The polymers are integral part of vast number of products used in day to day life due to their anomalous viscoelastic behaviour. The remarkable flow behaviour exhibited by the polymeric fluids including rod climbing, extrudate swell, tube-less siphon, viscoelastic jet, elastic recoil and sharkskin instability is attributed to the complex microstructures in the polymeric liquids that arise due to the interactions of long chain polymer molecules with each other and with the surrounding fluid particles. The significance of polymer in transportation, packaging, pharmaceutical, chemical, biomedical, textiles, food and polymer processing industries highlights the requirement to comprehend the complex rheology of polymeric fluids. First, we investigate the flow features exhibited by different shear thinning vis-coelastic fluids in rectangular cavities over a wide range of depth to width ratio. We have developed a viscoelastic flow solver in order to perform numerical simulations of highly elastic flow of viscoelastic fluids. In particular, we discuss the simulations of flows of constant viscosity Boger and shear thinning viscoelastic fluids in the complex flow problems using different constitutive equations. The effects of elasticity and inertia on the flow behaviour of two shear thinning vis-coelastic fluids modeled using Giesekus and linear PTT constitutive equations in rectangular cavities is studied. The size of the primary eddies and critical aspect ratio over which the corner eddies merge to yield a second primary eddy in deep cavities is discussed. We demonstrate that the flow in the shallow and deep cavities can be characterized using Weissenberg number, defined based on the shear rate, and Deborah number, specified based on the convective time scale, respectively. The study of flow in driven cavities is important in understanding of the mixing process during synthesis of blends and composites. Next, we study two phase polymeric flow in confined geometries. Nowadays, polymer processing industries prefer to develop newer polymer with the desired material properties mechanically by mixing and blending of different polymer components instead of chemically synthesizing fresh polymer. The microstructure of blends and emulsions following drop deformation, breakup and coalescence during mixing determines its macroscopic interfacial rheology. We developed a two phase viscoelastic flow solver using volume conserving sharp interface volume-of-fluid (VOF) method for studying the dynamics of single droplet subjected to the complex flow fields. We investigated the effects of drop and matrix viscoelasticity on the motion and deformation of a droplet suspended in a fully developed channel flow. The flow behaviour exhibited by Newtonian-Newtonian, viscoelastic-Newtonian, Newtonian-viscoelastic and viscoelastic-viscoelastic drop-matrix systems is presented. The difference in the drop dynamics due to presence of constant viscosity Boger fluid and shear thinning viscoelastic fluid is represented using FENE-CR and linear PTT constitutive equations, respectively. The presence of shear thinning viscoelastic fluid either in the drop or the matrix phase suppresses the drop deformation due to stronger influence of matrix viscoelasticity as compared to the drop elasticity. The shear thinning viscoelastic drop-matrix system further restricts the drop deformation and it displays non-monotonic de-formation. The constant viscosity Boger fluid droplet curbs the drop deformation and exhibits flow dynamics identical to the shear thinning viscoelastic droplet, thus indicating that the nature of the drop viscoelasticity has little influence on the flow behaviour. The matrix viscoelasticity due to Boger fluid increases drop deformation and displays non-monotonic deformation. The drop deformation is further enhanced in the case of Boger fluid in viscoelastic drop-matrix system. Interestingly, the pressure drop due to the presence of viscoelastic drop in a Newtonian matrix is lower than the single phase flow of Newtonian fluid. We also discuss the effects of inertia, surface tension, drop to matrix viscosity ratio and the drop size on these drop-matrix systems. Finally, we investigate the emulsion rheology by studying the motion of a droplet in the square lid driven cavity flow. The viscoelastic effects due to constant viscosity Boger fluid and shear thinning viscoelastic fluid are illustrated using FENECR and Giesekus rheological relations, respectively. The presence of viscoelasticity either in drop or matrix phase boosts the drop deformation with the drop viscoelasticity displaying intense deformation. The drop dynamics due to the droplet viscoelasticity is observed to be independent of the nature of vis-coelastic fluid. The shear thinning viscoelastic matrix has a stronger influence on the drop deformation and orientation compared to the Boger fluid matrix. The different blood components, cells and many materials of industrial importance are viscoelastic in nature. Thus, the present study has significant applications in medical diagnostics, drug delivery, manufacturing and processing industries, study of biological flows, pharmaceutical research and development of lab-on-chip devices.

