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Multiphase Modeling of Porous Media: Advances toward Widespread Applications

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A special issue of Applied Sciences (ISSN 2076-3417). This special issue belongs to the section "Materials Science and Engineering".

Deadline for manuscript submissions: closed (30 December 2021) | Viewed by 10754

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Dr. Giuseppe Sciumè

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Institute of Mechanics and Mechanical Engineering (I2M, CNRS UMR 5295), University of Bordeaux – CNRS – ENSAM – Bordeaux INP, Bordeaux, France
Interests: numerical modeling of heat and mass transport in deforming porous medium systems with applications in mechanics of cement-based materials (HTM behavior, creep, damage, creep-damage coupling) and multiphase modeling of healthy and pathologic biological tissues

Special Issue Information

Dear Colleagues,

Multiphase porous media mechanics is among the most fascinating branches of continuum mechanics since it can be applied many fields of science. Originally used for geomechanical problems, porous media mechanics is now extensively applied for modelling of building materials (e.g., concrete and wood) and in other research domains including development of efficient energy storage systems (e.g., porous electrode technology), biomechanics (e.g., teeth and bone decalcification, herniation of intervertebral discs), oncophysics (e.g., tumor growth), etc. The diversity of applications has generated a wide range of approaches. Some modelling approaches are non-reactive, whereas others include reactions (accounting for mass, momentum, and energy exchange between system constituents). Concerning the interaction between the fluid and the solid phases, in some cases (depending on the application), deformation of the solid scaffold can be neglected; in other cases, a strong or weak coupling between the solid behavior and inside fluid mechanics must be considered.

This Special Issue aims to collect a set of contributions covering diverse applications representative of the flexibility of multiphase porous media mechanics. The aim is not only to present applications but also to focus on theoretical approaches (traditional and more modern ones) on micro- (pore-scale) and macroscale (Darcy-scale) modelling and up-scaling; hence, papers reporting new and unpublished advances on applications and/or theoretical developments are welcomed.

Dr. Giuseppe Sciumè
Guest Editor

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Keywords

Reactive multiphase flow
Microscale (pore-scale) modeling
Macroscale (Darcy-scale) modelling
Averaging theories and application
Extension of Biot’s theory
Multiphase poroeleasticity
Multiphase poro-viscoelasticity or –elastoplasticity
Porous building materials
Living porous media
Biomechanics
Biophysics of healthy and pathologic tissues

Published Papers (4 papers)

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Research

20 pages, 2659 KiB

Open AccessFeature PaperArticle

The Human Meniscus Behaves as a Functionally Graded Fractional Porous Medium under Confined Compression Conditions

by Raphaël Bulle, Gioacchino Alotta, Gregorio Marchiori, Matteo Berni, Nicola F. Lopomo, Stefano Zaffagnini, Stéphane P. A. Bordas and Olga Barrera

Appl. Sci. 2021, 11(20), 9405; https://doi.org/10.3390/app11209405 - 11 Oct 2021

Cited by 12 | Viewed by 2379

Abstract

In this study, we observe that the poromechanical parameters in human meniscus vary spatially throughout the tissue. The response is anisotropic and the porosity is functionally graded. To draw these conclusions, we measured the anisotropic permeability and the “aggregate modulus” of the tissue, i.e., the stiffness of the material at equilibrium, after the interstitial fluid has ceased flowing. We estimated those parameters within the central portion of the meniscus in three directions (i.e., vertical, radial and circumferential) by fitting an enhanced model on stress relation confined compression tests. We noticed that a classical biphasic model was not sufficient to reproduce the observed experimental behaviour. We propose a poroelastic model based on the assumption that the fluid flow inside the human meniscus is described by a fractional porous medium equation analogous to Darcy’s law, which involves fractional operators. The fluid flux is then time-dependent for a constant applied pressure gradient (in contrast with the classical Darcy’s law, which describes a time independent fluid flux relation). We show that a fractional poroelastic model is well-suited to describe the flow within the meniscus and to identify the associated parameters (i.e., the order of the time derivative and the permeability). The results indicate that mean values of

λ_{β}, β

in the central body are

λ_{β} = 5.5443 \times 10^{- 10} \frac{m^{4}}{N s^{1 - β}}

β = 0.0434

, while, in the posterior and anterior regions, are

λ_{β} = 2.851 \times 10^{- 10} \frac{m^{4}}{N s^{1 - β}}

β = 0.0326

and

λ_{β} = 1.2636 \times 10^{- 10} \frac{m^{4}}{N s^{1 - β}}

β = 0.0232

, respectively. Furthermore, numerical simulations show that the fluid flux diffusion is facilitated in the central part of the meniscus and hindered in the posterior and anterior regions. Full article

(This article belongs to the Special Issue Multiphase Modeling of Porous Media: Advances toward Widespread Applications)

