Orientador: Geraldo de Freitas Maciel / Banca: Edson Del Rio Vieira / Banca: Jefferson B. Libardi Liborio / Resumo: Esta dissertação de mestrado traz à discussão o comportamento reológico de misturas formadas por água+colóides+detritos (areia fina), visando entender e esclarecer os processos físicos e mecânicos, tais como sedimentação e ressuspensão de materiais inertes no seio da massa fluida não-newtoniana (água+colóides), bem como verificar a validade ou adeqüabilidade do modelo reológico de Herschel-Bulkley (modelo previamente investigado e validado para misturas compostas de água+colóides) para misturas viscoplásticas com presença de grãos. A variação das propriedades reológicas das misturas, em função das características físicas dos grãos (diâmetro, massa específica e área superficial), é investigada, e um modelo de estimativa de tensão crítica é apresentado. Ademais foram realizados ensaios preliminares de escoamento de fluidos hiperconcentrados em canais inclinados, na tentativa de calibrar uma lei de atrito. Dentro dessas perspectivas, a dissertação é composta de 6 Capítulos com um denso Estado da Arte que descreve os fenômenos e mecanismos que regem os escoamentos desse tipo de compósito. Com base na literatura estudada e, a partir da análise dos resultados experimentais, pôde-se concluir que, para misturas compostas de água+colóides+detritos, o comportamento reológico das misturas é o mesmo que aquele do fluido intersticial (água+colóides), desde que a homogeneidade da mistura seja garantida (não ocorrência de sedimentação e ressuspensão sucessivas). Neste caso, o modelo reológico de Herschel-Bulkley continua sendo válido para explicar as curvas de escoamento ou de fluxo das misturas viscoplásticas com grãos. Para misturas que apresentem os fenômenos de sedimentação e ressuspensão, o modelo de Bagnold, adaptado a fluidos hiperconcentrados... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This work retakes the discussion about the rheological behavior of mixtures composed by water+ kaolinitic clay+fine sand in order to investigate the physical and mechanical processes such as sedimentation and suspension of inert materials into the non-Newtonian or interstitial fluid (water+colloids), as well as verify the adaptability of the Herschel-Bulkley rheological model (model previously investigated and validated for composed mixtures of water+ kaolinitic clay) for explain the viscoplastic+coarse materials rheological properties. The variation of the rheological properties of the mixtures in function of the coarse material characteristics (diameter, specific mass and superficial area) was investigated and a model predicting yield stress was proposed. Furthermore, some tests were performed in an inclined canal to determine a friction law for this kind of fluids. Inside of these perspectives, this dissertation is composed of 6 Chapters whit a dense State of the Art describing the phenomena and their mechanisms were pointed up. Based on literature and from the experimental results, one could concluded that the viscoplastic + coarse material mixtures behavior is the same of the interstitial fluid one, since that the homogeneity of the mixture is guaranteed (not occurrence of successive sedimentation and resuspension). In this case, Herschel-Bulkley rheological model is still valid to explain the curves of flow of the viscoplastic + coarse material. For mixtures that present the phenomena of sedimentation and resuspension, Bagnoldþs model, adapted to the hyperconcentrated fluids, describes well the variations of rheological parameters in function of the shear rates applied. Finally, it could be concluded that the experiments of free surface in canals, despite partial, can... (Complete abstract click electronic access below) / Mestre

O estudo de escoamentos de fluidos não-Newtonianos através de expansões desperta um grande interesse em pesquisadores nas diversas áreas da engenharia, devido a sua ampla aplicação em indústrias e no meio acadêmico. O objetivo principal desta Dissertação é simular problemas de escoamentos envolvendo fluidos viscoplásticos através de expansões axissimétricas abruptas. O modelo mecânico empregado é baseado nas equações de conservação de massa e de momentum para escoamentos isocóricos acoplados com a equação constitutiva de um Fluido Newtoniano Generalizada (GNL), com a função de viscosidade de Herschel-Bulkley regularizada pela equação de Papanastasiou. O modelo mecânico é aproximado por um modelo estabilizado de elementos finitos, denominado método Galerkin Mínimos-Quadrados, ou Galerkin Least-squares (GLS). Esse método (GLS) é usado a fim superar as dificuldades numéricas do modelo de Galerkin clássico: a condição de Babuška-Brezzi e a instabilidade inerente em regiões advectivas do escoamento. O método é construído adicionando termos de malha-dependentes a fim aumentar a estabilidade da formulação de Galerkin clássica sem danificar sua consistência. A formulação GLS é aplicada para estudar a