In the first part of this thesis we are concerned with the constitutive the- ory for incompressible fluids characterized by a continuous monotone rela- tion between the velocity gradient and the Cauchy stress. We, in particular, investigate a class of activated fluids that behave as the Euler fluid prior activation, and as the Navier-Stokes or power-law fluid once the activation takes place. We develop a large-data existence analysis for both steady and unsteady three-dimensional flows of such fluids subject either to the no-slip boundary condition or to a range of slip-type boundary conditions, including free-slip, Navier's slip, and stick-slip. In the second part we show that the W−1,q norm is localizable provided that the functional in question vanishes on locally supported functions which constitute a partition of unity. This represents a key tool for establishing local a posteriori efficiency for partial differential equations in divergence form with residuals in W−1,q . In the third part we provide a novel analysis for the pressure convection- diffusion (PCD) preconditioner. We first develop a theory for the precon- ditioner considered as an operator in infinite-dimensional spaces. We then provide a methodology for constructing discrete PCD operators for a broad class of pressure discretizations. The...

<p><b>Part I: Micromechanics of dense suspensions</b></p><p>Particulate suspensions are ubiquitous in the industry & nature. Fresh concrete, uncured solid rocket fuel, & biomass slurries are typical industrial applications, while milk & blood are examples of naturally occurring suspensions. These suspensions exhibit many non-Newtonian properties like rate-dependent rheology & normal stresses. Other than volume fraction, particle material, inter-particle interactions determine the rheological behavior of suspension. The average inter-particle gaps between the neighboring particles decrease significantly as the suspension volume fraction approaches the maximum packing fraction in dense suspensions. So, in this regime, the short-ranged non-contact interactions are important. In addition, the particles come into contact due to asperities on their surfaces. The surface asperities are present even in the case of so-called smooth particles, as particles in real suspensions are not perfectly smooth. Hence, contact forces become one of the essential factors to determine the rheology of suspensions.</p><p> </p><p>Part I of this thesis investigates the effects of microscopic inter-particle interactions on the rheological properties of dense suspensions of non-Brownian particles by employing discrete particle simulations. We show that increasing the roughness size results in a rise in the viscosity & normal stress difference in the suspensions. Furthermore, we observe that the jamming volume fraction decreases with the particle roughness. Consequently, for suspensions close to jamming, increasing the asperity size reduces the critical shear rate for shear thickening (ST) transition, resulting in an early onset of discontinuous ST (DST, a sudden jump in the suspension viscosity) in terms of volume fraction, & enhances the strength of the ST effect. These findings are in excellent agreement with the recent experimental measurements & provide a deeper understanding of the experimental findings. Finally, we propose a constitutive model to quantify the effect of the roughness size on the rheology of dense ST suspensions to span the entire phase-plane. Thus, the constitutive model and the experimentally validated numerical framework proposed can guide experiments, where the particle surface roughness is tuned for manipulating the dense suspension rheology according to different applications. </p><p> </p><p>A typical dense non-Brownian particulate suspension exhibits shear thinning (decreasing viscosity) at a low shear rate followed by a Newtonian plateau (constant viscosity) at an intermediate shear rate values which transition to ST (increasing viscosity) beyond a critical shear rate value and finally, undergoes a second shear-thinning transition at an extremely high shear rate values. This part unifies & quantitatively reproduces all the disparate rate-dependent regimes & the corresponding transitions for a dense non-Brownian suspension with increasing shear rate. The inclusion of traditional hydrodynamic interactions, attractive/repulsive DLVO (Derjaguin and Landau, Verwey and Overbeek), contact interactions, & constant friction reproduce the initial thinning as well as the ST transition. However, to quantitatively capture the intermediate Newtonian plateau and the second thinning, an additional interaction of non-DLVO origin & a