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 expérimentale et numérique s’intéresse à l’écoulement à inertie négligeable d’un fluide newtonien et d’un fluide à seuil autour d’une plaque ou d’un cylindre en présence d’une paroi. Les efforts générés et les structures d’écoulement ont été particulièrement étudiés. Pour le fluide à seuil, l’étude est centrée sur le domaine des effets de seuil grands par rapport aux effets visqueux. Pour l’approche expérimentale, un dispositif a été conçu permettant de mesurer simultanément les forces de traînée et de portance en fonction de la vitesse et de la distance obstacle/paroi. Les fluides étudiés sont un sirop de glucose Newtonien et un gel de Carbopol considéré comme un fluide à seuil modèle. Ces matériaux ont été finement caractérisés du point de vue rhéologique. Des simulations numériques utilisant le modèle viscoplastique anélastique d’Herschel-Bulkley régularisé par le modèle de Papanastasiou ont été réalisées. Les résultats obtenus avec le fluide newtonien ont permis de valider l’installation expérimentale et l’approche numérique. Les effets de la contrainte seuil, de la distance paroi/obstacle, de la rhéofluidification, de l’angle d’inclinaison de la plaque sur les coefficients de traînée et de portance ont été examinés en détail. Le régime de lubrification a été étudié pour le cylindre expérimentalement et théoriquement. La morphologie de l’écoulement (zones rigides) et les grandeurs locales ont été montrées. Des solutions analytiques de la traînée et de la portance ont été proposées. Les comparaisons entre les résultats expérimentaux et numériques ainsi qu’avec les solutions issues de la plasticité de la mécanique des sols sont analysées. Les écarts sont discutés en termes d’influence de l’élasticité et de plasticité du fluide à seuil. / This experimental and numerical thesis deals with the creeping flow of a Newtonian fluid and a yield stress fluid around a plate or a cylinder in the presence of a wall. The generated forces and the flow structures have been particularly studied. The study focuses for the yield stress fluid on large yield stress effects compared to the viscous effects. For the experimental approach, a device has been designed to measure simultaneously the drag and lift forces as a function of velocity and obstacle / wall distance. The fluids studied are a Newtonian glucose syrup and a Carbopol gel considered as a yield stress fluid model. These materials have been finely characterized from the rheological point of view. Numerical simulations using the Herschel-Bulkley anelastic viscoplastic model regularized by the Papanastasiou model were carried out. The results obtained with the Newtonian fluid allowed to validate the experimental set-up and the numerical approach. The effects of the yield stress, the wall / obstacle distance, the power law index and the inclined plate on the drag and lift coefficients were carefully examined. The lubrication regime has been studied for the cylinder both experimentally and theoretically. The morphology of the flow (rigid zones) and the local field quantities have been shown. Analytical solutions of drag and lift have been proposed. Comparisons between the experimental and numerical results as well as the solutions resulting from the plasticity of soil mechanics are analyzed. Deviations are discussed in terms of the elasticity and plasticity influence of the yield stress fluid.