influência do índice power-law, da tensão limite de cisalhamento e razão de aspecto na dinâmica do escoamento de fluidos de Herschel-Bulkley através de expansões axissimétricas abruptas de razão de aspecto 1:2 e 1:4. Os problemas que envolvem números de Reynolds desprezíveis, para uma escala do número de Herschel-Bulkley entre 0 e 100 e índice de comportamento entre 0,2 e 1,0 são apresentados. Os resultados são fisicamente detalhados e estão de acordo com a literatura. / The study of non-Newtonian fluid flows in expansions is of great interest for researchers in the several branches of engineering, due to their wide application both in industry and academy. The objective of this Dissertation is to simulate flow problems involving a viscoplastic fluid through an axisymmetric abrupt expansion. The mechanical model employed is based on the mass and momentum conservative equations for isochoric flows coupled with the Generalized Newtonian Liquid (GNL) constitutive equation, with the Papanastasiou-regularized Herschel-Bulkley viscosity function. The mechanical model is approximated by a stabilized finite element scheme, namely the Galerkin Least-squares method. This method (GLS) is used in order to overcome the numerical difficulties of the classical Galerkin method: the Babuška- Brezzi condition and the inherent instability in advective flow regions. The method is built adding mesh-dependent terms in order to increase the stability of the classical Galerkin formulation without damaging its consistency. The GLS formulation is applied to study the influence of power-law index, yield stress and aspect reason in the flow dynamics of Herschel- Bulkley fluids through an axisymmetric abrupt expansions of aspect reason 1:2 and 1:4. Problems involving negligible Reynolds numbers, for a Herschel-Bulkley number range between 0 and 100 and e power-law index range between 0.2 and 1.0 are presented. The results are physically comprehensive and are in accordance with the literature.

A grande maioria dos fluidos encontrados na natureza se comportam como fluidos não- Newtonianos o que torna o seu estudo muito importante para diversas áreas da engenharia. Este trabalho tem como objetivo simular o problema específico de escoamentos de fluidos viscoplásticos em expansões abruptas planares com razão de aspecto de 1:4. O problema em questão se mostra interessante pois em muitos sistemas industriais são apresentados a geometria proposta para estudo associada a fluidos viscoplásticos. Foi empregado o modelo mecânico multi-campos (mult-field) baseado nas equações de conservação de massa e balanço de momentum para escoamentos isocóricos acoplados com a equação constitutiva de um Fluido Newtoniano Generalizada (GNL), associada à função de viscosidade de Herschel-Bulkley regularizada através da equação de Papanastasiou. O modelo mecânico é aproximado por um modelo estabilizado de elementos finitos, denominado método Galerkin Mínimos-Quadrados (GLS). A fim de se pesquisar os fenômenos reológicos ali presentes é feito o estudo da influência do índice de power-law na topologia de um escoamento creeping flow (Re@0) para uma vasta faixa de números de Herschel-Bulkley variando entre 0.1 e 100. Os resultados mostraram-se satisfátorios, apresentando uma forte influencia do número de Herschel-Bulkley e do índice de power law na topologia e na dinâmica do escoamento. Obteve-se uma validação do trabalho comparando-se os resultados obtidos nesta dissertação com os obtidos em artigo de grande credibilidade e aceito por toda a academia científica. / The majority of fluids found in nature behave like non-Newtonian fluids what makes their study of great importance to various areas of engineering. The present work aims to simulate the specific problem of the viscoplastic fluids flows through in planar abrupt expansion with the aspect ratio of 1:4. The problem in question is interesting because in many industrial systems are the proposal to study geometry associated with viscoplastic fluid. It employed the multi-field mechanical model based on equations of conservation of mass and momentum balance for the isochoric flow coupled with the constitutive equation of the Generalized Newtonian Liquids (GNL), associated with the function of viscosity of Herschel-Bulkley regularized by the equation of Papanastasiou. The mechanical model is approximated by a stabilized finite element model, called Galerkin Least-Squares method (GLS). In order to research the rheological phenomena present is done studying the influence of power-law index in the topology of the creeping flow (Re@0) for a wide range of numbers of Herschel-Bulkley ranging between 0.1 and 100. The results have proved satisfactory, showing a strong influence on the number of Herschel-Bulkley and power law index of the topology and dynamics of the flow. Got to be a validation of the work comparing the results with those obtained in this thesis in an article of great credibility and accepted throughout the scientific academy.

