This dissertation is devoted to the finite element (FE) approximation of equations describing the motion of a class of non-Newtonian fluids. The main focus is on incompressible fluids whose viscosity nonlinearly depends on the shear rate and pressure. The equations of motion are discretized with equal-order d-linear finite elements, which fail to satisfy the inf-sup stability condition. In this thesis a stabilization technique for the pressure-gradient is proposed that is based on the well-known local projection stabilization (LPS) method. If the viscosity solely depends on the shear rate, the well-posedness of the stabilized discrete systems is shown and a priori error estimates quantifying the convergence of the method are proven. In the shear thinning case, the derived error estimates provide optimal rates of convergence with respect to the regularity of the solution. As is well-known, the Galerkin FE method may suffer from instabilities resulting not only from lacking inf-sup stability but also from dominating convection. The proposed LPS approach is then extended in order to cope with both instability phenomena. Finally, shear-rate- and pressure-dependent viscosities are considered. The Galerkin discretization of the governing equations is analyzed and the convergence of discrete solutions is...

O estudo do comportamento reológico de fluidos não Newtonianos tem grande importância em diversas áreas da engenharia. O aumento na demanda destes fluidos por exemplo, no uso doméstico, pessoal e em processos químicos acarreta em dificuldades que vão desde o processo de sua mistura ao seu manuseio. Dentre os fluidos não Newtonianos estão os viscoelásticos, os quais exibem deformação aparente quando os níveis de tensões são inferiores ao limite de escoamento do material e, dentro desta classe, alguns ainda podem apresentam comportamento elástico quando submetidos à baixa taxa de cisalhamento. Juntamente com os efeitos elasto-viscoplásticos, os materiais podem apresentar comportamento tixotrópico, onde devido as tensões sua reestruturação não é instantânea. Na presente Tese, fez-se um estudo numérico a fim de analisar o problema especifico de escoamentos de fluidos elasto-viscoplásticos com comportamento tixotrópico em uma expansão planar abrupta na razão de aspecto 4 : 1. O modelo mecânico aplicado consiste de uma equação viscoelástica para o campo de tensões, uma evolutiva para o parâmetro de estrutura do material, bem como as equações de conservação de massa e momento. O modelo mecânico aplicado mostrou-se capaz de prever o comportamento tixotrópico. A aproximação numérica do modelo aplicado foi feita através do método estabilizado de elementos finitos, especificamente o método Galerkin Mínimos-Quadrados (GLS), o qual foi implementado no código de elementos finitos para fluidos não Newtonianos em desenvolvimento no Laboratório de Mecânica dos Fluidos Aplicada e Computacional (LAMAC) da Universidade Federal do Rio Grande do Sul. Os fenômenos reológicos presentes no problema foram analisados a partir da influência da cinemática do escoamento, da elasticidade e da tixotropia, no nível de estruturação do material, na posição e tamanho das regiões não escoadas e na deformação elástica do material. Os resultados mostraram-se satisfatórios, pois condizem com os apresentados na literatura, apontando a boa predição do modelo mecânico aplicado bem como a robustez de sua implementação computacional. / The rheological behavior of non-Newtonian uids study is of great then importance in many areas of engineering. The increase in demand of these uids - for example, domestic use, personal and processes chemical - causes di culties ranging from the process of mixing it to handling. Among the non-Newtonian uids are viscoelastic, which exhibit apparent deformation when stress levels are lower than the yield limit of the material and, within this class, some still have elastic behavior when subjected to low shear rates. Together with the elastic-viscoplastic e ects, materials may exhibit thixotropic behavior, ie, due the restructuring strain is not instantaneous. In this thesis was made a numerical study to simulate the speci c problem of ow of elastic-viscoplastic uids with thixotropic behavior in abrupt planar expansion { common geometry in industrial systems associated with elastic-viscoplastic uids, whose ratio the aspect is 4:1. The mechanical behavior of most of these structured materials, are highly non-Newtonian, with this, there is need to make them more pseudoplastic, causing undesirable behaviors such as thixotropic which is a phenomenon somewhat characterized and modeled in the literature. The mechanical model applied is able to predict thixotropic behavior and is composed of a viscoelastic equation for the stress eld and an evolutionary to the material structure parameter in addition to the mass and momentum conservation equations. This mechanical model is approximated by a stabilized nite element model, called the Galerkin method of least squares (GLS). In order to study the rheological phenomena present in the problem is analyzed the in uence of the ow kinematics, elasticity and thixotropy in the level of structure of the material, in position and size of unyielded regions and the elastic deformation of the material. The results were satisfactory, since the the study of intensity the U the results agree with those reported in the literature pointing to good prediction of the mechanical model applied well as the hardiness of their computational implementation.The results of the elasticity showed quite spectacular behavior of unyielded regions of the material since for high values of relaxation time, the unyielded region of channel larger has the form of " ngers"because of the high exibility of the material along the line of symmetry of the channel. The results of the analysis of the elastic deformation show, that model correctly dosing the elasticity in the unyielded regions. The thixotropic e ects reported a slower structuring of the material with increasing characteristic time, in response to strain change caused by the expansion, results indicate that for high values of relaxation time, higher the distance between the unyielded regions of smaller channel and larger.