Submitted by Jorge Silva (jorgelmsilva@ufrrj.br) on 2018-05-10T18:21:02Z No. of bitstreams: 1 2017 - Bianca Rangel Antunes da Silva.pdf: 2187606 bytes, checksum: 927fe528eb48db49953e8f982d4320d5 (MD5) / Made available in DSpace on 2018-05-10T18:21:02Z (GMT). No. of bitstreams: 1 2017 - Bianca Rangel Antunes da Silva.pdf: 2187606 bytes, checksum: 927fe528eb48db49953e8f982d4320d5 (MD5) Previous issue date: 2017-12-21 / During the drilling of oil wells, the pressure differential between the rock formation and the annular region can cause a filtration process and consequent invasion of drilling fluid into the rocks, causing irreversible damage to the well. Therefore, studies to control the properties of the well formed mudcake are fundamental. The mudcake formed should be thin and of low permeability, thus minimizing the filtration and the invasion of the fluid. The main purpose of this work was to study the characteristics of the filtration pie formed during the drilling process of oil wells, using non-Newtonian fluids that follow the Power law model, and applying the simplified theory of filtration adapted for non-Newtonian fluids to achieve the specific objective that was the lifting of the parameters of permeability, porosity, thickness and correction factor obtained from experimental data of filtered volume versus time, in Static conditions, at different pressures. Experimental results were obtained in different filtration conditions (pressure, viscosifier agent and weighting material) seeking to compare and know the mechanisms that control filtration in static conditions. Filtration tests were carried out at 300 psi, 500 psi and 700 psi, using a HTHP cell and prepared non-Newtonian drilling fluids containing xanthan gum (XG) and carboxymethylcellulose (CMC) as viscosifier agent, in addition to calcite and barite. Filtration parameters such as permeability, porosity, pie thickness, filtration time and filtered volume have been evaluated. The permeability of the pie was determined, with the aid of a software of estimation of parameters, using the simplified theory of filtration adapted for non Newtonian fluids proposed by Massarani and Coelho de Castro(1980). The results obtained were confronted with those obtained by other methodologies. The experimental tests also showed that the properties of the pie vary with the filtration pressure. / Durante o processo de perfura??o de po?os de petr?leo, o diferencial de press?o entre a forma??o rochosa e a regi?o anular pode ocasionar um processo de filtra??o e consequente invas?o de fluido de perfura??o nas rochas, causando opera??es irrevers?veis ao po?o. Por isso, s?o fundamentais estudos para controlar as propriedades da torta de filtra??o formada na parede do po?o. A torta formada deve ser fina e de baixa permeabilidade, minimizando assim a filtra??o e a invas?o do fluido. Este trabalho teve como objetivo principal estudar as caracter?sticas da torta de filtra??o formada durante o processo de perfura??o de po?os de petr?leo, utilizando fluidos n?o Newtonianos que seguem a lei da pot?ncia,e aplicando a teoria simplificada da filtra??o adaptada para fluidos n?o Newtonianos para atingir o objetivo espec?fico que foi o levantamento dos par?metros de permeabilidade, porosidade, espessura e fator de corre??o obtidos a partir de dados experimentais de volume de filtrado versus tempo, em condi??es est?ticas, em diferentes press?es.Foram obtidos resultados experimentais em diferentes condi??es de filtra??o (press?o, viscosificante e adensante) buscando comparar e conhecer os mecanismos que controlam a filtra??o em condi??es est?ticas. Foram realizados ensaios de filtra??o a 300 psi, 500 psi e 700 psi, utilizando uma c?lula HTHP e preparados fluidos de perfura??o n?o-Newtonianos contendo Goma Xantana (GX) e carboximetilcelulose (CMC) como viscosificantes, al?m de barita e calcita. Foram avaliados os par?metros da filtra??o como permeabilidade, porosidade, espessura da torta, tempo de filtra??o e volume de filtrado. A permeabilidadeda torta foideterminada, com o aux?lio de umsoftware de estima??o de par?metros, utilizando-sea teoria simplificada da filtra??o adaptada para fluidos n?o Newtonianos proposta por Massarani e Coelho de Castro (1980). Os resultados obtidos foram confrontados com os obtidos por outras metodologias. Os ensaios experimentais mostraram tamb?m que as propriedades da torta variam com a press?o de filtra??o.