[pt] O escoamento de bolhas de gás em fluidos não-newtonianos é muito importante em diversas aplicações, tais como biorreatores, processamento de alimentos e operações de perfuração e cimentação de poços de petróleo, contudo poucos estudos abordam este tema. No presente trabalho é analisado o escoamento ascendente de bolhas de gás em fluido viscoplástico, modelado aqui como fluido Herschel-Bulkley. Utilizou-se uma abordagem bidimensional, aproximada por placas paralela. O escoamento multifásico foi numericamente simulado fazendo uso do método de volumes finitos VOF (volume of fluid), o qual resolve as equações de conservação de massa e momento aclopado a uma equação para a fração volumétrica dos fluidos. A influência de fatores tais como tensão limite de escoamento, dimensão da bolha, número de bolhas e distância entre as bolhas escoando em um fluido viscoplástico foram investigadas. Os resultados indicaram que a tensão limite de escoamento tem grande impacto na velocidade de deslocamento da bolha. No caso de mais de uma bolha escoando foi também observado que o deslocamento de uma bolha altera a velocidade de ascenção das outras, fazendo com que elas se unam, e a medida em que a distância entre as bolhas aumenta a interferência é eliminada e as mesmas escoam como bolhas individuais. Além disso, foi verificado que, dependendo do tamanho da bolha escoando, a parede interfere na sua velocidade de ascenção. Por fim foi analisada a mudança no formato da bolha, podendo-se observar que em número de Reynolds menores a mesma apresenta um formato esférico e a medida em que este parâmetro aumenta, a bolha vai se deformando e adquire uma forma elipsoidal. Os resultados qualitativos do presente estudo numérico foram comparados com alguns trabalhos experimentais encontrados na literatura e corresponderam relativamente bem. / [en] The gas bubble displacement in non-Newtonian fluids is important in many applications, including bioreactors, food processing and drilling and cementing of oil wells however a few studies have investigated this issue. The motion of gas bubbles in a viscoplastic fluid, modeled as a Herschel-Bulkley fluid, is analysed in the present work. A bidimensional approach was used, approximated by parallel plates. The multiphase flow was numerically simulated using the finite volume technique VOF (volume of fluid), which solves the conservation equations of mass and momentum coupled to an equation for the volume fraction of the fluids. Is was investigated the influence of factors such as fluid yield stress, bubble size, number of bubbles rising in the viscoplastic fluid and also the distance between them. The results indicated that the yield stress has great impact on the bubble rising velocity. In the case of multiple bubbles flowing it was also observed that the displacement of one bubble influences the rising velocity of the others, causing them to join together. As the distance between the bubbles increase the interference is eliminated and the bubbles flow separately. Furthermore, it was found that there was an wall interference depending on the size of the bubble. Lastly, it was analysed the change in the shape of the bubble. It could be observed that for lower Reynolds number the bubbles presented an spherical shape and as this parameter increases it turns into an elipsoidal shape. The qualitative results of the present study agreed relatively well with experimental works found in the literature.

