510 research outputs found

    Viscoplastic displacement flows in narrow channels

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    Les écoulements à déplacement se produisent fréquemment dans les applications naturelles et industrielles. Bien que les déplacements Newtoniens aient été pris en considération dans une grande variété d’études théoriques et expérimentales dans les dernières décennies, un nombre considérable de fluides pratiques présentent des caractéristiques viscoplastiques, rendant la prévision du comportement des écoulements plus difficile. Les écoulement de déplacement viscoplastiques sont généralement contrôlés par un équilibre entre diverses forces, y compris la force visqueuse, la force de flottabilité, la force d’inertie, contrainte d’écoulement, etc., en plus de caractéristiques miscibles et non miscibles. Une compétition entre ces forces peut conduire à des comportements imprévisibles et exotiques de déplacement. Permettant une compréhension approfondie de ces écoulements, dans cette thèse de doctorat nous avons étudié l’écoulement à déplacement d’un fluide viscoplastique par un fluide Newtonien dans une géométrie simple, c.-à-d. un canal étroit et confiné. Dans la première partie de cette thèse (chapitres 1 à 3), nous étudions expérimentalement les écoulements à déplacement non-miscibles d’un fluide viscoplastique par un fluide Newtonien. En particulier, nous analysons le mouvement d’air dans un gel de Carbopol, dans une cellule de Hele-Shaw de section rectangulaire. Cette géométrie est composée de deux plaques parallèles rigides. Nous étudions les résultats en termes d’efficacité de déplacement et de morphologie des modèles d’écoulement. Nous démontrons que les comportements complexes du gel Carbopol, c.-à-d. les fortes propriétés viscoplastiques et les faibles propriétés viscoélastiques, affectent les caractéristiques d’écoulement de déplacement. Ensuite, nous étendons cette étude au déplacement d’un gel de Carbopol par une huile de silicone afin de considérer les effets de la mouillabilité sur l’écoulement. Nous observons qu’une combinaison de comportements viscoplastiques et de mouillabilité exerce un impact significatif sur les modèles d’écoulement à déplacement, pour lesquels quatre régimes d’écoulement différents sont identifiés : un régime capillaire, un régime de contrainte d’écoulement, un régime visqueux et un régime élastoinertiel. Enfin, nous étudions les impacts du rapport d’aspect de la section transversale de la cellule sur les caractéristiques de déplacement viscoplastique. Dans la deuxième partie de cette thèse (chapitres 4 à 5), nous étudions numériquement les écoulements à déplacement miscibles d’un fluide viscoplastique par un fluide Newtonien dans un long canal plan 2D. Pour un déplacement «heavy-light», l’analyse des modèles d’écoulement en fonction de divers paramètres sans dimension nous permet d’identifier trois régimes d’écoulement distincts : déplacements «center-type»/«slump- type», «back flow»/«no-back flow» et déplacement «stable/instable». Nous décrivons les effets du rapport de viscosité des fluides, de la flottabilité, de la contrainte d’écoulement et de l’inclinaison du canal sur les régimes d’écoulement susmentionnés.Displacement flows frequently occur in natural and industrial applications. Although Newtonian displacements have been considered in a wide range of theoretical and experimental studies in the recent decades, a considerable number of practical fluids exhibit viscoplastic features, making it hard to predict the flow behaviors. Viscoplastic displacement flows are generally controlled by a balance between a variety of forces, including viscous, buoyant, inertial, yield stress, etc., in addition to miscible and immiscible features. A competition between these forces may lead to exotic, unpredictable displacement flow behaviors. To provide a deep understanding of these flows, in this Ph.D. thesis we investigate the displacement flow of a viscoplastic fluid by a Newtonian fluid in a simple flow geometry, i.e., a narrow confined channel. In the first part of this thesis (Chapters 1-3), we experimentally study immiscible displacement flows of a viscoplastic fluid by a Newtonian fluid. In particular, we analyze the invasion of air into a Carbopol gel in a rectangular cross-section Hele-Shaw cell. This flow geometry is composed of two rigid parallel plates with a small gap. We study the results in terms of the displacement efficiency and morphology of the flow patterns. We demonstrate that the complex behaviors of the Carbopol gel, i.e., strong viscoplastic properties and weak viscoelastic properties, affect the displacement flow features. We then extend this study to the displacement of a Carbopol gel by silicon oil in order to consider the effects of wettability on the flow. We observe that a combination of viscoplastic behaviors and wettability exerts a significant impact on the displacement flow patterns, for which four different flow regimes are identified a capillary regime, a yield stress regime, a viscous regime and an elasto-inertial regime. Finally, we investigate the impacts of the cell cross-section aspect ratio on viscoplastic displacement flow features. In the second part of this thesis (Chapters 4-5), we numerically study miscible displacement flows of a viscoplastic fluid by a Newtonian fluid in a long 2D plane channel. For a heavy-light displacement, analyzing the displacement flow patterns as a function of various dimensionless parameters allows us to identify three distinct flow regimes center/slump-type, back/no-backflow and stable/unstable displacements. We describe the effects of the viscosity ratio of fluids, buoyancy, yield stress and channel inclination on the aforementioned flow regimes