The main objective of this research was to exploit the interrelations between the rheological behavior and nano-microstructure of complex fluids in solving two state-of-the-art problems, one in the field of biomedical engineering: controlling the amount and characteristics of bioaerosol droplets generated during coughing, and the other in the bitumen-heavy oil industry: characterizing the nano-microstructure of asphaltene particles in bitumen and heavy oil from their rheological behavior. For the first problem, effect of viscoelastic and surface properties of artificial mucus simulant gels on the size distribution and amount of airborne bioaerosol droplets generated during simulated coughing were investigated. The results revealed that suppressing the generation of bioaerosol droplets and/or reducing the number of emitted droplets to a minimum during coughing are practically achievable through modulation of mucus viscoelastic properties. While variation of surface tension did not show any change in the droplet size distribution, an increase in particle size was observed as the samples changed from elastic solid type to viscoelastic type to viscous fluid type samples. This knowledge will help in the development of a new class of drugs being developed at the University of Alberta, aimed at controlling the transmission of airborne epidemic diseases by modifying the viscoelastic properties of mucus. For the second problem, studies of viscoelastic behavior of Athabasca bitumen (Alberta) and Maya crude (Mexico) oil samples, along with their Nano-filtered and chemically separated-plus-reconstituted samples were performed. The results revealed that the rheological behaviors of the bitumen-heavy oil samples are governed by their multiphase nature. The rheological behavior of all feeds, permeates and retentate samples followed a single master curve over the entire temperature interval, consistent with that of a slurry comprising a Newtonian liquid plus a dispersed solid comprising non-interacting hard spheres. The behavior of asphaltenes in the reconstituted samples, however, was found to be significantly different from that in nanofiltered samples. The information about the characteristics and behaviors of asphaltenes obtained in this study will help better understand the asphaltene structures, and support the effort to determine solutions for numerous asphaltene-related industrial problems. In the long run, this knowledge will help to create more efficient extraction and upgrading processes for bitumen and heavy oils. / Thermo Fluids

Peristalsis is a mechanism of pumping fluids in ducts when a progressive wave of area contraction or expansion propagates along the length of a distensible tube containing fluid. It induces in general propulsive and mixing movements and pumps the fluids against pressure rise. Physiologically, peristaltic action is an inherent property of smooth muscle contraction. It is an automatic and vital process that drives the urine from the kidney to the bladder, food through the digestive tract, bile from the gall-bladder into the duodenum, movement of ovum in the fallopian tube and many other situations. A major industrial application of this principle is in the design of roller pumps, which are used in pumping fluids without being contaminated due to the contact with the pumping machinery. Even though peristalsis is a well-known mechanism in biological system, the first theoretical and experimental analysis of its fluid dynamics aspects were given four decades ago. In reality, the peristaltic flow problems are unsteady moving free boundary value problems where the shape of the wave on flexible tube wall is not known apriori. But the mathematical models on peristaltic transport considered in the literature deal with a prescribed train of waves moving with constant speed on the flexible boundaries and they are studied in either a fixed frame or a wave frame moving with constant velocity of the wave. In a wave frame the moving walls become stationary wavy walls. Further the motion could be treated steady under the assumptions that the peristaltic wave train is periodic, the pressure difference across the length of the tube is constant and the tube length is an integral multiple of the wavelength. Some mathematical models of peristaltic flows representing some physiological situations are studied using a wave frame of reference in this thesis. The important characteristics of these flows namely pumping (variation of time averaged flux with difference in pressures across one wavelength), trapping (splitting of streamlines enclosing a bolus which moves as a whole along with the wave), reflux phenomena (the presence of some fluid particles whose mean motion over one cycle is against the net pumping direction) are discussed in detail. A brief general introduction to the peristaltic transport and their application in physiological fluid dynamics is presented in chapter one. In the second chapter, the peristaltic transport of an incompressible viscous Newtonian fluid in an asymmetric channel is studied under long wavelength and low-Reynolds number assumptions. Choosing the peristaltic wave train on the walls to have different amplitudes and phase produces the channel asymmetry. This study is motivated by the intra-uterine fluid flow induced by uterine wall contractions which represent a peristaltic flow in an asymmetric channel and this flow is responsible for embryo transport to a successful