Homogenisation of advective-diffusive transport in poroelastic media

International audienceAdvective-diffusive solute transport in a poroelastic medium is usually modelled at the macroscopic scale by considering a poro-elastic formulation associated with the classical advective-diffusive solute transport equation. The purpose of the present work is to rigorously determine the macroscopic model by starting with the pore-scale equations that describe transient advective/diffusive solute transport in a saturated deformable elastic porous medium. The macroscopic model is derived by using an homogenisation method. It includes Biot's model of consolidation and a transport equation of advective-diffusive type. This latter contains a coupling term which reveals a mechanically-induced solute transport mechanism

Flow of low pressure gas through dual-porosity media

Using the theory of homogenization we derive macroscopic models for describing flow of gas at low pressure in dual-porosity media. The case of a fractured porous medium is under consideration for the study, and the existence of a representative elementary volume that consists of open connected fractures surrounded by porous matrix blocks is assumed. The local flow is governed by either Klinkenberg's law or Knudsen's diffusion law in the matrix while either a non-slip flow or a slip flow occurs in the fractures. Six new models are derived by homogenization, which are compared to the three models which were obtained for Darcy's regime in an earlier work. Each of these nine models is characterized by its macroscopic flow regime and by the type of macroscopic behavior it describes. Besides Darcy's and Klinkenberg's macroscopic flow regimes, a transition regime between Klinkenberg's and Knudsen's regimes is identified. The types of macroscopic behaviors include a dual and a single porosity description and an intermediate behavior that describes a single-porosity behavior, but in which the porosity of the entire fractured porous medium is accounted for

On the quasi-static effective behaviour of poroelastic media containing elastic inclusions

The aim of the present study is to derive the effective quasi-static behaviour of a composite medium, made of a poroelastic matrix containing elastic impervious inclusions. For this purpose, the asymptotic homogenisation method is used. On the local scale, the governing equations include Biot's model of poroelasticity in the porous matrix and Navier equations in the inclusions, with elastic properties of the same order of magnitude. Biot's diphasic model of poroelasticity is obtained on the macroscopic scale, but with effective parameters that are strongly impacted by the distribution of inclusions, even at low volume fraction. The impact on fluid flow is strictly geometrical, showing that the inclusions do not play the role of a porous network

Effect of collagen network orientation on the cervical intervertebral disc response to flexion load

National audienc

Acoustics of a porous medium saturated by a bubbly fluid undergoing phase change

International audienceThe objective of this work is the derivation of the wave equations for describing acoustics in a deformable porous medium saturated by a bubbly fluid, when capillary, thermal and phase change effects are accounted for. This is performed using an homogenisation technique: the macroscopic model is obtained by upscaling the bubble-scale and the pore-scale descriptions. For convenience a bubbly fluid near the bubble point, in the bulk of which a small perturbation can generate small bubbles is considered. Although the derived macroscopic wave equations are similar in their structure to Biot's equations that describe wave propagation in saturated porous media, important differences appear as a result of the presence of bubbles. In effect, gas-liquid phase change considerably decreases the apparent rigidity of the bubbly fluid, and consequently decreases the wave velocity in the porous medium. Moreover, this phenomenon is amplified for very small bubbles, for which the apparent rigidity of the bubbly fluid can be negative. The influence of the bubbly liquid apparent rigidity on the wave velocity and attenuation is highlighted on an illustrative example: it is shown that they strongly differ from wave velocities and attenuations in porous media saturated by a liquid or by a gas

About non-Fickian hyperbolic diffusion

Fick's law expresses the proportionality of solute flux with respect to concentration gradient. Similar relations are Darcy's law for the fluid flow in porous media, Ohm's law for the electric flux and Fourier's law for heat transfers. When introduced in the corresponding balance equations, these flux laws yield diffusion equations of parabolic character. Different attempts have been made to obtain hyperbolic equations so as to point out propagative phenomena. This was done by adding a time derivative flux term to the flow law. In the paper we focus on solute transport. Two possible non-Fickian diffusion cases are addressed. We firstly investigate diffusion in fluids by a mechanistic approach. Secondly, we study the macroscopic diffusion law in composite materials with large contrast of diffusion coefficient. We show that the obtained diffusion law yields hyperbolicity for drastically small characteristic times or non-propagative waves, respectively

Exome sequencing identifies germline variants in DIS3 in familial multiple myeloma

[Excerpt] Multiple myeloma (MM) is the third most common hematological malignancy, after Non-Hodgkin Lymphoma and Leukemia. MM is generally preceded by Monoclonal Gammopathy of Undetermined Significance (MGUS) [1], and epidemiological studies have identified older age, male gender, family history, and MGUS as risk factors for developing MM [2]. The somatic mutational landscape of sporadic MM has been increasingly investigated, aiming to identify recurrent genetic events involved in myelomagenesis. Whole exome and whole genome sequencing studies have shown that MM is a genetically heterogeneous disease that evolves through accumulation of both clonal and subclonal driver mutations [3] and identified recurrently somatically mutated genes, including KRAS, NRAS, FAM46C, TP53, DIS3, BRAF, TRAF3, CYLD, RB1 and PRDM1 [3,4,5]. Despite the fact that family-based studies have provided data consistent with an inherited genetic susceptibility to MM compatible with Mendelian transmission [6], the molecular basis of inherited MM predisposition is only partly understood. Genome-Wide Association (GWAS) studies have identified and validated 23 loci significantly associated with an increased risk of developing MM that explain ~16% of heritability [7] and only a subset of familial cases are thought to have a polygenic background [8]. Recent studies have identified rare germline variants predisposing to MM in KDM1A [9], ARID1A and USP45 [10], and the implementation of next-generation sequencing technology will allow the characterization of more such rare variants. [...]French National Cancer Institute (INCA) and the Fondation Française pour la Recherche contre le Myélome et les Gammapathies (FFMRG), the Intergroupe Francophone du Myélome (IFM), NCI R01 NCI CA167824 and a generous donation from Matthew Bell. This work was supported in part through the computational resources and staff expertise provided by Scientific Computing at the Icahn School of Medicine at Mount Sinai. Research reported in this paper was supported by the Office of Research Infrastructure of the National Institutes of Health under award number S10OD018522. The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health. The authors thank the Association des Malades du Myélome Multiple (AF3M) for their continued support and participation. Where authors are identified as personnel of the International Agency for Research on Cancer / World Health Organization, the authors alone are responsible for the views expressed in this article and they do not necessarily represent the decisions, policy or views of the International Agency for Research on Cancer / World Health Organizatio