Orientador : Geraldo de Freitas Maciel. / Banca: Podalyro Amaral de Souza / Banca: Adriano Souza / Resumo: Em função da concentração de material sólido, misturas resultantes de argila e água conferem, via de regra, propriedades não-Newtonianas. Essa concentração passa a variar com a granulometria e a composição do mineral do sedimento, bem como com a qualidade da água. Algumas tentativas foram feitas na busca de melhor explicar a reologia e a dinâmica global dessas misturas nessa última década, notadamente no contexto de lavas torrenciais e misturas hiperconcentradas. Essa dissertação de mestrado tem por objetivo desenvolver uma caracterização reológica de misturas sólido-líquido (água+argila caulinítica e água+areia fina+argila caulinítica) com diferentes concentrações em volume (Cv) para as quais são determinadas, a partir de ensaios de reometria de precisão, as propriedades tais como a viscosidade aparente, tensão crítica de cisalhamento e curva de tensão de cisalhamento x taxa de deformação. Verificou-se, em condições controladas, a influência da temperatura, pH e concentração em volume (Cv) sobre a curva reológica dessas misturas, além de eventuais fenômenos de tixotropia e modo de preparo. O modelo reológico melhor ajustado para as argilas foi o de Herschel-Bulkley ( ( )n τ =τ c + k γ& ), onde: τ é a tensão de cisalhamento; τc é a tensão crítica (ou rigidez inicial); k é um termo de consistência (viscosidade aparente); n é o índice de escoamento; e dy γ& = du é a taxa de deformação. Obtém-se também, a partir de uma análise quantitativa global, leis de evolução dos diversos parâmetros reológicos em função da concentração em volume. Após a etapa de caracterização física e reológica das misturas, realizaram-se, sob condições controladas, ensaios dinâmicos através de escoamentos de lamas em canal inclinado. Nesses ensaios foram medidos os parâmetros lâmina normal, vazões... (Resumo completo, clicar acesso eletrônico abaixo). / According to solid concentration material, clay-water mixture can exhibit non- Newtonian properties. Mixture concentrations vary with the grain size distribution and the composition of the mineral sediment, as well as, with the water quality. In the last decade some attempts were realized to explain the rheology and the global dynamics of those mixtures, mainly in the context of mudflows and high mud concentrated suspensions. The purpose of this work is develop a rheological characterization of solid-liquid mixture (water + clay kaolinitic and water + fine sand + clay kaolinitic) with different solid volume concentrations (Cv) for which are determined, using a R/S Rheometer (Brookfield), rheological properties such as the apparent viscosity, yield stress and shear stress x shear rate curve. It was verified, under controlled conditions, the influence of the temperature, pH and solid volume concentration (Cv) on the rheological curve those mixtures, besides eventual tixotropy phenomenon and way of prepare. The rheological model adjusted for the clays was Herschel-Bulkley ( ( )n τ =τ c + k γ& ), where: τ is shear stress; τc is yield stress; k is a consistency term (apparent viscosity); n is flow index; and dy γ& = du is shear rate. It is also obtained, from a global quantitative analysis, evolution laws of the several rheologics parameters in function of the solid volume concentration. After the stage of rheological and physical characterization of mixing samples, dynamics experiments were made, under controlled conditions, than the flow of mud was observed in the open channel. These analyses were made in order to examine the behavior of parameters such as: normal depth, discharge and velocities. In fact, the experience showed that is possible to deduce wall friction laws from the rheological proprieties based on high mud concentrated suspensions and the dynamic of these muds. / Mestre

Cette thèse présente une étude expérimentale visant à caractériser les propriétés hydrauliquesd'écoulements à surface libre de fluides complexes: fluides viscoplastiques et mélangesfluides viscoplastiques-grains. Ce travail est motivé par la nécessité d'améliorer lesconnaissances sur les propriétés des écoulements de laves torrentielles, dans un contexte deprotection contre les risques naturels en montagne. Nous avons développé un dispositif delaboratoire original, un canal à fond mobile, permettant de générer des coulées gravitaires quisont globalement stationnaires dans le référentiel du laboratoire. Les coulées présentent unfront très raide, suivi à l'amont d'une zone d'épaisseur uniforme. Les fluides viscoplastiquesutilisés (carbopol et kaolin) ont été choisis de manière à modéliser la matrice des couléesboueuses naturelles en prenant en compte les critères de similitude adaptés. Ces fluidessuivent une loi de comportement de Herschel-Bulkley, et leurs propriétés rhéologiques ont étédéterminées au moyen d'un rhéomètre de laboratoire en accordant un soin particulier àl'établissement des incertitudes associées. Nous présentons des mesures précises de l'évolutionde l'épaisseur des coulées dans la zone uniforme en fonction de la vitesse du fond du canal etde la pente. Ces résultats sont comparés à des prédictions théoriques correspondant à unécoulement permanent et uniforme d'un fluide de Herschel-Bulkley, et nous montrons quel'accord est satisfaisant moyennant les incertitudes sur les mesures rhéologiques. Nous avonségalement analysé la forme du front des coulées et, là-aussi, l'accord avec des modèleshydrauliques (modèles de type Saint-Venant) est bon. Ces deux études permettent de validerles prédictions hydrauliques obtenues à partir de lois de comportement mesurées aurhéomètre. Enfin, dans une dernière partie, nous présentons une étude préliminaire de ladynamique de particules rigides isolées placées au sein de la coulée, en nous intéressant auxvitesses longitudinales et aux vitesses de chute pour différentes tailles et différentes densitésde particules.