implantation site. The solution for the stream function is obtained by neglecting inertia and curvature effects. The streamlines are plotted in both fixed and wave frames. The effects of different geometric parameters causing asymmetry like phase difference; varying channel width and wave amplitudes are investigated on the pumping characteristics, streamline pat-tern, trapping and reflux phenomena. It is observed that the pumping against pressure rise, trapping and reflux layer exists only when cross-section of the channel varies along the axis. The limits on the time averaged flux for trapping and reflux are obtained. The peristaltic waves on the walls with same amplitudes propagating in phase produce zero flux rate as the channel cross-section remains the same through out. The trapping and reflux regions reduce for asymmetric channels compared to symmetric channels. The flow of an incompressible viscous fluid driven by the traveling waves along the boundaries of an asymmetric channel is studied in the chapter three, when inertia and streamline curvature effects are not negligible. It was well documented that the inertial forces cannot be ignored in the pharyngeal phase of bolus transport. Choosing the wave train on the walls to have different amplitudes and phases produces the channel asymmetry here. An asymptotic solution is obtained in powers of a geometric parameter £, the ratio of the channel width to the wavelength, giving curvature and inertia effects. A domain transformation is used to transform the channel of variable cross section to a uniform cross section, and this facilitates in easy way of finding closed form solutions at higher orders. The solutions are presented upto second order in 6. It has been found that, the relation connecting the pressure gradient and time average flux rate is a cubic leading to a non-unique of flux for a given pressure gradient. A uniqueness criterion is derived which restricts the parameters to get a unique flux for a prescribed pressure difference. The effects of inertia and curvature on peristaltic pumping, trapping and shear stress are discussed for various parameters governing the flow for symmetric and asymmetric channels and compared with the existing results in the literature. Even under a favourable pressure gradient the possibility of fluid flow in a direction opposite to the direction of the waves propagating on the walls is detected as in the case of some non-Newtonian fluids. It is noticed that the Reynolds number and asymmetry of the wall geometry may play an important role in producing mixing. The appearance of a second trapped bolus near the down streamside of the channel for some Reynolds number is a new feature. Further, the non-zero curvature produces three trapped boluses for high Reynolds number in symmetric channel as well as for inertia free flow in an asymmetric channel. Another interesting phenomena is that the shear stress distribution on the walls vanishes at some points but it does not indicate any flow separation as the MRS criteria is not satisfied. The gastrointestinal tract is surrounded by a number of muscle layers having smooth muscle. The most important smooth muscle layers in gastrointestinal tract are submucosa and a layer of epithelial cells and these- are responsible for the absorption of nutrients and water in the intestine. These layers consist of many folds and there are pores through out the tight junctions of them. Thus a study of peristaltic transport with porous peripheral layer and porous boundaries of a duct are important. Motivated by this the flow in gastrointestinal tract is mathematically modeled by a peristaltic flow of two fluid system in a two-dimensional channel with a porous peripheral layer and a Newtonian fluid core layer, in chapter four. The fluid flow is investigated under the assumptions of long wavelength and low Reynolds number in a wave frame of reference. Brinkman extended Darcy equation is utilized to model the flow in the porous peripheral layer. A shear stress jump boundary condition of Ochoa-Tapia and Whitaker is used at the interface between porous and fluid regions together with continuity of velocity and normal stress conditions. Here one needs an extra assumption that the fluid interface and the peristaltic wave on the boundary have the same period in addition to the constant pressure difference at the ends of channel and the length of the channel to be an integral multiple of the wavelength, to consider the flow to be steady. The interface is determined as a part of the solution using the conservation of mass in both the porous and fluid regions independently. Matlab packages are used to solve the transcendental equation governing it. An interval of critical time averaged flux Q is obtained for the existence of a unique solution for the interphase. The physical quantities of importance in peristaltic transport namely, pumping, trapping and reflux are discussed for various parameters of interest governing the flow like Darcy number Da, porosity 6, shear-stress jump constant /3, viscosity ratio /i. It is observed that the peristalsis works as a pump against greater pressure rise with a porous medium in the peripheral layer than a viscous fluid. The limits on the time averaged flux Q for trapping in the core layer are obtained. The existence of reflux near the axis is observed for small values of Darcy number and large values of /?. Chapter five deals with the peristaltic transport in a tube with a