Explicações científicas são um dos elementos mais importantes do ensino de ciências. Elas estão relacionadas com a noção de natureza de ciência que reproduzimos, à compreensão adequada de conceitos e ao compartilhamento de hipóteses e princípios científicos. Embora não haja uma definição única de explicação científica que seja aceita de forma consensual por parte dos pesquisadores desse tema, nas últimas décadas ele tem sido abordado em um número crescente de trabalhos publicados em periódicos internacionais especializados em pesquisas sobre Ensino de Ciências. Apesar disso, consideramos que este tema tem recebido pouca atenção da comunidade de pesquisa em ensino de Ciências no Brasil, em particular no que diz respeito a atividades relacionadas à construção de explicações científicas durante a formação de professores. Neste trabalho investigamos elementos que fazem parte de explicações produzidas por futuros professores e a forma como estes elementos são relacionados entre si na organização da explicação. Para isso, propomos uma forma de estrutura organizacional de explicações científicas e a utilizamos para analisar seminários apresentados por alunos de um curso de licenciatura em Física durante uma das disciplinas deste curso, referente a tópicos relacionados ao conteúdo de mecânica. Nossa estrutura organizacional foi elaborada a partir de trabalhos realizados por James Wertsch (2008) sobre narrativas, a partir dos quais adaptamos para o estudo de explicações científicas duas estruturas que Wertsch propôs com respeito a narrativas: explicações específicas e moldes esquemáticos explicativos. Relacionamos as explicações específicas aos momentos explicativos propostos por Ogborn, Kress, Martins e Mcgillicuddy (1996) e os moldes esquemáticos explicativos a tipos de explicações propostos por filósofos das explicações – em particular o modelo Mecânico-Causal, as explicações de Unificação e explicações Funcionais. Em nossa análise empírica buscamos identificar objetivos pedagógicos que os diferentes tipos de explicações científicas identificadas se destinaram a atender e observamos uma (inesperada) baixa ocorrência de explicações científicas nos seminários que acompanhamos, acompanhada de uma forte ênfase no treinamento da habilidade de resolução de problemas matemáticos. Utilizamos estes resultados para problematizar questões relacionadas à formação de professores para a educação básica à luz do uso que é feito de explicações científicas. / Scientific explanations are among the most important elements in science teaching. They relate to the notion of nature of science we reproduce, to the better understanding of concepts and to share scientific principles and hypotheses. Although there is no single scientific explanation's definition consensually accept by researchers in this theme, in the last decades it has been addressed in an increasing number of papers published in international journals on science teaching. However, we believe that this issue has received little attention from the research community in science teaching in Brazil, specially about activities related to constructing scientific explanations during teacher training. In this work we investigate elements related to scientific explanations elaborated by future teachers, and the way those elements are related to each others in explanation organization. For this, we propose an organizational structure of scientific explanation and we use it to analyze seminars presented by students of a Brazilian physics' teacher graduation during one of its disciplines, about topics related to mechanics. Our organizational structure was drawn from works done by James Wertsch (2008) on narratives, from which we adapted two structures that Wertsch proposed with respect to narratives for the study of scientific explanation: specific explanations and explanatory schematic templates. We associated specific explanations with explicative moments proposed by Ogborn, Kress, Martins e Mcgillicuddy (1996) and the schematic explanatory templates to explanation types proposed by explanation philosophers – especially the Causal Mechanical model, the Unification approach and the functional explanations. In our empirical analyze we seek to identify teaching goals that the different types of scientific explanations identified intended to meet and We noticed a (unexpected) low occurrence of scientific explanation in the seminars we follow, beside a strong emphasis on education to provide training in mathematical problem solving abilities. We used those results to discuss issues related to training teachers to basic education in light of the way scientific explanations are used.