La convection de Rayleigh-Bénard est étudiée expérimentalement dans une cellule circulaire. Des fluides à seuil modèles (gels aqueux de Carbopol) sont mis en œuvre. Leurs comportements rhéologiques et leurs perméabilités en relation avec leurs microstructures ont été finement caractérisés. Dans toute la thèse, les expériences ont été menées sans glissement à la paroi. L'influence du seuil d'écoulement et de la distance entre plaques chaudes et froides sur les transferts thermiques a été approfondie. Trois mécanismes sont discutés pour expliquer le déclenchement de la convection: i) les propriétés visco-élastiques au-dessous du seuil, ii) le fluage au-dessous du seuil, iii) une approche d'un milieu poreux pour les gels de Carbopol considérés comme une suspension de micro-gels. On montre que le nombre de seuil Y, représentant le rapport entre la contrainte du seuil et la contrainte de la poussée d'Archimède est un paramètre important gouvernant l'apparition de l'instabilité. Les valeurs critiques de Y^(-1) sont déterminées entre 60 et 90. La visualisation à l'aide des cristaux liquides thermo-chromiques a permis une vue globale de la cinématique. Les structures observées dans les différents états thermiques montrent l'évolution de la convection. Une analyse qualitative du champ de température est également présentée. Enfin, la simulation numérique dans une cellule carré avec un modèle d'Herschel-Bulkley régularisé dans la gamme des nombres sans dimension utilisée dans les expérience a permis de mettre en évidence les paramètres critiques et la morphologie des champs thermiques et cinématique. Les ordres de grandeurs du nombre de seuil critique prédit se comparent raisonnablement avec les valeurs expérimentales. / In this thesis, three main mechanisms proposed in a recent paper (Darbouli et al., Physics of fluids, 25(2) 2013) have been discussed to explain the onset of Rayleigh Bénard Convection in a yield fluid (Carbopol gels): i) the elasto-visco-plasticity behavior of the material below the yield stress, ii) a viscosity at low values of shear rates by creep measurements below the yield stress, iii) a microscopic viewpoint considering the fluid as a porous two phases system. No-slip conditions have been achieved for all the experiments. The results with different Carbopol gels have proved the importance of Y, the yield number which presents the report of the yield stress and the buoyancy effect, as the governing parameter. The critical value of Y^(-1) with no-slip condition has been found between 60 and 90. A visualization measurement with the utilization of thermochromics liquid crystals presents a global view from above. Different structures have been observed in different states of thermal conditions, which describe the evolution of the convection. For several cases the color of the liquid crystals can indicate the temperature field in the whole experiment cell. Numerical simulations with a Herschel-Bulkley model have also been discussed in this thesis. The dimensionless parameters are defined approaching the values obtained in the experiments, so that we can compare the numerical results with some of experimental ones.

