Les procédés de séparation à l’aide de membranes liquides sous forme d’émulsions doubles (DE) ont fait l’objet d’un examen approfondi en vue d’applications potentielles dans des domaines tels que la récupération des métaux, la séparation des gaz, l’élimination des composés organiques, l’élimination des polluants et les bioséparations. Les difficultés d’application de ces procédés ne concernent pas le caractère sophistiqué des équipements ou des installations, mais réside plutôt dans une bonne compréhension des phénomènes complexes qui se produisent à l’intérieur de ces systèmes. Depuis leur invention, d’importants efforts ont permis d’améliorer la modélisation des procédés de séparation par émulsions doubles. Toutefois, une représentation mathématique détaillée des phénomènes de diffusion/réaction au sein de ces systèmes restait inachevée. C’est pourquoi, l’objectif de cette thèse est de décrire le transport réactif d’un soluté au sein d’une émulsion double, constituée de trois phases, au moyen d’une modélisation permettant d’intégrer à l’échelle macroscopique les mécanismes aux échelles locales. La méthode de prise de moyenne volumique est utilisée pour établir rigoureusement les équations à l’échelle d’un continu équivalent dans le contexte des transferts hors équilibre massique local (NLME). La modélisation proposée dans ce travail repose sur deux philosophies distinctes. Dans un premier temps, les DES sont considérées comme des systèmes constitués par trois phases où les changements de concentration dans chacune d’entre-elles se produisent à la même échelle de longueur. Dans un deuxième temps, les DES correspondent à deux régions homogènes où les changements de concentration se produisent à deux échelles de longueur différentes. Deux modèles macroscopiques différents sont ainsi obtenus : le modèle à trois phases et celui à deux régions. Dans les deux cas, ces modèles font intervenir les coefficients effectifs de transport comprenant l’information aux petites échelles. Ces derniers sont liés aux variables de fermeture dont la détermination est obtenue par la résolution des problèmes de fermeture associés. Enfin, une analyse d’un procédé de séparation par contact dans un réservoir agité a été effectuée en appliquant les deux modèles. / Liquid membrane separations as Double Emulsions (DE) have been extensively examined for potential application in fields such as metal recovery, gas separation, organic compound removal, pollutant removal, and bioseparations. The difficulties in the application of these processes do not consist in sophisticated equipment or installation but in a good understanding of the complex phenomena that occur inside these systems. Since its invention, efforts have been made for successful modeling of DE process separation; however, information about the diffusion and reaction phenomena inside the DE has not been included in the mathematical descriptions in detail yet. Therefore, the objective of this thesis is to describe the solute transport with chemical reaction through DE systems by means of rigorous modeling that can provide with valuable information from the micro-scale to be applied at the macro-scale.To accomplish this, a DE system has been analyzed as a three-phase system characterized by more than one disparate length scales.The method of volume averaging has been used to derive rigorous averaged equations in the context of the non-local mass equilibrium (NLME). The structure of the DES has been studied from two different perspectives: 1) the DES as a single domain where concentration changes occur in the same length scale and 2) the DES consists in two homogeneous regions where concentration changes occur at two different length scales. As a result of these different standpoints of representing the system, two different averaged macroscopic models were obtained: the three-phase and the two-region models. Both models present effective coefficients that include information about the micro-scale. These latter are related to closure variables which are solutions of associated boundary-value problems. Finally, an analysis of a DE-containing separation process in a stirred tank by applying both models was made.

