Cette thèse présente une étude expérimentale du problème de mélange dans les fluides complexes, étude menée en partenariat avec l’entreprise Sanofi Pasteur. Le mélange est un acte des plus fréquents dans la vie courante et aussi dans l’activité industrielle. On trouve dans la littérature de nombreuses études s’intéressant aux cuves de mélange pour en améliorer les performances à partir d’observations faites à grande échelle. Par contre, à notre connaissance, il y a peu de recherche sur l’hydrodynamique du mélange dans les fluides complexes. Dans notre travail, on étudie des fluides non-Newtoniens formés de solutions diluées de polymères caractérisés par leurs propriétés rhéofluidifiante et viscoélastique. Il s’agit de solutions aqueuses de Polyacrylamide (PAA) ou de la gomme de Xanthan (XG). Afin d’identifier la différence de comportement avec les fluides Newtoniens, une étude expérimentale avec de l’eau est effectuée dans les mêmes conditions que celles pour les fluides non-Newtoniens. Cette étude a été menée, en premier, sur un modèle réduit d’une cuve de mélange de Sanofi Pasteur. Les résultats obtenus, non représentés dans ce mémoire de thèse, nous ont amenés à mettre en place une étude fondamentale de l’écoulement dans un mélangeur de géométrie plus simple. Il s’agit alors de pouvoir contrôler les conditions initiales et de s’affranchir des effets secondaires de l’agitation pour ne s’intéresser qu’au mélange. Pour cela, la géométrie retenue est celle d’un mélangeur en T avec deux entrées perpendiculaires. L’exploration en 2D des champs de vitesse et de concentration de scalaire dans cette jonction en T est assurée simultanément aux moyens des techniques optiques (PIV et PLIF). Les observations montrent un effet non négligeable sur l’hydrodynamique et le mélange lié à la présence de polymères dans l’écoulement. De plus, les résultats obtenus permettent de calculer la tension de Reynolds uv et les flux de masse vc et uc. Ils seront utilisés par la suite pour vérifier leur conformité avec le modèle k epsilon couramment utilisé dans l’industrie. / This thesis presents an experimental study of the mixing in complex fluids which is conducted in partnership with Sanofi Pasteur. The mixture is one of the most common act in everyday life and also in industrial activities. We found in the literature many studies focusing on the mixing tanks with objective to improve performance based on observation of large scale. By cons, in our knowledge, there is few or no research on the hydrodynamics of a mixture in complex fluides. In our work, we study non-Newtonian fluids formed of diluted solution of polymer which characterized by their viscoelastic and shear thinning properties. We used in this study aqueous solutions of polyacrylamide (PAA) or xanthan gum (XG). To identify the difference in behavior with Newtonian fluid, an experimental study with water is carried out under the same conditions as those non-Newtonian fluids. At first, this study was on a reduced mixing tank of Sanofi Pasteur. The results, which not shown in this thesis, led us to develop a fundamental study of flow in a mixer with a simple geometry. The objective is to be able to control the initial conditions and to avoid the side effects of agitation to focus on the mixture. For this, we chose a mixer in a T shape with two perpendicular inputs. Exploring 2D velocity and scalar concentration fields in this T-junction is provided simultaneously of optical techniques (PIV and PLIF). Observations show a significant effect on the hydodynamic and mixture related to the presence of polymers in the flow. In addition, results are used to calculate the Reynolds stress uv and the scalar flux vc and uc. They will be used to check their compliance with the k epsilon model that commonly used in industry.