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33 pages, 2145 KiB

Open AccessFeature PaperArticle

Homogenized Balance Equations for Nonlinear Poroelastic Composites

by Laura Miller and Raimondo Penta

Appl. Sci. 2021, 11(14), 6611; https://doi.org/10.3390/app11146611 - 19 Jul 2021

Cited by 12 | Viewed by 1942

Abstract

Within this work, we upscale the equations that describe the pore-scale behaviour of nonlinear porous elastic composites, using the asymptotic homogenization technique in order to derive the macroscale effective governing equations. A porous hyperelastic composite can be thought of as being comprised of a matrix interacting with a number of subphases and percolated by a fluid flowing in the pores (which is chosen to be Newtonian and incompressible here). A general nonlinear macroscale model is derived and is then specified for a particular choice of strain energy function, namely the de Saint-Venant function. This leads to a macroscale system of PDEs, which is of poroelastic type with additional terms and transformations to account for the nonlinear behaviour of the material. Our new porohyperelastic-type model describes the effective behaviour of nonlinear porous composites by prescribing the stress balance equations, the conservation of mass and Darcy’s law. The coefficients of these macroscale equations encode the detailed microstructure of the material and are to be found by solving pore-scale differential problems. The model reduces to the following limit cases of (a) linear poroelastic composites when the deformation gradient approaches the identity, (b) nonlinear composites when there are no pores and (c) nonlinear poroelasticity when only the matrix–fluid interaction is considered. This model is applicable when the interactions between various hyperelastic solid phases occur at the pore-scale, as in biological tissues such as artery walls, the myocardium, lungs and liver. Full article

(This article belongs to the Special Issue Multiphase Modeling of Porous Media: Advances toward Widespread Applications)

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23 pages, 12481 KiB

Open AccessEditor’s ChoiceArticle

Hydrothermal and Entropy Investigation of Ag/MgO/H₂O Hybrid Nanofluid Natural Convection in a Novel Shape of Porous Cavity

by Nidal Abu-Libdeh, Fares Redouane, Abderrahmane Aissa, Fateh Mebarek-Oudina, Ahmad Almuhtady, Wasim Jamshed and Wael Al-Kouz

Appl. Sci. 2021, 11(4), 1722; https://doi.org/10.3390/app11041722 - 15 Feb 2021

Cited by 55 | Viewed by 3355

Abstract

In this study, a new cavity form filled under a constant magnetic field by Ag/MgO/H₂O nanofluids and porous media consistent with natural convection and total entropy is examined. The nanofluid flow is considered to be laminar and incompressible, while the advection inertia effect in the porous layer is taken into account by adopting the Darcy–Forchheimer model. The problem is explained in the dimensionless form of the governing equations and solved by the finite element method. The results of the values of Darcy (Da), Hartmann (Ha) and Rayleigh (Ra) numbers, porosity (

ε_{p}

), and the properties of solid volume fraction (ϕ) and flow fields were studied. The findings show that with each improvement in the Ha number, the heat transfer rate becomes more limited, and thus the magnetic field can be used as an outstanding heat transfer controller. Full article

(This article belongs to the Special Issue Multiphase Modeling of Porous Media: Advances toward Widespread Applications)

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27 pages, 6758 KiB

Open AccessArticle

Elucidating the Role of Matrix Porosity and Rigidity in Glioblastoma Type IV Progression

by Rui C. Pereira, Raffaella Santagiuliana, Luca Ceseracciu, Daniela P. Boso, Bernhard A. Schrefler and Paolo Decuzzi

Appl. Sci. 2020, 10(24), 9076; https://doi.org/10.3390/app10249076 - 18 Dec 2020

Cited by 4 | Viewed by 2257

Abstract

The highly infiltrating nature of glioma cells is the major cause for the poor prognosis of brain malignancies. Motility, proliferation, and gene expression of cells in natural and synthetic gels have been analyzed by several authors, yet quantitative studies elucidating the role of matrix porosity and rigidity in the development of whole malignant masses are missing. Here, an experimental-computational framework is introduced to analyze the behavior of U87-MG cells and spheroids in compact hyaluronic acid gels (HA), replicating the brain parenchyma; and fibrous collagen gels (COL), resembling the organized structures of the brain. Experimentally it was observed that individual U87-MG cells in COL assumed an elongated morphology within a few hours post inclusion (p.i.) and travelled longer distances than in HA. As spheroids, U87-MG cells rapidly dispersed into COL resulting in infiltrating regions as large as tumor cores (≈600 μm, at 8 days p.i.). Conversely, cells in HA originated smaller and denser infiltrating regions (≈300 μm, at 8 days p.i.). Notably, COL tumor core size was only 20% larger than in HA, at longer time points. Computationally, by introducing for the first time the effects of matrix heterogeneity in our numerical simulations, the results confirmed that matrix porosity and its spatial organization are key factors in priming the infiltrating potential of these malignant cells. The experimental-numerical synergy can be used to predict the behavior of neoplastic masses under diverse conditions and the efficacy of combination therapies simultaneously aiming at killing cancer cells and modulating the tumor microenvironment. Full article

(This article belongs to the Special Issue Multiphase Modeling of Porous Media: Advances toward Widespread Applications)

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