poroflexible wall and having a porous material layer in the peripheral region and a Newtonian fluid in the core region. Flow in tube may be more realistic to model a flow in gastrointestinal system. At the poroflexible wall, a slip boundary condition of Saffman.type is used. The fluid flow is studied in a wave frame of reference under lubrication approach. Brinkman extended Darcy equation in cylindrical polar coordinates is considered for the porous medium with a shear-stress jump boundary condition of Ochoa-Tapia and Whitaker at the interface of porous and fluid regions together with the continuity of velocity and normal stress. The interface is found as a part of the solutions using the conservation of mass in both the regions of deformable porous medium and fluid medium independently. The interface equation turns out to be a transcendental equation involving modified Bessel functions and it is solved by using Matlab packages. The uniqueness criterion of the solutions for the interface equation in the flow region is determined for certain values of time averaged flux Q. Pumping characteristics, trapping and reflux phenomena are discussed for various parameters of interest governing the flow like, wall slip constant fc, Darcy number Da, viscosity ratio /x. shear stress jump constant f) and peripheral layer thickness 7. The slip condition at the boundary, arising due to the poroflexible nature of the wall, enhances pumping. The trapped bolus volume in the core layer is observed to decrease with a decrease in Da, /i and k and an increase in /?. The reflux phenomena is discussed in detail. The trapping limits on the flux rate Q in the core region are obtained. As the behaviour of most of the physiological fluids is known to be non-Newtonian, the peristaltic flows of power-law and micro polar fluids are investigated in the next two chapters. In chapter six, the peristaltic transport of a power-law fluid in an axisymmetric tube having poroflexible wall is studied. The power-law model of Ostwald-de Waele type is considered, which accommodates the study of both shear thinning and shear thickening fluids. The flow characteristics are studied in wave frame analysis under lubrication approach. The slip boundary conditions of Beavers-Joseph and Saffman type are considered at the wall in obtaining solutions for the flow and resulting pumping characteristics are investigated with a straight section dominated (SSD) wave form other than the sinusoidal one. It is observed that the time mean flow becomes negative in free pumping for a shear thickening fluid with a SSD expansion wave and the same is observed for a SSD contraction wave in the case of shear thinning fluid. The pressure rise increases with increasing of Darcy number Da against which the peristalsis works as a pump and decreases for an increase in Beaver-Joseph constant a. Peristalsis works as a pump against a greater pressure rise for a shear thickening fluid and the opposite happens for a shear thinning fluid compared with Newtonian fluid. Trapping and reflux phenomena are discussed for various parameters of interest governing the flow like Da, a and the fluid behaviour index n. The trapping limits on Q are derived. The trapped bolus volume for sinusoidal wave is observed to decrease as the fluid behaviour index decreases, i.e as the fluid behaviour changes from shear thickening to shear thinning, where as it increases with an increase in Darcy number. The rheological properties of fluid, wave shape and porous nature of the wall play an important role in the peristaltic transport and may be useful in understanding the transport of chyme in small intestine. The chapter seven contains the study of peristaltic transport of a micropolar fluid in an axisymmetric tube. Micropolar fluids exhibit some microscopic effects arising from the local structure and micro motion of the fluid elements. Further, they can sustain couple stresses. It is speculated that, in microcirculation, peristalsis may be involved as well in the vasomotion of small blood vessels which change their diameters periodically. Therefore, modelling blood by a micropolar fluid may be more appropriate. The closed form solutions are obtained for velocity, microrotation components, as well as the stream function under the assumption of long wavelength and low Reynolds number. The solution contains new additional parameters namely, N the coupling number and m the microploar parameter. In the case of free pumping (pressure difference Ap = 0) the difference in pumping flux is observed to be very small for Newtonian and micropolar fluids but in the case of pumping (Ap > 0) the characteristics are significantly altered for different N and m. It is observed that the peristalsis in micropolar fluids works as a pump against a greater pressure rise compared with a Newtonian fluid. Streamline patterns which depict trapping phenomena aie presented for different parameter ranges. The limit on the trapping of the center streamline is obtained. The effects of N and m on friction force for different Ap are discussed. The nomenclature of symbols in each chapter is independent of the other. Each of the chapter has its own appendix and they are numbered with the corresponding roman number of the chapters. The purpose of the study here is not to represent exactly the functioning of various physiological applications, but rather to understand the fluid-mechanical aspects inherent in the problems of peristaltic transport.