decreasing coefficient of friction, respectively, are essential; thus, providing the first explanation for the presence these regimes. Expressions utilized for various interactions and friction are determined from experimental measurements, resulting in an excellent quantitative agreement with previous experiments. </p><p><br></p><p><b>Part II: Motion in a stratified fluid</b></p><p>Density variations due to temperature or salinity greatly influence the dynamics of objects like particles, drops, and microorganisms in oceans. Density stratification hampers the vertical flow & substantially affects the sedimentation of an isolated object, the hydrodynamic interactions between a pair, and the collective behavior of suspensions in various ways depending on the relative magnitude of stratification inertia (advection), and viscous (diffusion) effects. This part investigates these effects and elicits the hydrodynamic mechanisms behind some commonly observed fluid-particle transport phenomena in oceans, like aggregation in horizontal layers. The physical understanding can help us better model these phenomena and, hence, predict their geophysical, engineering, ecological, and environmental implications. </p><p><br></p><p>We investigate the self-propulsion of an inertial swimmer in a linear density stratified fluid using the archetypal squirmer model, which self-propels by generating tangential surface waves. We quantify swimming speeds for pushers (propelled from the rear) and pullers (propelled from the front) by direct numerical solution. We find that increasing stratification reduces the swimming speeds of swimmers relative to their speeds in a homogeneous fluid while reducing their swimming efficiency. The increase in the buoyancy force experienced by these squirmers due to the trapping of lighter fluid in their respective recirculatory regions as they move in the heavier fluid is one of the reasons for this reduction. Stratification also stabilizes the flow around a puller, keeping it axisymmetric even at high inertia, thus leading to otherwise absent stability in a homogeneous fluid. On the contrary, a strong stratification leads to instability in the motion of pushers by making the flow around them unsteady 3D, which is otherwise steady axisymmetric in a homogeneous fluid. Data for the mixing efficiency generated by individual squirmers explain the trends observed in the mixing produced by a swarm of squirmers. </p><p><br></p><p>In addition, the ubiquitous vertical density stratification in aquatic environments significantly alters the swimmer interactions affecting their collective motion &consequently ecological and environmental impact. To this end, we numerically investigate the interactions between a pair of model swimming organisms with finite inertia in a linear density stratified fluid. Depending on the squirmer inertia and stratification, we observe that the squirmer interactions can be categorized as i) pullers getting trapped in circular loops, ii) pullers escaping each other with separating angle decreasing with increasing stratification, iii) pushers sticking to each other after the collision and deflecting away from the collision plane, iv) pushers escaping with an angle of separation increasing with stratification. Stratification also increases the contact time for squirmer pairs. The results presented can help understand the mechanisms behind the accumulation of planktonic organisms in horizontal layers in a stratified environment like oceans and lakes. </p><p><br></p><p>Much work has been done to understand the settling dynamics of spherical particles in a homogeneous and stratified fluid. However, the effects of shape anisotropy on the settling dynamics in a stratified fluid are not entirely understood. To this end, we perform numerical simulations for settling oblate and prolate spheroids in a stratified fluid. We find that both the oblate and prolate spheroids reorient to the edge-wise and partially edge-wise orientations, respectively, as they settle in a stratified fluid completely different from the steady-state broad-side on orientation observed in a homogeneous fluid. We observe that reorientation instabilities emerge when the velocity magnitude of the spheroids falls below a particular threshold. We also report the enhancement of the drag on the particle from stratification. The torque due to buoyancy effects tries to orient the spheroid in an edge-wise orientation, while the hydrodynamic torque tries to orient it to a broad-side orientation. The buoyancy torque dominates below the velocity threshold, resulting in reorientation instability.<br></p>