Orientador: Geraldo de Freitas Maciel / Banca: Sérgio Said Mansur / Banca: Jean Paul Vila / Resumo: Denominam-se problemas tipo rompimento de barreira os fenômenos nos quais um fluido é liberado de maneira abrupta. Quando o fluido apresenta natureza hiperconcentrada, a relação entre a tensão de cisalhamento e a taxa de deformação pode se tornar não-linear, passando a apresentar reologia não-Newtoniana. Problemas deste tipo podem ser encontrados em muitos fenômenos tanto na natureza quanto em processos industriais. O estudo de tal problema é, geralmente, conduzido usando simplificações, como a aproximação de águas rasas e a separação do escoamento em regimes dominantemente inerciais ou viscosos. O presente trabalho é composto de duas partes, uma experimental e outra, numérica. No campo experimental, duas soluções controladas são usadas: soluções aquosas de açúcar e de Carbopol 940, esta última com várias concentrações volumétricas. O aparato experimental consiste em um canal retangular de acrílico, contendo uma comporta, a montante da qual, o fluido é retido e, pela ruptura (levantamento da comporta), começa a escoar. O escoamento é estudado através de técnicas avançadas de filmagem. No campo numérico, são realizadas simulações usando o programa CFX, no qual é usado um método de rastreamento de interface, o VOF e sem o emprego das simplificações citadas. Os resultados experimentais são comparados com os numéricos e com resultados da literatura que usam tais simplificações. Na comparação a aproximação de águas rasas, apesar de descrever bem a forma da interface, se distancia dos valores reais da posição da frente de onda. / Abstract: The dam break problem describes a phenomenon in which there is an abrupt release of fluid. When the fluid is hiperconcentrated, the relation between the shear stress and the strain rate can become non-linear, and so present a non-Newtonian rheology. The non-Newtonian dam break problem may be found in many phenomena in nature and industrial process. The study of such a problem is, generally, conducted using simplified hypothesis such as the shallow water approximation and the separation of the flow in inertial and viscous dominated regimes. The present work is composed of two parts, one experimental and other, numerical. In the experimental field, two controlled solutions were used: water solutions of sugar and of Carbopol 940, the last one with a wide range of volume concentrations. These fluids have, respectively, Newtonian and non-Newtonian rheologies. The experimental setup consists of an acrylic rectangular channel, which has a dam and upstream of that the fluid is retained and, by the rupture, it begins to flow. The flow is studied by using advanced filming techniques. In the numerical field, simulations are conducted using the CFX software, which uses an interface tracking method, the VOF, and without the shallow water approximation and the division of the flow. So the experimental, numerical and literature results, that uses such simplifications, are compared and it is showed that the shallow water approximation, however describes very well the shape of the surface, is not accurate in calculate the wave front position. / Mestre

<p dir="ltr">Non-Newtonian fluid models such as the Bingham and Herschel-Bulkley models are used to characterize the flow behavior of many complex fluids and soft solids. The three parameter Herschel-Bulkley model captures the yield stress behavior and the nonlinear power law behavior. In this thesis, the semi-analytical solution of Herschel-Bulkley fluids provided by Covey and Stanmore is used to experimentally characterize the squeeze flow behavior. A ‘Squeeze Flow and Thermal Resistance Tester’ was custom designed to perform velocity controlled squeeze flow experiments. The tester has an additional capability of performing thermal resistance characterization adhering to the ASTM-D5470 standard. A novel framework is described for characterizing the three Herschel-Bulkley parameters (τy, n and ηHB) using the developed tester. </p><p dir="ltr">Thermal Interface Materials (TIMs) are used to efficiently dissipate heat from a heat generating component to a heat sink in an electronic package. Thermal grease is a type of TIM comprising of a base material (e.g. polymer) loaded with highly conducting filler particles (e.g, boron nitride, alumina or sometimes conducting metals such as aluminum or silver). These greases are expected to exhibit Herschel-Bulkley flow behavior. Hence, thermal greases are used as candidate materials for squeeze flow characterization. In addition to the flow characterization, the thermal resistance across these thermal greases are also characterized using the custom designed tester. Characterization of mechanical and thermal