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The primary objective of this research is to develop and verify a methodology for modeling three dimensional discrete crack growth in concrete and reinforced concrete structures. Two main sources of damage, considered in this work, include the mechanical loading and the chemical interaction. The behavior of concrete is brittle in tension and becomes ductile behavior under compressive loading. At the same time, the chemical interaction triggers a progressive degradation of strength parameters. The main focus in this research is on numerical analysis of localized damage that is associated with formation of macrocracks. The specific form of chemical interaction examined here involves the alkali-silica reaction (ASR). The approach used in this work for describing the propagation of macrocraks is based on the volume averaging technique. This scheme represents a simplified form of strong discontinuity approach (SDA). It incorporates the notion of a ‘characteristic length’, which is defined as the ratio of area of the crack surface to the considered referential volume. It is demonstrated, based on an extensive numerical study, that this approach gives mesh-independent results which are consistent with the experimental evidence. The accuracy of the solutions is virtually the same as that based on SDA and/or the Extended Finite Element Method (XFEM), while the computational effort is significantly smaller. In order to describe the behavior of the fractured zone, a traction velocity discontinuity relation is formulated that is representative of different modes of damage propagation, including crack opening in tensile regime as well as shear band formation under compression. For tracing the discontinuity within domain, crack smoothening algorithm is employed to overcome any numerical instabilities that may occur close to ultimate load of the structure. The general methodology, as outlined above, has been enhanced by incorporating the chemoplasticity framework to describe the damage propagation in concrete affected by chemical interaction, i.e. continuing ASR. The latter is associated with progressive expansion of the silica gel that is coupled with degradation of strength properties. An implicit scheme has been developed, incorporating the return mapping algorithm, for the integration of the governing constitutive relations. The framework has been implemented in Abaqus software to examine the crack propagation pattern in structural elements subjected to continuing ASR. Another major topic addressed in this thesis is the ‘size effect’ phenomenon. The existing experimental studies, conducted primarily on various concrete structures, clearly show that the ultimate strength is strongly affected by the size of the structure. This phenomenon stems primarily from the effect of localized damage that accompanies the structural failure. The quantitative response depends on the geometry of the structure, type of loading and the material properties. The size effect has been investigated here for a number of notched and un-notched concrete beams, of different geometries, subjected to three-point bending. Both mechanical loading and the chemical interaction have been considered. The next topic considered in this study deals with analysis of localized fracture in 3D reinforced concrete structures. Here, a mesoscale approach is employed whereby the material is perceived as a composite medium comprising two constituents, i.e. concrete matrix and steel reinforcement. The response at the macroscale is obtained via a homogenization procedure that incorporates again the volume averaging. The latter incorporates a set of static and kinematic constraints that are representative of the response prior to the onset of fracture. After the formation of macrocracks, a traction-separation law within the fractured zone is modified by incorporating the Timoshenko beam theory in order to assess the stiffness characteristics in the presence of reinforcement. A number of numerical examples are given that examine the crack pattern formation and the associated fracture mechanism in concrete beams at different intensity of reinforcement. The final chapter of this thesis provides an illustrative example of the application of the proposed methodology to the analysis of a large scale structure. The focus here is on the assessment of structural damage in a hydraulic structure subjected to ASR continuing over of period of a few decades. The results, in term of the predicted extent of damage as well as the displacement history at some specific locations, are compared with in-situ monitoring. / Thesis / Doctor of Philosophy (PhD)

Ce travail s’inscrit dans le contexte général de l’ingénierie tissulaire du cartilage (culture in vitro) bien que la physique employée puisse s’appliquer à d’autres domaines. Après un rappel du modèle macroscopique de dispersion réactive obtenu en employant la prise de moyenne volumique, les problèmes de fermeture sont résolus numériquement afin de déterminer la macro-dispersion. Les solutions numériques sont tout d’abord validées dans des cas sans advection et/ou sans réaction. L’étude de la dispersion passive (sans réaction) sur des micro-géométries simples illustre la dépendance des coefficients de dispersion macroscopiques vis-à-vis de la géométrie (porosité, croissance directionnelle ou homothétique). Enfin, la simulation du cas complet (incluant la réaction) nous a permis de montrer l’influence de plusieurs paramètres : nombre cinétique, nombre de Sherwood, structure géométrique microscopique. / Abstract

L'objectif est d'élaborer un nouveau procédé de fabrication de mousses métalliques par voie de fonderie en modélisant l'infiltration et la solidification d'un métal liquide dans un milieu poreux. La modélisation est faite en deux étapes.Tout d'abord, à l'échelle locale un brin de la mousse métallique est considéré comme un tube capillaire et l'infiltration et solidification d'un métal liquide dans un moule cylindrique est étudiée. Deuxièmement,le modèle macroscopique de la solidification diffusive d'un métal liquide dans un milieu poreux est obtenu par prise de moyenne volumique. Le modèle local est codée dans un outil CFD opensource et trois études paramétriques ont été faites permettant la détermination des relations de la longueur et le temps d'infiltration en fonction de paramètres de fonctionnement. La modélisation de la solidification d’un métal liquide dans un milieu poreux est simplifié en considérant que le moule est complètement saturé par un métal liquide au repos,par suite la solidification se produit par diffusion pure (pas de convection). L'équilibre thermique local (LTE) est considéré entre les phases solide et liquide du métal tandis qu'un non équilibre thermique local (LTNE) est retenue entre la phase métallique et le moule. Les problèmes de fermeture associés ainsi que le problème macroscopique ont été résolus numériquement. / The objective of this work is to elaborate a new manufacturing process of metal foams via casting by modelling the infiltration and solidification of liquid metal inside a porous medium.However, due to the complexity of this problem the study is divided into two steps. First, at local scale one strut of the metal foam is considered as a capillary tube and the infiltration and solidification of liquid metal inside a cylindrical mould is studied. Second, a macroscopic model of diffusive solidification is derived using the volume average method. The local model is coded in an open source CFD tool and three parametric studies were done where the relations between the infiltration length and time as function of the operating parameters are determined. The modelling of the solidification of liquid metal inside a porous medium is simplified by considering that the mould is fully saturated by liquid metal at rest, solidification occurs by pure diffusion. Local thermal equilibrium (LTE) is considered between the solid and liquid phases of the metal while local thermal non equilibrium (LTNE) is retained between the metallic mixture and the mould. The associated closure problems as well as the macroscopic problem were numerically solved.