    Weakly nonlinear investigation of the Saffman-Taylor problem in a rectangular Hele-Shaw cell

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    We analyze the Saffman-Taylor viscous fingering problem in rectangular geometry. We investigate the onset of nonlinear effects and the basic symmetries of the mode coupling equations, highlighting the link between interface asymmetry and viscosity contrast. Symmetry breaking occurs through enhanced growth of sub-harmonic perturbations. Our results explain the absence of finger tip-splitting in the early flow stages, and saturation of growth rates compared with the predictions of linear stability.Comment: 42 pages, 5 figures, added references, minor changes, to appear in Int. J. Mod. Phys. B (1998

    Numerical study of Bingham flow in macrosopic two dimensional heterogenous porous media

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    The flow of non-Newtonian fluids is ubiquitous in many applications in the geological and industrial context. We focus here on yield stress fluids (YSF), i.e. a material that requires minimal stress to flow. We study numerically the flow of yield stress fluids in 2D porous media on a macroscopic scale in the presence of local heterogeneities. As with the microscopic problem, heterogeneities are of crucial importance because some regions will flow more easily than others. As a result, the flow is characterized by preferential flow paths with fractal features. These fractal properties are characterized by different scale exponents that will be determined and analyzed. One of the salient features of these results is that these exponents seem to be independent of the amplitude of heterogeneities for a log-normal distribution. In addition, these exponents appear to differ from those at the microscopic level, illustrating the fact that, although similar, the two scales are governed by different sets of equations

    Variational Methods and Planar Elliptic Growth

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    A nested family of growing or shrinking planar domains is called a Laplacian growth process if the normal velocity of each domain's boundary is proportional to the gradient of the domain's Green function with a fixed singularity on the interior. In this paper we review the Laplacian growth model and its key underlying assumptions, so that we may consider a generalization to so-called elliptic growth, wherein the Green function is replaced with that of a more general elliptic operator--this models, for example, inhomogeneities in the underlying plane. In this paper we continue the development of the underlying mathematics for elliptic growth, considering perturbations of the Green function due to those of the driving operator, deriving characterizations and examples of growth, developing a weak formulation of growth via balayage, and discussing of a couple of inverse problems in the spirit of Calder\'on. We conclude with a derivation of a more delicate, reregularized model for Hele-Shaw flow