behavior of TIMs is crucial to predicting their long-term reliability. </p><p dir="ltr">The effect of in-situ isothermal baking duration and test temperature on flow behavior is studied. The increase in duration of isothermal baking at test temperature of 55◦C showed that the material tends to stiffen with baking duration. The increase in test temperature from 5◦C to 100◦C resulted in a decrease in the power law index n and viscosity ηHB. </p><p dir="ltr">Finally, a numerical simulation strategy for performing squeeze flow simulations is described. The characterized flow parameters from the squeeze flow experiments were used as input material parameters for a dynamic mesh-based numerical simulation of squeeze flow between parallel surfaces. The results of the experimental force response and numerical simulation results were compared and found to be in close agreement. In order to simulate flow of thermal greases in a package undergoing deformation, a non-flat test setup was fabricated and squeeze experiments were performed. Numerical simulations were subsequently performed for the non-flat surface using material parameters extracted from previous experiments and the results were compared. The results from both experiments and numerical simulations showed that the force response of thermal greases under non-flat surfaces was significantly higher than the planar case.</p>

Ette thèse traite d’écoulements de fluides à seuil (ou viscoplastiques) en milieu confiné. Les difficultés analytiques et numériques sont dues à la multivaluation du tenseur des contraintes dans les zones plastiques ainsi qu’à la non-différentiabilité du problème de minimisation associé. Cette thèse s’articule en deux parties.Dans un premier temps, des simulations numériques parallèles très précises à l’aide d’algorithmes de dualité ont été effectuées. Elles ont permis de retrouver des résultats observés expérimentalement dont l’existence d’une ligne de glissement pour l’écoulement au dessus d’un obstacle et le caractère quasi-Poiseuille de la vitesse au-delà de cette ligne. Par ailleurs, la théorie de couche limite viscoplastique définie par Oldroyd (1947, à nombre de Bingham asymptotiquement grand) a été revisitée à nombre de Bingham modéré en milieu confiné. L’étude a mis en œuvre des allers-retours entre ces simulations et les expériences physiques de Luu et al. d’IRSTEA ainsi qu’une dérivation théorique. L’approximation de couche limite est vérifiée dans une certaine mesure à l’intérieur de la cavité. Une adaptation de la notion de couche limite viscoplastique est alors exhibée et permet d’étendre les scalings dérivés par Oldroyd (1947) et Balmforth et al. (J. of Fluid Mech, 2017). Ces scalings sont aussi généralisés au cas de la loi d’Herschel-Bulkley. Dans un second temps, on présente une analyse asymptotique des champs de vitesses et de contraintes pour des écoulements en faible épaisseur (ε). Un développement à l’ordre ε2 de la vitesse permet de trouver une équation de Reynolds à la même précision. Cette équation de Reynolds prolonge les résultats déjà existants dans le cadre newtonien, d’une part et dans le cadre fluide à seuil avec une surface libre, d’autre part. / This thesis is devoted to the flow of yield stress (or viscoplastic) fluids in pipes.Analytical and numerical difficulties lie in the multivaluation of the stress tensor in the plastic regions and in the non-differentiability of the associated minimization problem. This manuscript is organized following two main axes.First, very accurate numerical simulations were carried out using duality methods and parallel multifrontal solvers. Thus, experimental observations were recovered, namely the existence of a slip line for the flow over an obstacle and the Poiseuille-like behaviour of the velocity above this line. Moreover, the viscoplastic boundary layer theory defined by Oldroyd (1947 at high Bingham numbers) was revisited at moderate Bingham numbers in confined areas. This study provided an opportunity to go back and forth between these simulations and the physical measures of Luu et al. from IRSTEA and to perform a theoretical derivation. The boundary layer approximation is valid up to a certain extent in the cavity. An adaptation of the viscoplastic boundary layer definition is then given and allows to generalize the scalings shown by Oldroyd (1947) and Balmforth et al. (JFM 2017). These scalings are also generalized to the Herschel-Bulkley case. Then, an asymptotic analysis of the velocity and stress fields for thin layer (ε) flows is presented. A velocity development up to ε2 lets us find a Reynolds equation of same accuracy. This Reynolds equation extends the already existing results, on the one hand in the newtonian case and on the second hand for free surface flows.