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Submitted by Debora de Oliveira Medeiros null (deboraomedeiros@gmail.com) on 2017-06-13T19:08:30Z No. of bitstreams: 1 dissertacao_arquivar.pdf: 4524135 bytes, checksum: 33a027db23ff40bebc026b9090443d53 (MD5) / Approved for entry into archive by Luiz Galeffi (luizgaleffi@gmail.com) on 2017-06-19T12:58:15Z (GMT) No. of bitstreams: 1 medeiros_do_me_prud.pdf: 4524135 bytes, checksum: 33a027db23ff40bebc026b9090443d53 (MD5) / Made available in DSpace on 2017-06-19T12:58:15Z (GMT). No. of bitstreams: 1 medeiros_do_me_prud.pdf: 4524135 bytes, checksum: 33a027db23ff40bebc026b9090443d53 (MD5) Previous issue date: 2017-04-24 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / Neste trabalho é apresentado um estudo das equações de Navier Stokes incompressível com superfície livre e métodos de projeção com uma formulação recente denominada laplaciano superficial. Esta formulação tem como finalidade uma melhor descrição da força de tensão superficial e grandezas, como curvatura e vetores tangencial e normal, descritas sobre a interface. Assim, uma condição de tensão normal alternativa é definida, e esta quando discretizada implicitamente e combinada com o método de projeção, descrevem a formulação laplaciano superficial, cuja sua solução é utilizada como condições de contorno para resolver o sistema de equações que descrevem o escoamento. A nova formulação destina-se a resolver um sistema tridiagonal de equações gerado sobre a interface, e usar a solução deste sistema de equações como uma condição de contorno na superfície livre para o sistema linear da correção da pressão no interior do domínio, que é resultante da aplicação do método de projeção. A nova equação que define a condição de tensão normal conta com grandezas definidas na malha euleriana, no contexto Marker-And-Cell (MAC), que devem ser projetadas sobre a malha lagrangeana e também considera a curvatura e os vetores tangente e normal na sua descrição, sendo importante um estudo detalhado de geometria diferencial. Finalmente, variações da formulação laplaciano superficial com tensão superficial para diferenças finitas são aplicadas para resolver os testes numéricos da oscilação da gota e da gota apoiada que possuem solução de referência, além da simulação de um problema com movimento de interface (fountain flow). Nestes testes, concluímos que a variação mais precisa e estável é aquela que aplica uma discretização da equação da tensão normal utilizando médias de valores alocados na malha MAC. / This work presents a study of the Navier-Stokes equations incompressible with free surface and a projection methods with a recent formulation defined as surface laplacian. The purpose of this formulation is to improve the description of the force of stress tension and quantities, as curvature and tangent and normal vectors, present at the interface. Thus, an alternative normal stress condition is defined, and when this is discretized implicitly and combined with the employ of projection method, describe the surface laplacian formulation, whose solution is used as boundary condition to solve the system of equations describing the flow. The new formulation is intended to solve the tridiagonal system of equations generated at the interface, and to use this solution as a boundary condition at free surface for the linear system of the pressure correction inside of domain, which results of the application of the projection method. The new equation used to define the normal stress condition considers quantities defined in the Eulerian mesh, in the Marker-And-Cell context (MAC), that should be projected on the Lagrangian mesh. In addition, in the new equation, it is also considered the influence of the curvature and normal and tangential vectors in your description, so that a detailed study of differential geometry for this computation is important. Finally, variations of the surface laplacian formulation for finite differences are applied for solving numerical tests of the drop oscillation and sessile drop which have reference solutions, beyond of the simulation of a problem with free surface moving (fountain flow). In these tests, we concluded that the most accurate and stable variation is the one that applies a discretization of the normal stress equation using the mean of values in the MAC mesh. / FAPESP: 2015/01243-0