[pt] Esta dissertação investiga escoamentos multifásicos de deslocamento de fluidos em geometrias anulares envolvidas em operações de cimentação de poços com fluidos espumados. A cimentação desempenha um papel relevante na integridade de poços e algumas aplicações requerem pastas leves com alta resistência à compressão, e o cimento espumado atende a este propósito. Para modelar adequadamente a complexidade do escoamento - que compreende comportamento não-newtoniano e elevada compressibilidade - um modelo tridimensional de dinâmica computacional de fluidos (CFD) foi desenvolvido a partir do código aberto OpenFOAM. As equações de conservação da massa, momento e fases são solucionadas em uma geometria anular, considerando o efeito da pressão na densidade e na reologia dos fluidos, e o método Volume of Fluid (VoF) foi usado para capturar a interface entre fluidos. Os modelos foram validados com soluções exatas para escoamento monofásico axissimétrico com fluidos incompressíveis e compressíveis, e com modelos constitutivos newtonianos e não-newtonianos. Além disso, simulações multifásicas estimaram a eficiência de deslocamento do fluido de perfuração pela pasta de cimento em diferentes condições – constraste de densidade e de viscosidade, ecentricidade e vazões de bombeio – e com diferentes correlações para a reologia dos fluidos espumados. Finalmente, simulações de deslocamento com fluidos com densidade e reologia constante (não-espumados) foram utilizadas para comparação. Os resultados indicam que a eficiência no deslocamento com a técnica de cimentação espumada é superior em condições similares e ilustra que as pastas espumadas são menos suceptíveis a gerarem falhas quanto condições desafiadoras estão presentes. / [en] This master dissertation investigates multiphase displacement flow in annular geometries involved in well cementing operations with foamed cement slurries and spacers. Well cementing plays a relevant role in well integrity and some applications require combining a low-density cement slurry with high compressive strength, and foamed cement suits this purpose. To properly model the displacement complexity involving foamed fluids flow - pressure and temperature dependent densities and non-Newtonian rheology - a 3-dimensional computational fluid dynamics (CFD) model was developed from the open-source OpenFOAM toolbox. The mass, momentum and phase conservation equations are solved in an annular geometry, taking the effect of pressure in the fluid density and rheology, and the volume-of-fluid (VoF) method was used to capture the interface between the fluids. The models were validated using exact solutions for axisymmetric single-phase flow with incompressible and compressible fluids, and Newtonian and non-Newtonian constitutive models. Further, multiphase simulations were performed to estimate the removal efficiency of the drilling fluid by the foamed cement slurry/spacer in different conditions – density and viscosity contrast, eccentricities, and flow rate - and with different correlations for the foamed cement rheological behavior. Finally, the displacement simulations with constant density and rheology displacing fluids (unfoamed) were performed and used to compare the results with the foamed displacing fluids. The results indicate that the displacement efficiency with a foamed cement technique outperforms constant density lightweight cement slurries with similar conditions and are much less sensitive to impairment when challenging conditions are present.

CAPES; Petrobras / Fluidos de perfuração apresentam comportamento viscoplástico, que é definido por uma tensão limite de escoamento. Se a tensão imposta não supera a tensão limite de escoamento, o material se comporta como um sólido elástico, e quando esta tensão é excedida, o fluido escoa como um líquido viscoso. Durante o processo de perfuração de poços de petróleo, válvulas posicionadas na extremidade da coluna de perfuração são atuadas por diferenças de pressão no fluido. Argumenta-se, entretanto, que pressões aplicadas na superfície não são totalmente transmitidas até a válvula, impedindo sua operação. Logo, a transmissão de pressão em fluidos viscoplásticos demanda mais estudo. Para suprir a falta de estudos experimentais sobre o assunto, uma avaliação experimental da transmissão de pressão em um fluido viscoplástico é realizada neste trabalho. O aparato experimental construído para este propósito consiste de uma longa tubulação em formato helicoidal (serpentina) mantida sob temperatura controlada, ao longo da qual estão instalados transdutores de pressão relativa. O fluido é bombeado a uma vazão controlada por uma bomba do tipo helicoidal. Durante os testes, o fluido de trabalho é pressurizado na serpentina