[pt] Este trabalho descreve experimentos relacionamentos com o movimento relativo entre partículas sólidas e fluido não-newtoniano, confinados no interior de um duto circular. Medições da pressão dinâmica adicional, devida unicamente à presença da partícula (fonte de perturbação no escoamento) e do arrasto viscoso foram conduzidas de forma a se verificar a validade da Teoria de Brenner (1962). Esta teoria, já confirmada para fluidos newtonianos, permite que parâmetros característicos do escoamento perturbado sejam determinados, convenientemente, através de parâmetros do escoamento não-perturbado (ausência de partícula). Para o caso de fluido não-newtoniano, denominados puramente viscosos, do tipo Power-law, a teoria se mostrou perfeitamente aplicável. O valor da razão Delta P mais A/D descrito por Brenner foi confirmado com uma precisão de 3 por cento, num total de 70 experimentos realizados. Para fluidos não-newtonianos, viscoelásticos, com função viscosidade tipo Power-law, a validade da teoria parece, entretanto, depender de um parâmetro capaz de descrever na natureza constitutiva do fluido utilizado. Experimentos realizados com três diferentes fluidos viscoelásticos (expoentes power-law n igual 0,303; 0,343; 0,483) conduziram à identificação deste parâmetro, o Segundo Número Elástico, El2. Para valores de El2, inferiores a 14, caracterizando um escoamento predominantemente viscoso, o valor da razão Delta P mais A/D novamente é confirmado com precisão inferior a 4 por cento. Para valores de El2 superiores a 40 a razão Delta P mais A/D não mais pode ser avaliada com base em parâmetros do escoamento perturbado, analogamente ao que havia sido proposto por Brenner para o caso de fluidos newtonianos. Neste trabalho incluem-se também registros contínuos dos experimentos enfatizando os efeitos viscoelásticos envolvidos, bem como uma análise dos efeitos de parede associados ao movimento relativo entre fluidos não-newtonianos e partículas sólidas. Todos os experimentos foram realizados num regime de Reynolds variando de 0,1 a 90 e num regime de Weissenberg (calculando com base no modelo de Powell-Eyring) variando de 850 a 3800. / [en] This work describes experiments related to relative motion between solid particles and mon-newtonian fluid, inside a circular duct. Measurements of the aditional dynamic pressure, due to the presence of the particle (a source of disturbance in the flow) ando f the viscous drag, were conducted to verify the validity of Brenner’s Theory (1962). This theory, already confirmed for newtonian fluids, allows the determination of the characteristic parameters of the disturbed flow using parameters of non-disturbed flow (without particle). In the case of purely viscous non-newtonian fluids, of the power-law type, the theory was confirmed. The value of the ratio Delta P plus A/D, described by Brenner, was confirmed. The value an accuracy of 3 per cent, in a total of 70 experiments. For viscoelastic fluids, with Power-law viscosity function, it appears that the validity of the theory depends on the Second Elastic Number, El2. Experiments conducted with three different viscoelastic fluids (power-law exponents, n equal 0,303; 0,343 and 0,483) shows that for values of El2 bellow 14, which characterizes a predominantly viscous flow, the value of of the ratio Delta P plus A/D is agair confirmed, with na accuracy of 4 per cent. For values of the El2, parameter above 40, the ratio Delta P plus A/D cannot be determined using parameters of the non-disturbed flow, as proposed by Brenner for newtonian fluids. In this work are also included graphic registers of the experiment, showing the complex viscoelastic effects, as well as na analysis of the wall effects associated with the relative motion between non- newtonian fluid and solid particles. All the experiments were conducted with Reynolds number between 0,1 and 90 and a Weissenberg number (based in Powell-Eyring model) between 850 and 38.00.