A simulação computacional de escoamentos incompressíveis multifásicos tem avançado continuamente e é uma área extremamente importante em Dinâmica de Fluidos Computacional (DFC) por suas várias aplicações na indústria, em medicina e em biologia, apenas para citar alguns exemplos. Apresentamos modelos matemáticos e métodos numéricos tendo em vista simulações computacionais de fluidos bifásicos newtonianos e viscoelásticos (não newtonianos), em seus regimes transiente e estacionário de escoamento. Os ingredientes principais requeridos são o Modelo de Um Fluido e o Método da Fronteira Imersa em malhas adaptativas, usados em conjunto com os métodos da Projeção de Chorin-Temam e de Uzawa. Tais metodologias são obtidas a partir de equações a derivadas parciais simples as quais, naturalmente, são resolvidas em malhas adaptativas empregando métodos multinível-multigrid. Em certas ocasiões, entretanto, para escoamentos modelados pelas equações de Navier-Stokes (e.g. em problemas onde temos altos saltos de massa específica), tem-se problemas de convergência no escopo destes métodos. Além disso, no caso de escoamentos estacionários, resolver as equações de Stokes em sua forma discreta por tais métodos não é uma tarefa fácil. Verificamos que zeros na diagonal do sistema linear resultante impedem que métodos de relaxação usuais sejam empregados. As dificuldades mencionadas acima motivaram-nos a pesquisar por, a propor e a desenvolver alternativas à metodologia multinível-multigrid. No presente trabalho, propomos métodos para obter explicitamente as matrizes que representam os sistemas lineares oriundos da discretização daquelas equações a derivadas parciais simples que são a base dos métodos de Projeção e de Uzawa. Ter em mãos estas representações matriciais é vantajoso pois com elas podemos caracterizar tais sistemas lineares em termos das propriedades de seus raios espectrais, suas definições e simetria. Muito pouco (ou nada) se sabe efetivamente sobre estes sistemas lineares associados a discretizações em malhas compostas bloco-estruturadas. É importante salientarmos que, além disso, ganhamos acesso ao uso de bibliotecas numéricas externas, como o PETSc, com seus pré-condicionadores e métodos numéricos, seriais e paralelos, para resolver sistemas lineares. Infraestrutura para nossos desenvolvimentos foi propiciada pelo código denominado ``AMR2D\'\', um código doméstico para problemas em DFC que vem sendo cuidado ao longo dos anos pelos grupos de pesquisa em DFC do IME-USP e da FEMEC-UFU. Estendemos este código, adicionando módulos para escoamentos viscoelásticos e para escoamentos estacionários modelados pelas equações de Stokes. Além disso, melhoramos de maneira notável as rotinas de cálculo de valores fantasmas. Tais melhorias permitiram a implementação do Método dos Gradientes Bi-Conjugados, baseada em visitas retalho-a-retalho e varreduras da estrutura hierárquica nível-a-nível, essencial à implementação do Método de Uzawa. / Numerical simulation of incompressible multiphase flows has continuously of advanced and is an extremely important area in Computational Fluid Dynamics (CFD) because its several applications in industry, in medicine, and in biology, just to mention a few of them. We present mathematical models and numerical methods having in sight the computational simulation of two-phase Newtonian and viscoelastic fluids (non-Newtonian fluids), in the transient and stationary flow regimes. The main ingredients required are the One-fluid Model and the Immersed Boundary Method on dynamic, adaptive meshes, in concert with Chorin-Temam Projection and the Uzawa methods. These methodologies are built from simple linear partial differential equations which, most naturally, are solved on adaptive grids employing mutilevel-multigrid methods. On certain occasions, however, for transient flows modeled by the Navier-Stokes equations (e.g. in problems where we have high density jumps), one has convergence problems within the scope of these methods. Also, in the case of stationary flows, solving the discrete Stokes equations by those methods represents no straight forward task. It turns out that zeros in the diagonal of the resulting linear systems coming from the discrete equations prevent the usual relaxation methods from being used. Those difficulties, mentioned above, motivated us to search for, to propose, and to develop alternatives to the multilevel-multigrid methodology. In the present work, we propose methods to explicitly obtain the matrices that represent the linear systems arising from the discretization of those simple linear partial differential equations which form the basis of the Projection and Uzawa methods. Possessing these matrix representations is on our advantage to perform a characterization of those linear systems in terms of their spectral, definition, and symmetry properties. Very little is known about those for adaptive mesh discretizations. We highlight also that we gain access to the use of external numerical libraries, such as PETSc, with their preconditioners and numerical methods, both in serial and parallel versions, to solve linear systems. Infrastructure for our developments was offered by the code named ``AMR2D\'\' - an in-house CFD code, nurtured through the years by IME-USP and FEMEC-UFU CFD research groups. We were able to extend that code by adding a viscoelastic and a stationary Stokes solver modules, and improving remarkably the patchwise-based algorithm for computing ghost values. Those improvements proved to be essential to allow for the implementation of a patchwise Bi-Conjugate Gradient Method which ``powers\'\' Uzawa Method.

