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.

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.

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.

Des panaches sont connus pour migrer à travers le manteau ductile et quasi-Newtonien ; alors que les dikes se fracturent et se propagent dans la lithosphère solide. Cependant, la lithosphère est en fait visco-élastique. Afin de déterminer ce qui se passe dans ce cas complexe, nous avons réalisé une étude expérimentale et numérique sur le développement de panaches thermiques dans des solutions aqueuses de Carbopol, un gel de polymères formant un réseau continu d'éponges microscopiques. Ce fluide est rhéofluidifiant et présente un seuil de contrainte σ₀, de sorte que l'écoulement ne se produit que si la contrainte locale dépasse cette valeur critique σ₀. En dessous de cette valeur, le fluide agit comme un solide élastique. Les propriétés rhéologiques des solutions peuvent être systématiquement ajustées en variant la concentration de Carbopol. Le dispositif consiste en une source locale de chaleur de puissance constante placée au centre d'une cuve cubique. Selon la valeur du rapport entre la contrainte d'origine thermique et la contrainte seuil, Y₀, on peut observer trois régimes différents. A faible Y₀<Yc₁, aucun mouvement n'est détecté ; tandis que pour Yc₁<Y₀<Yc₂ une cellule se développe, puis évolue vers un panache pour Y₀>Yc₂. Nous montrons que les paramètres critiques (Yc₁,Yc₂) dépendent fortement de la géométrie du chauffage. Des mesures simultanées de température et de champs de vitesse montrent que la morphologie du panache ressemble à un doigt, contrairement à la forme de champignon rencontrée dans les fluides newtoniens. Utilisant des simulations numériques avec une description purement visqueuse, où la rhéologie du fluide est décrite par un modèle de Herschel-Bulkley régularisé, sont suffisantes pour rendre compte de la dynamique du panache. Une étude détaillée des paramètres indiquent que la dynamique du panache est gouvernée par la compétition entre la contrainte seuil, la contrainte induite par la flottabilité et les contraintes visqueuses. Nous avons identifié deux paramètres adimensionnés : le paramètre seuil Ψ comparant la contrainte induite par la flottabilité et la contrainte seuil, et le nombre de Bingham Bi comparant la contrainte seuil et les contraintes visqueuses. Un panache ne peut s'élever que si les deux paramètres sont supercritiques, i.e. la contrainte induite par la flottabilité et les contraintes visqueuses sont plus importantes que la contrainte seuil. Par conséquent, le panache peut s'arrêter avant d'atteindre la surface. Des lois d'échelles dans le conduit du panache ont été déterminées pour la vitesse, la température et la taille de la région cisaillée en régime permanent. Elles décrivent raisonnablement le comportement du conduit bien que seul l'effet rhéofluidifiant soit pris en compte. L'application de ces paramètres adimensionnés à la Terre contraignent significativement la limite de plasticité du manteau et de la lithosphère. La contrainte seuil maximale qui permet à une instabilité thermique de pénétrer dans la lithosphère ou le manteau supérieur est entre 100 kPa et 100 MPa, et elle dépend fortement de la taille et de l'anomalie de densité de l'intrusion. / Plumes are known to migrate through the ductile quasi-Newtonian mantle, while dikes fracture and propagate through the solid lithosphere. However, depending on the timescale, the lithosphere presents solid as well as viscous properties. To determine what happens in the complex case, where instabilities propagate through a visco-elastic matrix, we performed a combined study of laboratory experiments and numerical simulations. Here we investigate the development of thermal plumes in aqueous solutions of Carbopol, a polymer gel, forming a continuous network of micrometric sponges. This fluid is shear thinning and has a yield-stress σ₀, whereby flow occurs only if the local stress exceeds this critical value σ₀. Below this value, the fluid acts as an elastic solid. The rheological properties of the solutions can be systematically varied by varying the Carbopol concentration. The setup consists of a localized heat-source operated at constant power, placed at the centre of a square tank. Depending on the ratio of the thermally induced stresses and the yield stress, Y₀, three different regimes may be obtained. For low Y₀<Yc₁ no motion occurs, whereas for Yc₁<Y₀<Yc₂ a cell develops, that evolves into a plume for Y₀>Yc₂. We show that the critical parameters (Yc₁,Yc₂) strongly depend on the geometry of the heating. Combined temperature and velocity field measurements show that the morphology of the plume resembles a finger, contrary to the mushroom-like shape encountered in Newtonian fluids. Numerical simulations using a purely viscous description, where the rheology of the fluid is described by a regularized Herschel-Bulkley model, are sufficient to capture the plume dynamics. A detailed parametric study shows that the plume dynamics are governed by the interplay between yield stress, buoyancy induced stress and viscous stresses. We identify two non-dimensional parameters: the yield parameter Ψ comparing the buoyancy induced stress to the yield stress, and the Bingham number Bi comparing the yield stress to the viscous stresses. We show that a plume can rise only if both parameters are supercritical, i.e. if buoyancy induced stress and viscous stresses each overcome the yield stress. Therefore the plume may come to a halt before it reaches the surface. We propose scaling laws for the plume stem velocity, temperature and the size of the shear zone in the steady state. We show that the scaling laws describe the behaviour in the plume stem reasonably well, if the yield stress is neglected and only the shear thinning behaviour is taken into account. Applying the non-dimensional parameters to Earth places severe constraints on the strength of mantle and lithosphere. The maximum strength that allows for thermal instabilities to penetrate the lithosphere or upper mantle is in between 100 kPa and 100 MPa, and strongly depends on the size and buoyancy of the anomaly.