[pt] A perfuração de poços de petróleo, principalmente em ambientes offshore, é uma operação que demanda um custo muito elevado, portanto a minimização de problemas e danos ao reservatório produtor é muito importante. O projeto de um fluido de perfuração que garanta a mínima invasão na rocha reservatório é um tópico fundamental, como consequência a indústria petrolífera tem investido em estudos com o intuito de evitar que este problema ocorra. Sendo assim, nesse trabalho estudou-se o escoamento de fluidos em um meio poroso ideal, a célula de Hele-Shaw. Para realizar esse trabalho foram utilizados dois fluidos não newtonianos: uma solução aquosa de um polímero flexível, a poliacrilamida; e uma solução aquosa de um polímero rígido, a goma xantana. Esses fluidos não newtonianos representaram o fluido de perfuração, já o papel do petróleo presente na rocha reservatório foi desempenhado pelo óleo mineral. A partir desse experimento é possível observar a instabilidade de Saffman-Taylor ou viscous fingers, que é um fenômeno observado quando um fluido de menor viscosidade desloca outro de maior viscosidade. Esse fenômeno é muito importante em diversas aplicações, tais como: invasão de fluido de perfuração em meios porosos (caso que será estudado), recuperação secundária e terciária de petróleo, fraturamento hidráulico, processamento de polímeros, hidrologia e filtração. O experimento consiste em analisar a evolução da interface entre os dois fluidos através de uma câmera filmadora. A partir das imagens é determinada qualitativamente a eficiência do deslocamento. Com o conjunto de imagens é possível observar também em quais parâmetros dinâmicos e reológicos ocorre a transição fingers (interface instável) para plug (interface estável), e viceversa. Também foram realizados testes reológicos nos quais foi possível conhecer o comportamento dos fluidos não newtonianos utilizados. Com base nos dados coletados observou-se que tanto para a poliacrilamida quanto para a goma xantana a transição ocorre a uma taxa de cisalhamento adimensional próxima de 3. / [en] The drilling of oil wells, particularly in offshore environments, is an operation which demands a high cost, thus, the minimization of problems and damage to the producing reservoir is very important. The design of a drilling fluid that ensures minimum invasion into the reservoir rock is a major topic, consequently the oil industry has invested in research in order to prevent this problem from occurring. Therefore, this research studied the displacement of fluids in an ideal porous medium, a Hele-Shaw cell. To accomplish this task, the following two non-Newtonian fluids were used: an aqueous solution of a flexible polymer, polyacrylamide; and the other an aqueous solution of a rigid polymer, xanthan gum. Such non-Newtonian fluids represent the drilling fluid, while the function of oil present in the reservoir rock was represented by mineral oil. From this experiment it is possible to observe the Saffman-Taylor instability or viscous fingers, which is a phenomenon observed when a low viscosity fluid displaces a higher viscosity fluid. This phenomenon is very important in many applications, such as drilling fluid invasion in porous media, secondary and tertiary oil recovery, hydraulic fracturing, polymer processing, hydrology and filtration. The experiment consists in analyzing the evolution of the interface between two fluids through a digital camera, and determining the displacement efficiency qualitatively from the imagens. With the set of images is possible to observe in which dynamic and rheological parameters the transition from fingers (unstable interface) to plug (stable interface) occurs, and vice versa. Also, rheological tests were performed in which it was possible to know the behavior of non-Newtonian fluids used in the study. From the data collected it was observed that both the polyacrylamide and for xanthan gum transition occurs near the dimensionless shear rate of 3.

The thesis deals with the description of the unstable flow of non-Newtonian fluid in a slit-flow rheometer, which negatively affects its behaviour. The initiators of unstable fluid flow are the roughness of the rheometer slit walls, the slip on the rheometer walls, and the influence of the inlet and outlet region geometry of the rheometer slit. The work contains methodical procedures for mathematical consideration of individual unstable fluid flow initiators and design of change of slit geometry of slit-flow rheometer. Part of the work is also a comparison of the most commonly used rheological models, derivation of general relations for the creation of the velocity profile of individual rheological models and their subsequent implementation in the rheological application, which significantly simplifies the process of evaluation of measured data when measured on slit-flow rheometer. This application can be used to determine basic parameters in CFD simulations or as a teaching aid.

Main topic of this thesis are magnetic fluids. These are specific type of fluids which can simplistically be considered as Bingham fluids. Main issues regarding the magnetic fluids mentioned in this thesis are: rheological properties of the magnetic fluids, behaviour of the magnetic fluids and the use of the magnetic fluids in industrial applications. Main goal is to apply Binghams model on the the magnetic fluids assuming that this model can be applied with a good accuracy. Equations which describe behaviour of the Bingham fluids are constructed. Some assumptions which have to be respected to use this analytical equations for magnetic fluids are formulated. Flow of bingham fluid is analytically solved in some simplificated cases with consideration of laminar flow. Analytical results are confronted with numerical ones obtained from CFD software Fluent for the purpose of verification.