A simulação computacional de escoamentos incompressíveis multifásicos tem avançado continuamente e é uma área extremamente importante em Dinâmica de Fluidos Computacional (DFC) por suas várias aplicações na indústria, em medicina e em biologia, apenas para citar alguns exemplos. Apresentamos modelos matemáticos e métodos numéricos tendo em vista simulações computacionais de fluidos bifásicos newtonianos e viscoelásticos (não newtonianos), em seus regimes transiente e estacionário de escoamento. Os ingredientes principais requeridos são o Modelo de Um Fluido e o Método da Fronteira Imersa em malhas adaptativas, usados em conjunto com os métodos da Projeção de Chorin-Temam e de Uzawa. Tais metodologias são obtidas a partir de equações a derivadas parciais simples as quais, naturalmente, são resolvidas em malhas adaptativas empregando métodos multinível-multigrid. Em certas ocasiões, entretanto, para escoamentos modelados pelas equações de Navier-Stokes (e.g. em problemas onde temos altos saltos de massa específica), tem-se problemas de convergência no escopo destes métodos. Além disso, no caso de escoamentos estacionários, resolver as equações de Stokes em sua forma discreta por tais métodos não é uma tarefa fácil. Verificamos que zeros na diagonal do sistema linear resultante impedem que métodos de relaxação usuais sejam empregados. As dificuldades mencionadas acima motivaram-nos a pesquisar por, a propor e a desenvolver alternativas à metodologia multinível-multigrid. No presente trabalho, propomos métodos para obter explicitamente as matrizes que representam os sistemas lineares oriundos da discretização daquelas equações a derivadas parciais simples que são a base dos métodos de Projeção e de Uzawa. Ter em mãos estas representações matriciais é vantajoso pois com elas podemos caracterizar tais sistemas lineares em termos das propriedades de seus raios espectrais, suas definições e simetria. Muito pouco (ou nada) se sabe efetivamente sobre estes sistemas lineares associados a discretizações em malhas compostas bloco-estruturadas. É importante salientarmos que, além disso, ganhamos acesso ao uso de bibliotecas numéricas externas, como o PETSc, com seus pré-condicionadores e métodos numéricos, seriais e paralelos, para resolver sistemas lineares. Infraestrutura para nossos desenvolvimentos foi propiciada pelo código denominado ``AMR2D\'\', um código doméstico para problemas em DFC que vem sendo cuidado ao longo dos anos pelos grupos de pesquisa em DFC do IME-USP e da FEMEC-UFU. Estendemos este código, adicionando módulos para escoamentos viscoelásticos e para escoamentos estacionários modelados pelas equações de Stokes. Além disso, melhoramos de maneira notável as rotinas de cálculo de valores fantasmas. Tais melhorias permitiram a implementação do Método dos Gradientes Bi-Conjugados, baseada em visitas retalho-a-retalho e varreduras da estrutura hierárquica nível-a-nível, essencial à implementação do Método de Uzawa. / Numerical simulation of incompressible multiphase flows has continuously of advanced and is an extremely important area in Computational Fluid Dynamics (CFD) because its several applications in industry, in medicine, and in biology, just to mention a few of them. We present mathematical models and numerical methods having in sight the computational simulation of two-phase Newtonian and viscoelastic fluids (non-Newtonian fluids), in the transient and stationary flow regimes. The main ingredients required are the One-fluid Model and the Immersed Boundary Method on dynamic, adaptive meshes, in concert with Chorin-Temam Projection and the Uzawa methods. These methodologies are built from simple linear partial differential equations which, most naturally, are solved on adaptive grids employing mutilevel-multigrid methods. On certain occasions, however, for transient flows modeled by the Navier-Stokes equations (e.g. in problems where we have high density jumps), one has convergence problems within the scope of these methods. Also, in the case of stationary flows, solving the discrete Stokes equations by those methods represents no straight forward task. It turns out that zeros in the diagonal of the resulting linear systems coming from the discrete equations prevent the usual relaxation methods from being used. Those difficulties, mentioned above, motivated us to search for, to propose, and to develop alternatives to the multilevel-multigrid methodology. In the present work, we propose methods to explicitly obtain the matrices that represent the linear systems arising from the discretization of those simple linear partial differential equations which form the basis of the Projection and Uzawa methods. Possessing these matrix representations is on our advantage to perform a characterization of those linear systems in terms of their spectral, definition, and symmetry properties. Very little is known about those for adaptive mesh discretizations. We highlight also that we gain access to the use of external numerical libraries, such as PETSc, with their preconditioners and numerical methods, both in serial and parallel versions, to solve linear systems. Infrastructure for our developments was offered by the code named ``AMR2D\'\' - an in-house CFD code, nurtured through the years by IME-USP and FEMEC-UFU CFD research groups. We were able to extend that code by adding a viscoelastic and a stationary Stokes solver modules, and improving remarkably the patchwise-based algorithm for computing ghost values. Those improvements proved to be essential to allow for the implementation of a patchwise Bi-Conjugate Gradient Method which ``powers\'\' Uzawa Method.