até um certo patamar ao mesmo tempo em que as pressões são medidas. Os resultados dos testes com fluidos viscoplásticos corroboram a literatura, que afirma que um fluido com tensão limite de escoamento confinado em uma tubulação fechada não transmite totalmente a pressão imposta na entrada ao longo do restante da tubulação. Além disso, foi observado que a diferença de pressão entre dois pontos da tubulação quando o fluido está em repouso é proporcional à tensão limite de escoamento deste fluido. Os resultados experimentais foram comparados com resultados de simulações numéricas de dois modelos matemáticos desenvolvidos no Centro de Pesquisas em Reologia e Fluidos Não newtonianos (CERNN), com boa concordância. / Drilling fluids exhibit a viscoplastic behavior, which is defined by a yield stress. If the stress imposed to the fluid does not surpass the yield stress, the material behaves like an elastic solid; if the yield stress is exceeded, it flows like a viscous liquid. In well drilling operations, some valves installed on the drillpipe near the bottom of the hole are actuated by pressure differences in the drilling fluid. However, it has been argued that the pressure applied at the surface is not fully transmitted to the valve’s position, preventing its actuation. Therefore, the pressure transmission in viscoplastic fluids demands further investigation. In order to compensate for the lack of experimental studies about the problem, an experimental analysis of the pressure transmission in yield stress fluids has been performed in this work. The experimental rig consists of a long thermally-controlled helical pipe, on which are installed relative pressure transducers. Fluid is displaced by a helical pump at a controlled flow rate. During the experiments, the fluid is pressurized inside the closed pipeline while the pressures are measured and recorded. The results showed that, in agreement with literature, the pressure at one end of a closed pipeline filled with a yield stress fluid is not fully transmitted to the other end. Moreover, it was observed that the pressure gradient in the pressurized fluid is proportional to its yield stress, which indicates a relation between pressure transmission and the presence and magnitude of the yield stress. The experiments were compared to simulation work developed at the Research Center for Rheology and Non-Newtonian Fluids with good agreement.

CERNN / Neste trabalho, propõe-se o estudo numérico do escoamento de fluidos de lei de potência e Bingham junto à interface entre uma região livre e outra porosa (interface fluido-porosa) utilizando o método lattice Boltzmann. Para tanto, considera-se o escoamento entre placas planas e paralelas entre as quais se faz presente um meio poroso abordado de forma heterogênea (resolução espacial da ordem de grandeza dos poros), representado através de obstáculos sólidos quadrados uniformemente distribuídos na parte inferior do canal. As análises realizadas mostram o efeito dos diversos parâmetros adimensionais que descrevem o problema sobre o fator de atrito na região livre do canal. De um modo geral, constata-se que a discrepância entre os fatores de atrito na região livre do canal e para o escoamento entre placas planas e paralelas cresce com o aumento da porosidade e do número de Bingham e com as reduções do número de obstáculos que compõem o meio poroso, número de Reynolds e índice de lei de potência. Ademais, propõe-se a adaptação do modelo analítico para a representação da interface fluido- porosa para escoamento de fluido newtoniano proposto por Ochoa-Tapia e Whitaker (1995b) ao escoamento de fluido de lei de potência, verificando-se a possibilidade de incorporar o comportamento não newtoniano do fluido ao parâmetro empírico do modelo. / The goal of this work is to numerically investigate the flow of power law and Bingham fluids next to the interface between a free and a porous region (fluid-porous interface) using the lattice Boltzmann method. For this, the flow between parallel plates partially filled by a porous material is studied, with the porous medium being represented by a set of solid square obstacles uniformly distributed in lower half of the channel. Results show the influence of non-dimensional parameters in the free region friction factor. In geral, it is observed that the friction factor decreases when porosity or Bingham number are increased and number of obstacles, Reynolds number or power law index are lowered. Moreover, it is porposed the application of the fluid-porous interface model proposed by Ochoa-Tapia e Whitaker (1995b) to the flow of power law fluids by varying the stress jump coefficient with the power law index.