Este trabalho tem como propósito investigar como a variação geométrica de determinados parâmetros envolvidos na construção de uma geometria bifurcada de seção circular, em forma de Y, afeta a resistência ao escoamento, tanto de fluidos newtonianos como não newtonianos. As geometrias estudadas foram construídas utilizando-se o princípio do Design Construtal. Os parâmetros variados foram a relação entre os comprimentos dos dutos pais e filhos, a relação entre os diâmetros dos mesmos dutos, e o ângulo central da estrutura em forma de Y. Para as relações geométricas lineares foram utilizados os valores de 0,5; 0,6; 0,7; 0,8; 0,9 e 1, enquanto para os ângulos, foram utilizados os valores de 155°, 135°, 115°, 95°, 75°, 45°, 25° e 10°. Os fluidos utilizados foram do tipo newtoniano e não newtoniano, dentre estes últimos, foram estudados fluidos pseudoplásticos e dilatantes. O trabalho foi realizado através de simulações numéricas, implementadas com a utilização do software comercial Ansys Fluent, o qual resolve as equações governantes através do método dos volumes finitos. As malhas utilizadas foram do tipo poliédrica. Os resultados indicam que há uma diferença em relação ao que se espera da literatura para as relações entre os diâmetros e os comprimentos. A Lei Hess-Murray indica que estas relações ótimas seriam de 2-1/3 para as relações entre os diâmetros e comprimentos. No presente trabalho, foram determinadas relações entre os diâmetros próximas de 0,6, e entre os comprimentos, iguais a 1. Os ângulos ótimos ficaram localizados no intervalo entre 100° e 135°. / This work aims to investigate how the geometric variation of certain parameters involved in the construction of a bifurcated Y-shaped circular cross-section geometry affects the flow resistance of both Newtonian and non-Newtonian fluids. The geometries studied were constructed using the Constructal Design principle. The parameters were the relationship between the lengths of the daughter and parent ducts, the relationship between the diameters of the same ducts, and the central angle of the Y-shaped structure. For the linear geometric relations, values of 0.5; 0.6; 0.7; 0.8; 0.9 and 1 where used, for the angles, the values of 155 °, 135 °, 115 °, 95°, 75 °, 45 °, 25 ° and 10 ° were used. The fluids used were of the Newtonian and non-Newtonian type, among the latter, pseudo plastic and dilatant fluids were studied. The work was carried out through numerical simulations, implemented with the commercial software Ansys Fluent, which solves the governing equations through the finite volume method. The meshes used were of the polyhedral type. The results indicate that there is a difference in relation to what is expected from the literature for the relationships between diameters and lengths. The Hess-Murray Law indicates that these optimal relations would be 2-1/3 for the relationships between diameters and lengths. In the present work, relationships between the diameters close to 0,6 were found and s equal to 1 between the lengths. The optimum angles were located in the range between 100 ° and 135 °.