Atualmente diversos produtos são fabricados por meio de injeção de polímeros, num processo denominado moldagem por injeção: material fundido é injetado em um molde no qual resfria e endurece. Contudo, ao contrário de outros processos de produção, a qualidade da peça criada por meio de moldagem por injeção não depende apenas do material e da sua forma geométrica, mas também da maneira na qual o material é processado durante a moldagem. Por esse motivo, o uso de modelagem matemática e simulações numéricas tem aumentado consideravelmente como maneira de auxiliar o processo de produção e tem-se tornado uma ferramenta indispensável. Desta forma, este projeto tem o propósito de simular o escoamento de fluidos durante a fase de preenchimento do processo de moldagem por injeção, utilizando o modelo 21/2-dimensional, composto por uma equação bidimensional para a pressão, conhecida como equação de Hele-Shaw, e uma equação tridimensional para a temperatura do fluido. Um modelo bidimensional para a temperatura é também desenvolvido e apresentado. Este projeto de doutorado propõe duas estratégias numéricas para a solução da equação de Hele-Shaw. A primeira delas é baseada em uma formulação euleriana do método Smoothed Particle Hydrodynamics, onde os pontos utilizados na discretização não se movem, e não há utilização de malhas. A segunda estratégia é baseada na criação de malhas dinamicamente construídas na região do molde que já encontra-se parcialmente cheio de fluido e subseqüente aplicação do método Control Volume Finite Element Method. Uma estratégia dinâmica do método semi lagrangeano é apresentada e aplicada à solução da equação bidimensional da temperatura. O projeto também pretende investigar três novas abordagens para o tratamento da superfície livre. Duas delas são baseadas na técnica Volume of Fluid e uma delas é uma adaptação meshless do método Front-Tracking. O comportamento não newtoniano do fluido é caracterizado por uma família de modelos de viscosidade. Testes numéricos indicando a confiabilidade das metodologias propostas são conduzidos / Currently, several plastic products are manufactured by polymer injection, in a process named injection molding: molten material is injected into a thin mold where it cools and solidifies. However, unlike other manufacturing processes, the quality of injection-molded parts depends not only on the material and shape of the part, but also on how the material is processed throughout the molding. For this reason, the use of mathematical modelling and numerical simulations has been increasing in order to assist in the manufacturing process, and it has become an essential tool. Therefore, this Sc.D. project has the purpose of simulating the fluid flow during the filling stage of the injection molding process, using the 21/2-dimensional model, compounded by a two-dimensional equation for the pressure field (also known as Hele-Shaw equation) and a three-dimensional equation for the temperature of the fluid. A simpler two-dimensional model for the temperature field is also derived and presented. This project proposes two novel numerical strategies for the solution of Hele-Shaw equation. The first one is based on an Eulerian formulation of the Smoothed Particle Hydrodynamics method, where the particles used in the discretization do not move along as the simulation evolves, thereby avoing the use of meshes. In the second strategy, local active dual patches are constructed on-the-fly for each active point to form a dynamic virtual mesh of active elements that evolves with the moving interface, then the Control Volume Finite Element Method is applied for the pressure field approximation. A dynamic approach of the semi-Lagrangian scheme is applied to the solution of the two-dimensional temperature equation. The project also assesses three new approaches for the treatment of the free surface of the fluid flow. Two of them are based on the Volume of Fluid technique and one of them is a meshless adaptation of the Front-Tracking method. The non-Newtonian behavior is characterized by a family of generalized viscosity models. Supporting numerical tests and performance studies, which assess the accuracy and the reliability of the proposed methodologies, are conducted