Neste trabalho, propomos um conjunto de estratégias para enfrentar os obstáculos epistemológicos à aprendizagem da cinemática na Teoria da Relatividade Restrita. Tais estratégias são baseadas na proposta da noção de perfil conceitual de referencial (Ayala & Frezza, 2007) e visam promover uma interação cognitiva entre a Mecânica Newtoniana e Relativística. O perfil conceitual (Mortimer, 1995-2000) é um modelo para compreender a evolução conceitual em sala de aula. Para tais objetivos, foi desenvolvido um conjunto de ações em uma seqüência de aplicações de pré-testes e pós-testes com a finalidade de explicitar a concepção dos alunos sobre o aspecto a ser investigado e avaliar a evolução conceitual destes. A diferenciação entre as concepções dos alunos e aquelas cientificamente aceitas deu-se através da interpretação das concepções apresentadas, de discussões teóricas acerca do tema e da apresentação de animações construídas com o software Modellus. O público-alvo deste trabalho é formado por alunos de Licenciatura em Física, e o objetivo do mesmo é contribuir para a formação destes estudantes, futuros professores de Física. / In this work, we propose a set of strategies to face the epistemological obstacles to learning the kinematics in the Restricted Theory of Relativity. Such strategies are based on the proposal of the notion of conceptual profile of reference (Ayala & Frezza, 2007) and promote an interaction between cognitive Newtonian Mechanics and Relativistic Mechanics. The conceptual profile (Mortimer, 1995-2000) is a model for understanding the conceptual evolution of students in classroom. For these goals, we developed a set of actions in a sequence of applications of pre-tests and post-tests in order to explain the conception of students on the aspect to be investigated, and to assess your conceptual evolution. The differentiation between the students' conceptions and scientifically acceptable ones came through the interpretation of the concepts presented, theoretical discussions about the topic and the presentation of animations built with the software Modellus. The target of this work is formed by graduation students in Physics in order to contribute to your formation as future physics teachers.

O leite ovino se diferencia do das demais espécies devido à sua riqueza em sólidos. Contudo, mesmo no caso de raças especializadas, a produção de leite é representativamente menor, em termos de volume, quando comparado ao leite de vaca. Em função disso, o resfriamento prolongado ou o congelamento do leite podem ser uma alternativa ao produtor e à indústria. Sendo assim, os objetivos do presente estudo foram avaliar o efeito do resfriamento e do congelamento, por sete dias, sobre as características físico-químicas do leite de ovelhas da raça Lacaune, considerando a influência dos meses do ano, sobre o rendimento da coalhada produzida e as características físicas do soro obtido. Também foi verificada a influência do resfriamento e do congelamento no comportamento reológico, viscosidade e distribuição do tamanho de partículas do leite. Foram realizadas coletas mensais de leite, no período de janeiro a dezembro de 2011, em quatro propriedades produtoras de leite de ovelha, localizadas no Rio Grande do Sul, sendo as amostras encaminhadas ao Laboratório LEITECIA, da UFRGS. Cada amostra foi dividida em três alíquotas: a primeira era analisada no mesmo dia e as restantes armazenadas até sete dias, uma em refrigeração (5ºC) e outra em congelamento doméstico (- 18ºC). As análises realizadas foram: determinação da densidade, pH, acidez titulável, estabilidade ao etanol e estabilidade térmica. Uma alíquota de cada amostra era encaminhada ao Laboratório de Qualidade do Leite, da Embrapa Clima Temperado, para determinação da composição química do leite. Avaliou-se o rendimento da coalhada obtida com cada uma das amostras compostas de leite fresco, resfriado e congelado. O volume de soro foi medido e realizou-se análise de determinação da densidade, pH e acidez titulável. A viscosidade das amostras de leite foi determinada utilizando-se viscosímetro rotacional (Brookfield DV-II + Pro Viscometer, modo LVF, spindle CS4-25). A descrição do comportamento reológico foi feita através da