La pyrolyse est la décomposition thermochimique de la biomasse en gaz de synthèse valorisables en biocarburants. Cette technologie, propre et renouvelable, nécessite aujourd’hui des efforts de recherche et de développement afin de prouver sa compétitivité par rapport aux autres sources d’énergie. L’objectif de cette thèse est de développer un modèle macroscopique de la pyrolyse en utilisant la méthode de prise de moyenne volumique. Le modèle sera ensuite utilisé pour faire des études numériques afin de caractériser le procédé et améliorer les performances des réacteurs. Une approche en deux temps a été établie afin d’atteindre notre objectif. D’abord, des modèles macroscopiques d’écoulements à masse volumique variable en milieu poreux ont été développés. Ce type d’écoulements est similaire à celui mis en jeu en pyrolyse pour deux deux raisons: la masse volumique varie sous l’effet de gradients forts de température et le réacteur de pyrolyse peut être considéré comme un milieu poreux à double porosité (porosité à l’échelle du lit et porosité à l’échelle de la particule). Les résultats théoriques ont montré que les équations de conservation macroscopiques (continuité, quantité de mouvement et énergie) et les propriétés effectives (masse volumique, perméabilité et diffusivité thermique) font apparaitre de nouveaux termes résultants de la variation de densité. La forme explicite de ces termes a été établie et validée par simulations numériques. Les résultats obtenus ont été utilisés dans un deuxième temps afin de développer un modèle macroscopique de la pyrolyse. / Pyrolysis is a thermo-chemical conversion of biomass into bio-fuels. This technology has not been fully developed and its competitiveness against other sources of energy is yet to be proven. The aim of this work is to derive a macroscopic model of pyrolysis by means of volume averaging method. The obtained macroscopic model can then be used to conduct fast and low-cost numerical simulations to characterize the process and improve the reactor efficiency. To achieve our objective, a two-steps methodology has been established. First, the fundamental problem of variable density flow in porous media has been investigated. The physical phenomena in this kind of problem are very similar to those involved in pyrolysis for two reasons: the fluid density varies due to high temperature gradients and the pyrolysis reactor can be considered as a double porosity medium (porosity at the reactor scale and porosity at the biomass particle scale). The obtained macroscopic conservation equations (continuity, momentum and energy) and the effective properties (density, permeability and thermal diffusivity) contain additional terms resulting from the fluid density variation. The explicit form of these terms has been established and their components have been computed. The resulting models of the first step have then been used to develop a macroscopic model of the pyrolysis in the second part of our study.

Supercritical fluid extraction has been used to recover biomaterials from natural matrices. Mathematical modeling of the extraction is required for process design and scale up. Existing models in literature are correlative and dependent upon the experimental data. Construction of predictive models giving reliable results in the lack of experimental data is precious. The long term objective of this study was to construct a predictive mass transfer model, representing supercritical fluid extraction of biomaterials in packed beds by the method of volume averaging. In order to develop mass transfer equations in terms of volume averaged variables, velocity and velocity deviation fields, closure variables were solved for a specific case and the coefficients of volume averaged mass transfer equation for the specific case were computed using one and two-dimensional geometries via analytical and numerical solutions, respectively. Spectral Element method with Domain Decomposition technique, Preconditioned Conjugate Gradient algorithm and Uzawa method were used for the numerical solution. The coefficients of convective term with additional terms of volume averaged mass transfer equation were similar to superficial velocity. The coefficients of dispersion term were close to diffusivity of oil in supercritical carbon dioxide. The coefficients of interphase mass transfer term were overestimated in both geometries. Modifications in boundary conditions, change in geometry of particles and use of three-dimensional computations would improve the value of the coefficient of interphase mass transfer term.