CERNN / Neste trabalho, propõe-se o estudo numérico do escoamento de fluidos de lei de potência e Bingham junto à interface entre uma região livre e outra porosa (interface fluido-porosa) utilizando o método lattice Boltzmann. Para tanto, considera-se o escoamento entre placas planas e paralelas entre as quais se faz presente um meio poroso abordado de forma heterogênea (resolução espacial da ordem de grandeza dos poros), representado através de obstáculos sólidos quadrados uniformemente distribuídos na parte inferior do canal. As análises realizadas mostram o efeito dos diversos parâmetros adimensionais que descrevem o problema sobre o fator de atrito na região livre do canal. De um modo geral, constata-se que a discrepância entre os fatores de atrito na região livre do canal e para o escoamento entre placas planas e paralelas cresce com o aumento da porosidade e do número de Bingham e com as reduções do número de obstáculos que compõem o meio poroso, número de Reynolds e índice de lei de potência. Ademais, propõe-se a adaptação do modelo analítico para a representação da interface fluido- porosa para escoamento de fluido newtoniano proposto por Ochoa-Tapia e Whitaker (1995b) ao escoamento de fluido de lei de potência, verificando-se a possibilidade de incorporar o comportamento não newtoniano do fluido ao parâmetro empírico do modelo. / The goal of this work is to numerically investigate the flow of power law and Bingham fluids next to the interface between a free and a porous region (fluid-porous interface) using the lattice Boltzmann method. For this, the flow between parallel plates partially filled by a porous material is studied, with the porous medium being represented by a set of solid square obstacles uniformly distributed in lower half of the channel. Results show the influence of non-dimensional parameters in the free region friction factor. In geral, it is observed that the friction factor decreases when porosity or Bingham number are increased and number of obstacles, Reynolds number or power law index are lowered. Moreover, it is porposed the application of the fluid-porous interface model proposed by Ochoa-Tapia e Whitaker (1995b) to the flow of power law fluids by varying the stress jump coefficient with the power law index.

[pt] Este trabalho apresenta aplicações da técnica de otimização topológica para problemas de escoamento com fluidos não Newtonianos, usando o método dos elementos virtuais (VEM) em domínios bidimensionais arbitrários. O objetivo é projetar a trajetória ótima, a partir da minimização da energia dissipativa, de um escoamento governado pelas equações de Navier-Stokes-Brinkman e do modelo não Newtoniano de Carreau-Yasuda. A abordagem de porosidade proposta por (Borrvall e Petersson, 2003) [1] é usada na formulação do problema de otimização topológica. Para resolver este problema numericamente é usado o método VEM, recentemente proposto. A principal característica que diferencia o VEM do método dos elementos finitos (FEM) é que as funções de interpolação no interior dos elementos não precisam ser computadas explicitamente. Isso ocorre porque a integração é feita em funções polinomiais e bases de ordem inferior, permitindo assim uma grande flexibilidade no que diz respeito ao uso de elementos não convexos. Portanto, o cálculo das matrizes e vetores elementares se reduz à avaliação de grandezas geométricas nos contornos desses elementos. Finalmente, são apresentados exemplos numéricos representativos para demonstrar a eficiência do VEM em comparação com o FEM e a aplicabilidade da otimização topológica para esta classe de problemas de escoamento. / [en] This work presents selected applications of topology optimization for non-Newtonian fluid flow problems using the virtual element method (VEM) in arbitrary two-dimensional domains. The objective is to design an optimal layout into a fluid flow domain to minimize dissipative energy governed by the Navier-Stokes-Brinkman and non-Newtonian Carreau-Yasuda model equations. The porosity approach proposed by (Borrvall and Petersson, 2003) [1] is used in the topology optimization formulation. To solve this problem numerically, the recently proposed VEM method is used. The key feature that distinguishes VEM from the standard finite element method (FEM) is that the interpolation functions in the interior of the elements do not need to be computed explicitly. This is because the integration is on lower-order polynomial and basis functions, and there is great flexibility by using a non-convex element. Therefore, the computation of the main element matrices and vectors are reduced to the evaluation of geometric quantities on the boundary of the elements. Finally, several numerical examples are provided to demonstrate the efficiency of the VEM compared to FEM and the applicability of the topology optimization to fluid flow problems.