Atualmente diversos produtos são fabricados por meio de injeção de polímeros, num processo denominado moldagem por injeção: material fundido é injetado em um molde no qual resfria e endurece. Contudo, ao contrário de outros processos de produção, a qualidade da peça criada por meio de moldagem por injeção não depende apenas do material e da sua forma geométrica, mas também da maneira na qual o material é processado durante a moldagem. Por esse motivo, o uso de modelagem matemática e simulações numéricas tem aumentado consideravelmente como maneira de auxiliar o processo de produção e tem-se tornado uma ferramenta indispensável. Desta forma, este projeto tem o propósito de simular o escoamento de fluidos durante a fase de preenchimento do processo de moldagem por injeção, utilizando o modelo 21/2-dimensional, composto por uma equação bidimensional para a pressão, conhecida como equação de Hele-Shaw, e uma equação tridimensional para a temperatura do fluido. Um modelo bidimensional para a temperatura é também desenvolvido e apresentado. Este projeto de doutorado propõe duas estratégias numéricas para a solução da equação de Hele-Shaw. A primeira delas é baseada em uma formulação euleriana do método Smoothed Particle Hydrodynamics, onde os pontos utilizados na discretização não se movem, e não há utilização de malhas. A segunda estratégia é baseada na criação de malhas dinamicamente construídas na região do molde que já encontra-se parcialmente cheio de fluido e subseqüente aplicação do método Control Volume Finite Element Method. Uma estratégia dinâmica do método semi lagrangeano é apresentada e aplicada à solução da equação bidimensional da temperatura. O projeto também pretende investigar três novas abordagens para o tratamento da superfície livre. Duas delas são baseadas na técnica Volume of Fluid e uma delas é uma adaptação meshless do método Front-Tracking. O comportamento não newtoniano do fluido é caracterizado por uma família de modelos de viscosidade. Testes numéricos indicando a confiabilidade das metodologias propostas são conduzidos / Currently, several plastic products are manufactured by polymer injection, in a process named injection molding: molten material is injected into a thin mold where it cools and solidifies. However, unlike other manufacturing processes, the quality of injection-molded parts depends not only on the material and shape of the part, but also on how the material is processed throughout the molding. For this reason, the use of mathematical modelling and numerical simulations has been increasing in order to assist in the manufacturing process, and it has become an essential tool. Therefore, this Sc.D. project has the purpose of simulating the fluid flow during the filling stage of the injection molding process, using the 21/2-dimensional model, compounded by a two-dimensional equation for the pressure field (also known as Hele-Shaw equation) and a three-dimensional equation for the temperature of the fluid. A simpler two-dimensional model for the temperature field is also derived and presented. This project proposes two novel numerical strategies for the solution of Hele-Shaw equation. The first one is based on an Eulerian formulation of the Smoothed Particle Hydrodynamics method, where the particles used in the discretization do not move along as the simulation evolves, thereby avoing the use of meshes. In the second strategy, local active dual patches are constructed on-the-fly for each active point to form a dynamic virtual mesh of active elements that evolves with the moving interface, then the Control Volume Finite Element Method is applied for the pressure field approximation. A dynamic approach of the semi-Lagrangian scheme is applied to the solution of the two-dimensional temperature equation. The project also assesses three new approaches for the treatment of the free surface of the fluid flow. Two of them are based on the Volume of Fluid technique and one of them is a meshless adaptation of the Front-Tracking method. The non-Newtonian behavior is characterized by a family of generalized viscosity models. Supporting numerical tests and performance studies, which assess the accuracy and the reliability of the proposed methodologies, are conducted

<p>The present dissertation focuses on two themes: (i) elastic instability of flow and (ii) elastic instability of microscopic filaments.