relação entre a taxa de deformação e a tensão de cisalhamento e da aplicação do modelo da Lei da Potência. A comparação dos valores de viscosidade quando os fluidos apresentaram comportamento newtoniano foi realizada a 60 rpm. A distribuição do tamanho de partículas do leite foi determinada através da técnica de difração de laser. Os parâmetros utilizados foram diâmetro médio das partículas, uniformidade da distribuição (Span) e a área de superfície específica. A composição do leite não apresentou variação significativa quando comparados os diferentes tratamentos (P>0,05). Contudo, os teores de proteína e lactose apresentaram variação sazonal. O resfriamento do leite afetou as características físicas das amostras, apresentando menor pH e maior acidez titulável, com a consequente diminuição da estabilidade térmica. Na produção da coalhada, o resfriamento e o congelamento do leite ovino não afetaram o rendimento. A densidade dos soros obtidos não apresentou variação. Porém, o soro da coalhada de leite resfriado apresentou-se mais ácido. As amostras de leite de ovelha analisadas demonstraram comportamento newtoniano. A viscosidade das amostras não foi afetada pelo congelamento do leite, porém o resfriamento provocou aumento deste parâmetro analisado. O diâmetro médio das partículas não apresentou variações. Conclui-se que o congelamento do leite, por até sete dias, não interfere na sua caracterização físico-química. / Ewe milk differs from other species due to its richness in solids. However, even in the case of specialized breeds, milk production is representatively smaller in volume compared to cow milk. As a result, prolonged chilling or freezing of the milk can be an alternative to the dairy producer and the industry. The objectives of this study were to evaluate the effect of cooling and freezing for seven days, on the physicochemical characteristics of milk from Lacaune ewes, considering the influence of the months of the year on the income produced curd and physical characteristics of the whey obtained. The effect of chilling and freezing on rheological properties, viscosity and particle size distribution of the milk were also observed. Milk samples were collected monthly from January to December 2011 in four dairy of Lacaune sheep located in Rio Grande do Sul. Samples were sent to the laboratory LEITECIA, UFRGS. Each sample was divided into three aliquots: the first was analyzed on the same day and the remaining stored up to seven days, one under refrigeration (5ºC) and other under freezing (- 18ºC). Density, pH, titratable acidity, ethanol stability and thermal stability were performed in three aliquots. One aliquot of each sample was sent to the Milk Quality Laboratory of Embrapa Clima Temperado for determination of chemical composition. The three aliquots were used to produce cheese. The yield of the obtained curd in each of the samples comprised from fresh, chilled and frozen milk was determined, as well as volume, density, pH and titratable acidity from whey. Viscosity of milk samples was determined using a rotational viscometer. The description of rheological behavior was made using the relationship between shear rate and shear stress by application of Potency Law model. Comparison of viscosity values, as the fluid showed Newtonian behavior, was performed at 60 rpm. Particle size distribution was determined by laser diffraction technique. Parameters used were average particle diameter, uniformity of distribution (Span) and specific surface area. Milk composition did not change significantly when comparing the different treatments (P> 0.05). However, protein and lactose showed seasonal variation. Milk chilling affected the physical characteristics of the samples, with lower pH and higher acidity, with a consequent decrease in thermal stability. In the production of curd, chilling and freezing of ewe milk did not affect yield. Whey density did not change, although chilled milk produced more acidic whey. Viscosity of the samples was not affected by freezing, but chilling caused an increased viscosity. Average particle diameter showed no variations. In conclusion, freezing of ewe milk for seven days does not interfere with its physic-chemical characterization.