    Mesoscale fluid simulation with the Lattice Boltzmann method

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    PhDThis thesis describes investigations of several complex fluid effects., including hydrodynamic spinodal decomposition, viscous instability. and self-assembly of a cubic surfactant phase, by simulating them with a lattice Boltzmann computational model. The introduction describes what is meant by the term "complex fluid", and why such fluids are both important and difficult to understand. A key feature of complex fluids is that their behaviour spans length and time scales. The lattice Boltzmann method is presented as a modelling technique which sits at a "mesoscale" level intermediate between coarse-grained and fine-grained detail, and which is therefore ideal for modelling certain classes of complex fluids. The following chapters describe simulations which have been performed using this technique, in two and three dimensions. Chapter 2 presents an investigation into the separation of a mixture of two fluids. This process is found to involve several physical mechanisms at different stages. The simulated behaviour is found to be in good agreement with existing theory, and a curious effect, due to multiple competing mechanisms, is observed, in agreement with experiments and other simulations. Chapter 3 describes an improvement to lattice Boltzmann models of Hele-Shaw flow, along with simulations which quantitatively demonstrate improvements in both accuracy and numerical stability. The Saffman-Taylor hydrodynamic instability is demonstrated using this model. Chapter 4 contains the details and results of the TeraGyroid experiment, which involved extremely large-scale simulations to investigate the dynamical behaviour of a self-assembling structure. The first finite- size-effect- free dynamical simulations of such a system are presented. It is found that several different mechanisms are responsible for the assembly; the existence of chiral domains is demonstrated, along with an examination of domain growth during self-assembly. Appendix A describes some aspects of the implementation of the lattice Boltzmann codes used in this thesis; appendix B describes some of the Grid computing techniques which were necessary for the simulations of chapter 4. Chapter 5 summarises the work, and makes suggestions for further research and improvement.Huntsman Corporation Queen Mary University Schlumberger Cambridge Researc

    Buoyant miscible displacement flows of Newtonian and non-Newtonian fluids : stationary and oscillating geometries

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    Cette thèse vise l’étude des écoulement de déplacement de fluides miscibles à l’intérieur d’un long tuyau stationnaire vertical et d’un tuyau en mouvement. Concernant la géométrie des mouvements, le tuyau oscille comme un pendule inversé avec une fréquence maximale faible, c’est-à-dire, ˆf= 0.2(Hz) et une oscillation maximale de faible amplitude, soit 15 (◦) par rapport à l’axe du tuyau. Les écoulement de déplacement se produisent à un nombre de Péclet élevé et aux petits nombres d’Atwood. L’accent est mis sur les types de fluides et de géométries (tuyau fixe ou en mouvement). Les approches expérimentales détaillées sont utilisées de manière intégrée. Dans cette thèse, la configuration de densité est la densité instable. La majeure partie des travaux en cours se concentre sur les écoulements de déplacement de fluides Newtoniens isovisqueux, mais nous étudions également l’écoulement de déplacement à contrainte au seuil de plasticité dans un long tuyau vertical. Pour un écoulement de déplacement Newtonien isovisqueux dans un tuyau stationnaire, nous remarquons un effet stabilisant imposé au débit principal et signalant l’existence de deux régimes d’écoulement principaux à long moment introduits par un écoulement de déplacement stable et un écoulement de déplacement instable. La transition entre ces deux régimes se produit à un nombre critique de Reynolds modifié (RetThis thesis aims to investigate buoyant displacement flows of miscible fluids in a long, vertical stationary pipe or a moving pipe. For the case of the moving geometry, the pipe oscillates like an inverted pendulum with a small maximum frequency, i.e.ˆf= 0.2(Hz) and a small maximum oscillation amplitude, i.e. 15 (◦) with respect to the pipe axis. The displacement flows occur at the high Péclet number and small Atwood numbers. The focus is on the type of fluids and geometries (stationary or moving pipe). Detailed experimental approaches are employed in an integrated fashion. The density configuration in this thesis is the density unstable. The main part of the current work is concentrated on displacement flows of iso-viscous Newtonian fluids. We also study the yield stress displacement flow in a long vertical pipe. For iso-viscous Newtonian displacement flow in a stationary pipe, we uncover the stabilizing effect of the mean imposed flow and report the existence of two main flow regimes at long times introduced as a stable displacement flow and an unstable displacement flow. The transition between these two regimes occurs at a critical modified Reynolds number (Re
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