</p> <p><br></p> <p>(i) The presence of macromolecules often leads to the viscoelastic nature of industrial and biological fluids. The flow of viscoelastic fluids in porous media is important in many industrial, geophysical, and biological applications such as enhanced oil recovery, groundwater remediation, biofilm formation, and drug delivery. The stretching of polymeric chains as the viscoelastic fluid passes through the microstructure of the porous media induces large elastic stresses, which leads to viscoelastic instability at the Weissenberg number greater than a critical value, where the Weissenberg number quantifies the ratio of elastic to viscous forces. Viscoelastic instability can lead to a time-dependent chaotic flow even at negligible inertia, which is sometimes also known as elastic turbulence due to its analogous features to traditional inertial turbulence. In the present thesis, we investigate the pore-scale viscoelastic instabilities and the flow states induced by the instabilities in symmetric and asymmetric geometries. We found that the topology of the polymeric stress field regulates the formation of different flow states during viscoelastic instabilities. Viscoelastic instability-induced flow states exhibit hysteresis due to the requirement of a finite time for the transformation of polymeric stress topology. Further, we study viscoelastic flows through ordered and disordered porous geometries and explore the effect of viscoelastic instability on sample-scale transport properties. Viscoelastic instability enhances transverse transport in ordered porous media and longitudinal transport in disordered porous media. We also derive a relationship between the polymeric stress field and the Lagrangian stretching field. The Lagrangian stretching field helps to predict the feature of flow states and transport in complex flows. The experimental measurement of the polymeric stress field is extremely challenging. The framework established here can be used to obtain the topology of the polymeric stress field directly from the easily measured velocity field.  </p> <p><br></p> <p><br></p> <p>(ii) The interaction between flow and elastic filaments plays an important role in sperm and bacterial motility and cell division. The sperm cells of many organisms use long elastic flagellum to propel themselves and also face complex flows and boundaries during their search for egg cells. Strong flows have the potential to mechanically inhibit flagellar motility through elastohydrodynamic interactions. We explore the effects of an extensional flow on the buckling dynamics of sperm flagella through detailed numerical simulations and microfluidic experiments. Compressional fluid forces lead to rich buckling dynamics of the sperm flagellum beyond a critical dimensionless sperm number, which represents the ratio of viscous force to elastic force. Shear flows navigate the sperm cells in complex geometries and flows. We have also studied the effect of flow strength and flagellar elastic deformation on the sperm trajectory in simple shear and Poiseuille flows.</p>

Die vorliegende Arbeit beschreibt eine experimentelle Untersuchung der Schichtbildung von nichtnewtonschen Flüssigkeiten im Tiefdruckverfahren auf nicht saugfähigen Substraten. Das fluiddynamisch bedingte „viscous fingering“ beim Farbspaltungsprozess soll mittels Hydrophobieren der Druckform gehemmt werden. Ziel ist es, möglichst homogene sowie wellenfreie Schichten zu erzeugen. Um ein direkt miteinander vergleichbares Druckergebnis zu erhalten, wird der Druckstoff parallel mit einer unbehandelten und hydrophobierten Form bedruckt. Als Druckstoff werden anstelle von Druckfarbe funktionale Materialien (vorzugsweise PEDOT:PSS) verwendet und variiert, wobei die elektrischen und geometrischen Schichteigenschaften, beispielsweise der elektrische Widerstand und die Rauheit, zur Ermittlung der gesetzten Ziele untersucht wurden. Hiermit und mittels Nutzung einer hydrophobierten Druckform kann eine deutliche Minderung der Wellenbildung (viscous fingering) bei vielen Druckstoffarten beobachtet werden. Die Minderung des viscous fingering im Farbspaltungsprozess und eine nahezu vollständige Leerung der hydrophobierten Tiefdruckform haben einen wesentlichen Nutzwert für den künftigen Einsatz nicht nur für die „gedruckte Elektronik“. / In this work is described experimental research about layer forming from non-Newtonian fluids in gravure printing on non-porous substrates. The viscous fingering, caused through fluid dynamics at splitting of printed material should be decreased by hydrophobic-surface modification of gravure printing form. The aim was to print wave-free homogenous layers. To achieve comparable results, modified and pure form were used simultaneously to print the same material. The printed material was mainly PEDOT:PSS and other, which is used in printed electronics. The properties (surface tension, viscosity) of printed materials were varied by additives. Printing conditions were varied too. The characteristic of printed layers were studied: resistivity, roughness, density, etc. The results shows decreasing of waviness, roughness and viscous fingering in final layer through use of hydrophobic gravure printing form, compared to print results with common printing form. This can be applied not only in the field of printed electronics.