This thesis investigates three problems in the general area of environmental fluid mechanics. The first two problems are related to liquid or gas flow through clay-water suspensions, with relevance for the underground storage of radioactive waste and also for understanding the mechanism of eruption in mud volcanoes. The third problem centres on the different problem of mixing in a turbulent buoyant plume. First, the injection of gas and water from a central source into a two-dimensional layer of clay confined between two circular horizontal plates is investigated. This provides a model of the potential pressurisation and failure of the seal rock around a radioactive waste repository as may arise if gas is continuously generated in the repository. As the gas injection pressure is gradually increased the cell walls deform and the clay moves radially outwards. However, at a critical radius, the liquid-clay interface becomes unstable and a series of channels propagate through the clay. When one of the channels reaches the edge of the domain the gas escapes and the pressure is released. As a result, the domain relaxes by elastic deformation and the clay seals the channel. In this way, continuous fluid injection leads to episodic release of gas from the cell. The second problem concerns the flow of mud along a vertical conduit driven by the combined effect of reservoir pressure and buoyancy associated with the gas injected at the base of the conduit. This represents an analogue model of the eruption of a mud volcano, in which mud rises from a deep reservoir to the surface. I find that the pressure associated with the reservoir and any buoyancy force produced by the migration of gas from deep in the reservoir to the surface leads to a continuous eruption if the net pressure is greater than the yield stress of the clay. If the reservoir pressure falls during such an event, the eruption will eventually stop, once the pressure reaches a dynamic yield stress condition. Only later, if the reservoir pressure increases to the static yield stress of the clay will the eruption start again, and this can lead to a series of eruption cycles which depend on the non-Newtonian rheology of the clay. In contrast, if this pressure is smaller than the yield stress of the clay, a series of episodic gas burst events can occur until the conduit is cleared of mud. The third problem relates to the mixing in a turbulent buoyant plume. Through a series of new experiments and some complementary theoretical modelling I show that the mixing in a turbulent plume is strongly affected by the eddies and leads to significant longitudinal dispersion in the flow. The implications of the modelling for determining the residence time distribution of the fluid in the plume is discussed.

Magnetic resonance (MR) is a highly versatile technique with great potential for use in industrial applications; from the in situ study of unit operations to the optimisation of product properties. This thesis, concerned with the latter, is divided into two parts. Firstly, dynamic MR is applied to characterise the flow behaviour, or rheology, of process fluids. Such characterisation is typically performed using conventional rheometry methods operating offline, with an online, or inline, method sought for process control and optimisation. Until recently, MR was an unlikely choice for this application due to the requirement of high-field MR hardware. However, recent developments in low-field MR hardware mean that the potential of MR in such applications can now be realised. Since the implementation of MR flow imaging is challenging on low-field MR hardware, two new approaches to MR rheometry are described using pulsed field gradient (PFG) MR. A cumulant analysis of the PFG MR signal is first used to characterise the rheology of model power-law fluids, namely xanthan gum-in-water solutions, accurate to within 5% of conventional rheometry, the data being acquired in only 6% of the time required when using MR flow imaging. The second approach utilises a Bayesian analysis of the PFG MR signal to characterise the rheology of model Herschel--Bulkley fluids, namely Carbopol 940-in-water solutions; data are acquired in only 12% of the time required for analysis using MR flow imaging. The suitability of the Bayesian MR approach to study process fluids is demonstrated through experimental study on an alumina-in-acetic acid slurry used by Johnson Matthey. Secondly, MR imaging is used to provide insights into the origins and mechanisms of colloidal gel collapse. Many industrial products are colloidal gels, a space-spanning network of attractive particles with a yield stress. Colloidal gels are, however, known to undergo gravitational collapse after a latency period, thus limiting the shelf-life of products. This remains poorly understood, with a more detailed understanding of both fundamental interest and practical importance. To this end, MR imaging is applied offline to investigate the phase behaviour of colloidal gels. In particular, a comparison of the simulated and experimental phase diagrams suggests gravitational gel collapse to be gravity-driven. Furthermore, measurement of the colloid volume fraction using MR imaging indicates the formation of clusters of colloids at the top of the samples. Whether such clusters initiate gravitational gel collapse is yield stress-dependent; the gravitational stress exerted by a cluster must be sufficient to yield the colloidal gel.