[pt] Umas das etapas mais complexas e críticas durante a construção de poços de petróleo é o processo de cimentação primária, definido como: O processo de instalação de cimento no anular entre o revestimento e a formação exposta ao poço [1]. Ela fornece isolamento zonal permanente para evitar contaminação ou migração de fluidos indesejáveis no anular, protege o revestimento da ocorrência de corrosão e fornece estabilidade hidráulica e mecânica para o revestimento ao longo da vida produtiva do poço de petróleo. Neste processo, ainda na etapa de perfuração, irregularidades na seção transversal (washouts) podem ser geradas como resultado de diversos colapsos parciais da seção do poço aberto em decorrência da presença de rochas pouco consolidadas da formação. Uma operação de cimentação primária bem sucedida dependerá se o sistema de fluidos espaçadores e a pasta de cimento deslocam de forma adequada e completa o fluido de perfuração do anular e washouts. Motivados por esse problema industrial, a presente dissertação usa um simulador numérico DNS (Direct Numerical Simulation) com o objetivo de analisar sistematicamente o comportamento hidrodinâmico e calcular a eficiência do deslocamento entre dois fluidos newtonianos miscíveis através de um anular contendo uma expansão seguida de uma contração abrupta. Investigamos como diferentes viscosidades e densidades dos fluidos, um injetado e outro deslocado, a miscibilidade entre eles, a taxa de injeção e a dimensão do washout retangular afetam o escoamento bifásico. Consideramos uma geometria axissimétrica durante processos de deslocamentos verticais, e as equações governantes são resolvidas em coordenadas cilíndricas, permitindo investigar diferentes aberturas anulares. Devido à miscibilidade entre os fluidos, nossos resultados preveem eficiências de deslocamento altíssimas, próximas a 100 Fluidos não-newtonianos são usualmente utilizados durante o processo industrial de cimentação primária de poços de petróleo. Contudo, as altas eficiências de deslocamentos encontradas em nossos resultados motivam estudos futuros sobre a influência da miscibilidade em deslocamentos de fluidos complexos. Estes resultados também motivam o uso de fluidos espaçadores para tentar controlar as propriedades de interface. Desta forma, é possível que a utilização de sistemas que se aproximem das condições reológicas e hidrodinâmicas de deslocamento entre fluidos newtonianos miscíveis poderá contribuir para um aumento da eficiência de deslocamento e, consequentemente, otimizar o processo de deslocamento de sistemas de fluidos, tendo em vista melhorias na integridade da cimentação de poços de petróleo. / [en] One of the most complex and critical stages during the construction ofoil wells is the primary cementing process, defined as the process of installingcement in the annulus between the casing and the exposed formation to thewell [1]. Primary cementing provides permanent zonal isolation to preventcontamination or migration of unwanted fluids in the annulus, protects thecasing from corrosion, and provides hydraulic and mechanical stability forthe casing throughout the productive life of the oil well. In this process,during the drilling stage, irregularities in the cross-section (washouts) can begenerated because of various partial collapses of the open wellbore section dueto the presence of poorly consolidated rocks in the formation. A successfulprimary cementing operation will depend on whether the spacer fluid systemand cement slurry adequately and completely displace the drilling fluid fromthe annulus and washouts.Motivated by this industrial problem, the present dissertation uses aDirect Numerical Simulation (DNS) numerical simulator to systematically analyze the hydrodynamic behavior and calculate the displacement efficiency between two miscible newtonian fluids through an annulus containing an expansion followed by an abrupt contraction. We investigate how different viscositiesand densities of the injected and displaced fluids, their miscibility, injectionrate, and the dimension of the rectangular washout affect the two-phase flow.We consider an axisymmetric geometry during vertical displacement processes,and the governing equations are solved in cylindrical coordinates, allowing theinvestigation of different annular clearances. Due to the miscibility betweenthe fluids, our results predict very high displacement efficiencies, close to 100Non-newtonian fluids are commonly used during the industrial processof primary cementing of oil wells. However, the high displacement efficienciesfound in our results motivate further studies on the influence of miscibilityin displacements of complex fluids. These results also encourage the use ofspacer fluids attempting to control the interfacial properties. Therefore, the useof systems that approximate the rheological and hydrodynamic conditions ofdisplacement between miscible newtonian fluids may contribute to an increasein displacement efficiency and, consequently, optimize the displacement processof fluid systems, aiming at improvements in the integrity of well cementing.