La contamination des ressources en eaux souterraines par une phase organique non miscible à l'eau couramment appelée NAPL (Non Aqueous Phase Liquid) constitue aujourd'hui un défi scientifique majeur compte tenu de la durée de vie d'un tel polluant. Bien que l'activité bactérienne (généralement présente sous forme de biofilm) joue un rôle crucial dans le devenir à long terme de ces effluents, peu d'études existent à l'heure actuelle sur son impact dans des conditions multiphasiques (i.e., à proximité de la source). En effet, dans la zone saturée, sous l'action des forces capillaires, le NAPL se retrouve souvent piégé, en effet, sous forme de «gouttelettes» au niveau des pores. Ce comportement spécifique au polluant modifie la dynamique du système biofilm/milieu poreux saturé et d'importantes questions restent encore ouvertes : accessibilité du polluant, modification de la tension interfaciale, production de biosurfactant, effet de toxicité (inhibition de la croissance bactérienne). Pour tenter de répondre à ces questions, nous avons adopté une approche aussi bien théorique qu'expérimentale. L'approche théorique porte sur le développement d'un modèle macroscopique décrivant le transport multiphasique en milieu poreux pour un système eau/NAPL/biofilm. Elle repose sur la méthode de prise de moyenne volumique, appliqué aux équations décrivant le couplage écoulement/transport à l'échelle du pore, permettant d'effectuer le changement d'échelle et dériver un modèle à deux équations. Le modèle est établit sous les hypothèses d'équilibre de masse local à l'interface fluide/biofilm et les contraintes associées à ces hypothèses ont étés définies. L'influence des caractéristiques microscopiques (arrangement des grains, fraction volumique du biofilm, distribution des blobs de NAPL, mouillabilité) sur les propriétés effectives du milieu (coefficient de dispersion, coefficient d'échange de masse) est discutée au travers des résultats issus des simulations. Ensuite, le modèle macroscopique a été comparé avec succès à la simulation numérique direct à l'échelle du pore pour la géométrie 2D complexe considérée. Quant à l'approche expérimentale, elle consiste à étudier le transport et la biodégradation du toluène en présence des bactéries Pseudomonas Putida F1 à l'aide d'un milieu poreux transparent 2D (micromodèle). Premièrement, nous avons étudié la dissolution du toluène résiduel sans bactéries et des courbes de dissolution du toluène ont été obtenues. Les résultats de dissolution du toluène en condition abiotique ont été comparés avec succès aux résultats du modèle théorique. Ensuite, l'étude expérimentale en micromodèle a porté sur la dissolution du toluène en condition biotique. Les résultats de ces études (courbes de dissolution et évolution de la saturation résiduelle) ont montré un impact significatif de la présence des bactéries sur les processus de dissolution par comparaison au cas abiotique. / Contamination of groundwater resources by an immiscible organic phase commonly called NAPL (Non Aqueous Phase Liquid) represents a major scientific challenge considering the residence time of such a pollutant. Although bacterial activity (usually in the form of biofilm) plays a crucial role in the long term fate of these effluents, very few works are focused on the study of such processes in multiphase conditions (oil/water/biofilm systems). The NAPL often gets trapped, in fact, under the action of capillary forces in the saturated zone in the form of «droplets» within the pores. This specific pollutant behavior changes the dynamics of biofilm /saturated porous medium system where important questions remain open: accessibility of the pollutant, changes in interfacial tension, biosurfactant production, toxicity effect (inhibition of bacterial growth). Modeling the transport of chemical species in the presence of bacteria is an extremely complex issue in terms of scale. We will use an experimental and theoretical approach to address these questions. In this thesis, we developed a macroscopic model describing multiphase transport in porous media for a water/NAPL/biofilm system. A volume averaging method has been applied here to the equations at the pore scale to make the upscaling and derive the model. This two-equation model is established under the assumptions of local mass equilibrium at the fluid/biofilm interface and the constraints associated with these assumptions were defined. The effect of microscopic features (arrangement of grains, volume fraction of the biofilm, distribution of NAPL blobs, wettability) on the effective properties of the media (dispersion coefficient, mass exchange coefficient) is discussed through some results from simulations. Subsequently, the macroscopic model has been successfully compared with the direct numerical simulation at pore scale for a 2D complex geometry. The experimental approach consists of studying transport and biodegradation of toluene in the presence of bacteria Pseudomonas Putida F1 using a flowcell. First, we studied the dissolution of toluene in abiotic conditions and toluene dissolution curves were obtained. The results of toluene dissolution in abiotic conditions were compared with success the results of the theoretical model. Finally, an experimental study in flowcell on the dissolution of toluene under biotic conditions was performed. The results of these studies (dissolution curve and evolution of toluene saturation) showed a significant impact of the presence of bacteria on the dissolution process compared to the abiotic case.