Thesis (MTech (Mechanical Engineering))--Cape Peninsula University of Technology, 2011. / Despite the extensive research work carried out on flow through short square-edged orifice plates over the last century (e.g. Johansen, 1930; Benedict, 1977; Alvi et al., 1978; Swamee, 2005; ESDU, 2007), gaps in the engineering data still exist for certain ranges of flow conditions and geometries. The majority of data available in the literature are for Newtonian fluids in the turbulent flow regime (ESDU, 2007). Insufficient data have been observed for the orifice with pipe diameter ratio, β = 0.2, in the laminar flow regime. There are no experimental data for β = 0.3 and 0.57. The objective of this thesis was to conduct wide-ranging experimental studies of the flow in orifice plates, which included those geometrical configurations, by measuring pressure loss coefficients and discharge coefficients across the orifice plates using both Newtonian fluids and non-Newtonian fluids in both laminar and turbulent flow regimes. The test work was conducted on the valve test rig at the Cape Peninsula University of Technology. Four classical circular short square-edged orifice plates having, β = 0.2, 0.3, 0.57 and 0.7, were tested. In addition, two generation 0 Von Koch orifice plates (Von Koch, 1904), with equivalent cross sectional area were also tested for β = 0.57. Water was used as Newtonian fluid to obtain turbulent regime data and also for calibration purposes to ensure measurement accuracy and carboxymethyl cellulose, bentonite and kaolin slurries were used at different concentrations to obtain laminar and transitional loss coefficient data. The hydraulic grade line method was used to evaluate pressure loss coefficients (Edwards et al., 1985), while the flange tap arrangement method was used to determine the discharge coefficients (ESDU, 2007). A tube viscometer with three different pipe diameters was used to obtain the rheological properties of the fluids. The results for each test are presented in the form of pressure loss coefficient (kor) and discharge coefficient (Cd) against pipe Reynolds number (Re)

Thesis (DTech (Mechanical Engineering))--Cape Peninsula University of Technology, 2013 / The flow of reactive viscous fluids in porous media presents a theoretically challenging problem and has a broad range of scientific, technological and engineering applications. Real life areas where such flow systems are encountered include drying of food, geothermal energy extraction, nuclear waste disposal, the flow of heat and fluid inside human organs, insulation of buildings, groundwater movement, oil and gas production, astrophysical plasmas, magnetohydrodynamic (MHD) pumps and generators, metal extraction and granulation of metals, aerospace and ship propulsion and automobile exhaust systems. The reactions within such flow systems are inherently exothermic. It is in this view that we carry out studies of thermal effects and thermal stability criteria for unsteady flows of reactive variable viscosity non-Newtonian fluids through saturated porous media. The study focuses on non-Newtonian fluids mainly because the majority of industrial fluids exhibit non-Newtonian character. Particular focus will be on fluids of the differential type exemplified by third grade fluid. Both analytical and numerical techniques were employed to solve the nonlinear partial differential equations that were derived from the conservation principles, namely the principles of conservation of mass, momentum and energy balance. Graphical representations were adopted in trying to explain the response of solutions to various flow parameter variations. In chapter 1 we defined important terms and expressions, laid down a summary of important applications, carried out literature survey, stated the statement of the problem, the aims and objectives of the study as well as an outline of the envisaged research methodology. Chapter 2 focuses on the derivations of the fundamental equations that derive the flow system. These are the continuity equation, the momentum equation and the energy equation. In chapter 3 we computationally investigated the unsteady flow of a reactive temperature dependent viscosity third grade fluid through a porous saturated medium with asymmetric convective boundary conditions. The response of velocity and temperature fields to each of the various flow parameters was analysed and interpreted. A transient increase in both the velocity and temperature profiles with an increase in the reaction strength, viscous heating and fluid viscosity parameter was observed. On the other hand, a transient decrease in the field properties was observed with increase in non-Newtonian character and the porous medium shape parameter. The reaction was noticed to blow-up if, depending on other flow parameters, the reaction strength is not carefully controlled.

