisms occur. These mechanisms are diffusion, advection and dispersion, all of which depend on the microstructure of the porous…

Fluid Dynamics · Physics 2024-10-16 Lucy C Auton , Mohit P. Dalwadi , Ian M. Griffiths

The paper presents a new type of weakly nonlinear two-scale model of inflatable periodic poroelastic structures saturated by Newtonian fluids. The periodic microstructures incorporate fluid inclusions connected to the fluid channels by…

Analysis of PDEs · Mathematics 2025-08-28 Eduard Rohan , Vladimír Lukeš

Models of porous media are often applied to relatively small systems, which leads not only to system-size-dependent results, but also to phenomena that would be absent in larger systems. Here we investigate one such finite-size effect:…

In this work we develop a homogenisation methodology to upscale mathematical descriptions of microcirculatory blood flow from the microscale (where individual vessels are resolved) to the macroscopic (or tissue) scale. Due to the assumed…

Tissues and Organs · Quantitative Biology 2024-01-23 Y. Ben-Ami , B. D. Wood , J. M. Pitt-Francis , P. K. Maini , H. M. Byrne

Anisotropy of the permeability tensor in statistically uniform porous media of sizes used in typical computer simulations is studied. Although such systems are assumed to be isotropic by default, we show that de facto their anisotropic…

Fluid Dynamics · Physics 2015-05-13 Zbigniew Koza , Maciej Matyka , Arzhang Khalili

Flows enabled by phoretic mechanisms are of significant interest in several biological and biomedical processes, such as bacterial motion and targeted drug delivery. Here, we develop a homogenization-based macroscopic boundary condition…

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