[pt] Filmes finos de líquido estão presentes em uma variedade de sistemas e aplicações. Estamos interessados em filmes compostos por duas camadas, que são comuns no processo de revestimento por cortina. No revestimento por cortina, o líquido cai de uma matriz formando uma cortina formada por um filme fino antes de molhar o substrato em movimento. Um dos limites mais importantes do processo é a ruptura da cortina, que define um limite inferior para a vazão do líquido de revestimento. Consequentemente, este limite inferior da vazão define a espessura mínima viável do filme depositado. Evidências experimentais mostraram que o uso de uma cortina compostas por duas camadas, com uma das camadas sendo mais fina e viscoelástica, pode atrasar a ruptura da cortina para taxas de fluxo mais baixas. A quebra de filmes líquidos de duas camadas, compostas por um líquido newtoniano e um viscoelástico, é estudado por meio da resolução das equações diferenciais que descrevem a evolução da configuração do filme até seu rompimento. O efeito de diferentes parâmetros no tempo de ruptura é determinado. Os resultados mostram o mesmo comportamento observado experimentalmente, a fina camada de líquido viscoelástico retarda o rompimento, estabilizando o filme líquido. / [en] Thin liquid sheets are present in a variety of systems and applications. Here, we are interested in double-layered sheets, which are common in the curtain coating process. In curtain coating, the liquid falls from a die forming a thin curtain before wetting the moving substrate. One of the most important process limits is the curtain breakup, which sets a lower limit for the coating liquid flow rate. Consequently, this flow rate lower limit defines the feasible minimum deposited film thickness. Experimental evidence have shown that using a two-layer curtain, with a viscoelastic thin layer, may delay the curtain breakup to lower flow ratios. The breakup of two-layer liquid sheets, composed of a Newtonian and a viscoelastic liquid, is studied by solving the differential equations that describe the evolution of the liquid sheet configuration until breakup. The effect of different parameters on the breakup time is determined. The results show the same behavior observed experimentally, thin viscoelastic liquid layer delays the breakup, stabilizing the liquid sheet.

No description available.

In present finite element study, the dynamics of incompressible isothermal flows of Newtonian and two generalised non-Newtonian models through complex mixing-separating planar channel and circular pipe filled with and without porous media, including Darcy's term in momentum equation, is presented. Whilst, in literature this problem is solved only for planar channel flows of Newtonian and viscoelastic fluids. The primary aim of this study is to examine the laminar flow behaviour of Newtonian and inelastic non-Newtonian fluids, and investigate the robustness of the numerical algorithm. The rheological properties of non-Newtonian fluids are defined utilising a range of constitutive equations, for inelastic non-Newtonian fluids non-linear viscous models, such as Power Law and Bird-Carreau models are used to capture the shear thinning behaviour of fluids. To simulate such complex flows, steady-state solutions are sought employing time-dependent finite element algorithm. Temporal derivatives are discretised using second order Taylor series expansion, while, spatial discretisation is achieved through Galerkin approximation in combination to deal with incompressibility a pressure-correction scheme adopted. In order to achieve the algorithm of semi-implicit form Darcy's-Brinkman equation is utilized for the conversion in Darcy's terms and diffusion, while Crank-Nicolson approach is adopted for stability and acceleration. Simple and complex flows for various complex flow bifurcations of the combined mixing-separating geometries, for both two-dimensional planar channel in Cartesian coordinates, as well as axisymmetric circular tube in cylindrical polar coordinates system are investigated. These geometries consist of a two-inverted channel and pipe flows connected through a gap in common partitions, initially filled with non-porous materials and later with homogeneous porous materials. Computational domain is having variety it has been investigated with many configurations. These computational domains have been appeared in industrial applications of combined mixing and separating of fluid flows both for porous and non-porous materials. Fully developed velocity profile is applied on both inlets of the domain by imposing analytical solutions found during current study for porous materials. Numerical study has been conducted by varying flow rates and flow direction due to a variety in the domain. The influence of varying flow rates and flow directions are analysed on flow structure. Also the impact of increasing inertia, permeability and power law index on flow behaviour and pressure difference are investigated. From predicted solution of present numerical study, for Newtonian fluids a close agreement is realised between numerical solutions and experimental data. During simulations, it has been noticed that enhancing fluid inertia (flow rates), and permeability has visible effects on the flow domains. When the Reynolds number value increases the size and power of the vortex for recirculation increases. Under varying flow rates an early activity of vortex development was observed. During change in flow directions reversed flow showed more inertial effects as compared with unidirectional flows. Less significant influence of inertia has been observed in domains filled with porous media as compared with non-porous. The power law model has more effects on inertia and pressure as compared with Bird Carreau model. Change in the value of permeability gave significant impact on pressure difference. Numerical simulations for the domain and fluids flow investigated in this study are encountered in the real life of mixing and separating applications in the industry. Especially this purely quantitative numerical investigation of flows through porous medium will open more avenues for future researchers and scientists.