O estudo do comportamento reológico de fluidos não Newtonianos tem grande importância em diversas áreas da engenharia. O aumento na demanda destes fluidos por exemplo, no uso doméstico, pessoal e em processos químicos acarreta em dificuldades que vão desde o processo de sua mistura ao seu manuseio. Dentre os fluidos não Newtonianos estão os viscoelásticos, os quais exibem deformação aparente quando os níveis de tensões são inferiores ao limite de escoamento do material e, dentro desta classe, alguns ainda podem apresentam comportamento elástico quando submetidos à baixa taxa de cisalhamento. Juntamente com os efeitos elasto-viscoplásticos, os materiais podem apresentar comportamento tixotrópico, onde devido as tensões sua reestruturação não é instantânea. Na presente Tese, fez-se um estudo numérico a fim de analisar o problema especifico de escoamentos de fluidos elasto-viscoplásticos com comportamento tixotrópico em uma expansão planar abrupta na razão de aspecto 4 : 1. O modelo mecânico aplicado consiste de uma equação viscoelástica para o campo de tensões, uma evolutiva para o parâmetro de estrutura do material, bem como as equações de conservação de massa e momento. O modelo mecânico aplicado mostrou-se capaz de prever o comportamento tixotrópico. A aproximação numérica do modelo aplicado foi feita através do método estabilizado de elementos finitos, especificamente o método Galerkin Mínimos-Quadrados (GLS), o qual foi implementado no código de elementos finitos para fluidos não Newtonianos em desenvolvimento no Laboratório de Mecânica dos Fluidos Aplicada e Computacional (LAMAC) da Universidade Federal do Rio Grande do Sul. Os fenômenos reológicos presentes no problema foram analisados a partir da influência da cinemática do escoamento, da elasticidade e da tixotropia, no nível de estruturação do material, na posição e tamanho das regiões não escoadas e na deformação elástica do material. Os resultados mostraram-se satisfatórios, pois condizem com os apresentados na literatura, apontando a boa predição do modelo mecânico aplicado bem como a robustez de sua implementação computacional. / The rheological behavior of non-Newtonian uids study is of great then importance in many areas of engineering. The increase in demand of these uids - for example, domestic use, personal and processes chemical - causes di culties ranging from the process of mixing it to handling. Among the non-Newtonian uids are viscoelastic, which exhibit apparent deformation when stress levels are lower than the yield limit of the material and, within this class, some still have elastic behavior when subjected to low shear rates. Together with the elastic-viscoplastic e ects, materials may exhibit thixotropic behavior, ie, due the restructuring strain is not instantaneous. In this thesis was made a numerical study to simulate the speci c problem of ow of elastic-viscoplastic uids with thixotropic behavior in abrupt planar expansion { common geometry in industrial systems associated with elastic-viscoplastic uids, whose ratio the aspect is 4:1. The mechanical behavior of most of these structured materials, are highly non-Newtonian, with this, there is need to make them more pseudoplastic, causing undesirable behaviors such as thixotropic which is a phenomenon somewhat characterized and modeled in the literature. The mechanical model applied is able to predict thixotropic behavior and is composed of a viscoelastic equation for the stress eld and an evolutionary to the material structure parameter in addition to the mass and momentum conservation equations. This mechanical model is approximated by a stabilized nite element model, called the Galerkin method of least squares (GLS). In order to study the rheological phenomena present in the problem is analyzed the in uence of the ow kinematics, elasticity and thixotropy in the level of structure of the material, in position and size of unyielded regions and the elastic deformation of the material. The results were satisfactory, since the the study of intensity the U the results agree with those reported in the literature pointing to good prediction of the mechanical model applied well as the hardiness of their computational implementation.The results of the elasticity showed quite spectacular behavior of unyielded regions of the material since for high values of relaxation time, the unyielded region of channel larger has the form of " ngers"because of the high exibility of the material along the line of symmetry of the channel. The results of the analysis of the elastic deformation show, that model correctly dosing the elasticity in the unyielded regions. The thixotropic e ects reported a slower structuring of the material with increasing characteristic time, in response to strain change caused by the expansion, results indicate that for high values of relaxation time, higher the distance between the unyielded regions of smaller channel and larger.