We study the turbulent flow of a fluid over a canopy, that we model as a deformable porous medium. This porous medium is more precisely a carpet of fibres that bend under the hydrodynamic load, hence initiating a fluid-structure coupling at the scale of a fibre's height (honami). The objective of the thesis is to develop a macroscopic model of this fluid-structure interaction in order to perform numerical simulations of this process. The volume averaging method is implemented to describe the large scales of the flow and their interaction with the deformable porous medium. An hybrid approach is followed due to the non-local nature of the solid phase; While the large scales of the flow are described within an Eulerian frame by applying the method of volume averaging, a Lagrangian approach is proposed to describe the ensemble of fibres. The interface between the free-flow and the porous medium is handle with a One-Domain- Approach, which we justify with the theoretical development of a mass- and momentum- balance at the fluid/porous interface. This hybrid model is then implemented in a parallel code written in C$++$, based on a fluid- solver available from the \openfoam CFD toolbox. Some preliminary results show the ability of this approach to simulate a honami within a reasonable computational cost. Prior to implementing a macroscopic model, insight into the small-scale is required. Two specific aspects of the small-scale are therefore studied in details; The first development deals with the inertial deviation from Darcy's law. A geometrical parameter is proposed to describe the effect of inertia on Darcy's law, depending on the shape of the microstructure of the porous medium. This topological parameter is shown to efficiently characterize inertia effects on a diversity of tested microstructures. An asymptotic filtration law is then derived from the closure problem arising from the volume averaging method, proposing a new framework to understand the relationship between the effect of inertia on the macroscopic fluid-solid force and the topology of the microstructure of the porous medium. A second research axis is then investigated. As we deal with a deformable porous medium, we study the effect of the pore-scale fluid-structure interaction on the filtration law as the flow within the pores is unsteady, inducing time-dependent fluidstresses on the solid- phase. For that purpose, we implement pore-scale numerical simulations of unsteady flows within deformable pores, focusing for this preliminary study on a model porous medium. Owing to the large displacements of the solid phase, an immersed boundary approach is implemented. Two different numerical methods are compared to apply the no-slip condition at the fluid-solid interface: a diffuse interface approach and a sharp interface approach. The objective is to find the proper method to afford acceptable computational time and a good reliability of the results. The comparison allows a cross-validation of the numerical results, as the two methods compare well for our cases. This numerical campaign shows that the pore-scale deformation has a significant impact on the pressure drop at the macroscopic scale. Some fundamental issues are then discussed, such as the size of a representative computational domain or the form of macroscopic equations to describe the momentum transport within a soft deformable porous medium.

L’utilisation des matériaux à faibles impacts environnementaux devient essentielle dans le secteur du bâtiment à cause de sa forte consommation d’énergie et de ressources naturelles. Cette thèse porte sur les isolants bio-sourcés et spécialement les laines de chanvres possédant des propriétés thermiques et hydriques intéressantes. La laine de chanvre, étant composée essentiellement de fibres végétales, constitue un matériau fibreux anisotrope et fortement poreux, et possède à l’échelle microscopique une structure complexe et aléatoire. D’où l’intérêt de décrire précisément la morphologie de ce type de laine et de caractériser sa structure par analyse d’images tomographiques à rayons X et des images MEB. Puis nous avons mis en place un modèle macroscopique couplé de transfert de chaleur et de masse, permettant de comprendre le comportement thermohydrique de ces laines en utilisant la méthode de changement d’échelle par prise de moyenne. Pour prendre en compte la complexité géométrique de la microstructure nous avons eu recours à un double changement d’échelle. / The use of low environmental impact materials becomes essential in the construction industry due to its high consumption of energy and natural resources. In this thesis it was focused on the bio-based and especially wool hemp insulation with interesting thermal and water properties. Hemp wool, being composed substantially of plant fibers, is an anisotropic, fibrous and highly porous material. At the microscopic level it possesses a complex and random structure, hence the interest of an accurate description to the morphology of this type of wool and to characterize its structure analysis by X-ray tomographic images and SEM images. Then a macroscopic model of coupled heat transfer and mass transport is set up to understand the behavior of these wools using the scaling method average gain. To take into account the geometric complexity of the microstructure a double change of scale was used.