O estudo do comportamento reológico de fluidos não Newtonianos tem grande importância em diversas áreas da engenharia. O aumento na demanda destes fluidos por exemplo, no uso doméstico, pessoal e em processos químicos acarreta em dificuldades que vão desde o processo de sua mistura ao seu manuseio. Dentre os fluidos não Newtonianos estão os viscoelásticos, os quais exibem deformação aparente quando os níveis de tensões são inferiores ao limite de escoamento do material e, dentro desta classe, alguns ainda podem apresentam comportamento elástico quando submetidos à baixa taxa de cisalhamento. Juntamente com os efeitos elasto-viscoplásticos, os materiais podem apresentar comportamento tixotrópico, onde devido as tensões sua reestruturação não é instantânea. Na presente Tese, fez-se um estudo numérico a fim de analisar o problema especifico de escoamentos de fluidos elasto-viscoplásticos com comportamento tixotrópico em uma expansão planar abrupta na razão de aspecto 4 : 1. O modelo mecânico aplicado consiste de uma equação viscoelástica para o campo de tensões, uma evolutiva para o parâmetro de estrutura do material, bem como as equações de conservação de massa e momento. O modelo mecânico aplicado mostrou-se capaz de prever o comportamento tixotrópico. A aproximação numérica do modelo aplicado foi feita através do método estabilizado de elementos finitos, especificamente o método Galerkin Mínimos-Quadrados (GLS), o qual foi implementado no código de elementos finitos para fluidos não Newtonianos em desenvolvimento no Laboratório de Mecânica dos Fluidos Aplicada e Computacional (LAMAC) da Universidade Federal do Rio Grande do Sul. Os fenômenos reológicos presentes no problema foram analisados a partir da influência da cinemática do escoamento, da elasticidade e da tixotropia, no nível de estruturação do material, na posição e tamanho das regiões não escoadas e na deformação elástica do material. Os resultados mostraram-se satisfatórios, pois condizem com os apresentados na literatura, apontando a boa predição do modelo mecânico aplicado bem como a robustez de sua implementação computacional. / The rheological behavior of non-Newtonian uids study is of great then importance in many areas of engineering. The increase in demand of these uids - for example, domestic use, personal and processes chemical - causes di culties ranging from the process of mixing it to handling. Among the non-Newtonian uids are viscoelastic, which exhibit apparent deformation when stress levels are lower than the yield limit of the material and, within this class, some still have elastic behavior when subjected to low shear rates. Together with the elastic-viscoplastic e ects, materials may exhibit thixotropic behavior, ie, due the restructuring strain is not instantaneous. In this thesis was made a numerical study to simulate the speci c problem of ow of elastic-viscoplastic uids with thixotropic behavior in abrupt planar expansion { common geometry in industrial systems associated with elastic-viscoplastic uids, whose ratio the aspect is 4:1. The mechanical behavior of most of these structured materials, are highly non-Newtonian, with this, there is need to make them more pseudoplastic, causing undesirable behaviors such as thixotropic which is a phenomenon somewhat characterized and modeled in the literature. The mechanical model applied is able to predict thixotropic behavior and is composed of a viscoelastic equation for the stress eld and an evolutionary to the material structure parameter in addition to the mass and momentum conservation equations. This mechanical model is approximated by a stabilized nite element model, called the Galerkin method of least squares (GLS). In order to study the rheological phenomena present in the problem is analyzed the in uence of the ow kinematics, elasticity and thixotropy in the level of structure of the material, in position and size of unyielded regions and the elastic deformation of the material. The results were satisfactory, since the the study of intensity the U the results agree with those reported in the literature pointing to good prediction of the mechanical model applied well as the hardiness of their computational implementation.The results of the elasticity showed quite spectacular behavior of unyielded regions of the material since for high values of relaxation time, the unyielded region of channel larger has the form of " ngers"because of the high exibility of the material along the line of symmetry of the channel. The results of the analysis of the elastic deformation show, that model correctly dosing the elasticity in the unyielded regions. The thixotropic e ects reported a slower structuring of the material with increasing characteristic time, in response to strain change caused by the expansion, results indicate that for high values of relaxation time, higher the distance between the unyielded regions of smaller channel and larger.