Cette thèse est consacrée à l’étude mathématique des écoulements complexes dans des tubes minces. Les difficultés ne sont pas seulement liées à la rhéologie complexe, mais aussi aux conditions au bord sur la pression en entrée et en sortie (qui sont moins habituelles, mais réalistes du point de vue physique). Dans une première partie, des écoulements quasi-newtoniens stationnaires sont étudiés. D’abord, on utilise la petitesse du domaine pour montrer l’existence de la solution. Ensuite, on écrit un développement asymptotique de cette solution et on calcule formellement ses coefficients. Finalement, on justifie rigoureusement la validité de ce développement en démontrant des estimations d’erreur. Dans une deuxième partie, on considère des écoulements de fluides visco-élastiques décrits par la loi d’Oldroyd en régime stationnaire. Le modèle que nous avons choisi contient un terme diffusif en contrainte, dont l’ordre de grandeur est lié à la petitesse du domaine. Similairement à la première partie, un développement asymptotique est complètement justifié du point de vue mathématique. Dans le cas particulier de domaines axisymétriques une solution numérique est cherchée afin de la comparer à la solution obtenue via la technique asymptotique. Dans une dernière partie, on étudie les équations de Navier-Stokes non stationnaires. Un résultat d’existence des solutions fortes pour des données petites est démontré. Malheureusement, la méthode directe ne nous a pas permis pas d’avoir suffisamment de contrôle par rapport à la petitesse du domaine. Pour obtenir le résultat désiré, on utilise l’approche à la Kato, basé sur la théorie de C0 semigroupes. / This thesis is devoted to the mathematical analysis of complex flows in thin pipes. The difficulties stem not only from the complex rheology, but also from the boundary conditions used involving the pressure (which are rather atypical, but realistic from a physical point of view).In the first part, we study stationary, quasi-newtonian flows. The existence of a solution is shown using the smallness of the domain as a key ingredient. Furthermore, an asymptotic expansion of this solution is sought and its coefficients are formally computed. Lastly, the validity of this expansion is rigorously justified by proving error estimates. In the second part, we consider visco-elastic flows represented by Oldroyd’s law in stationary regime. The model which we have chosen contains a diffusive stress term, whose order of magnitude is related to the smallness of the domain. Similarly to the first part, a complete asymptotic expansion in mathematically justified. For the special case of axisymmetric domains a numerical solution is sought in order to compare it against the one obtained via the asymptotic technique. In the last part we study the non stationary Navier-Stokes equations. An existence result of strong solutions for small initial data is proven. Unfortunately, the direct method – based on energy estimates – doesn’t give us an optimal control of the smallness constant with respect to the size of the domain. To obtain the desired result, we employ the method of C 0 semigroups of linear operators.

[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.

Cette thèse comporte trois chapitres indépendants, consacrés à l’étude mathématique de trois problèmes physiques distincts, ayant pour modèles trois équations aux dérivées partielles différentes. Ces équations relèvent plus précisément de la méthode des surfaces de niveau, de la théorie de l’écoulement incompressible des matériaux non newtoniens et de la théorie cinétique des gaz raréfiés. Le premier chapitre de la thèse porte sur la dynamique des frontières en mouvement et contient une justification mathématique de la procédure numérique dite de ré-initialisation, dont les applications sont nombreuses dans le contexte de la célèbre méthode des surfaces de niveau. Nous appliquons ces résultats pour une classe d’équations issues de la méthode des surfaces de niveau de premier ordre. Nous écrivons la procédure de ré-initialisation comme un algorithme de décomposition et nous étudions la convergence de l’algorithme en utilisant des techniques d’homogénéisation dans la variable temporelle. Grâce à cette analyse rigoureuse nous introduisons également une nouvelle méthode pour l’approximation de la fonction de distance dans le contexte de la méthode des surfaces de niveau. Dans le cas où l’on cherche seulement une fonction de l’ensemble de niveau avec un gradient minoré proche du niveau zéro, nous proposons une approximation plus simple. Dans le cas général, où le niveau zéro pourrait présenter des changements de topologie, nous introduisons une nouvelle notion de limites relâchées. Dans le deuxième chapitre de la thèse, nous étudions un problème de frontière libre résultant de l’étude de l’écoulement incompressible d’un matériau non-newtonien, avec limite d’élasticité de type Drucker-Prager, sur un plan incliné et sous l’effet de la pesanteur. Nous obtenons une équation sous-différentielle, que nous formulons comme un problème variationnel avec un terme à croissance linéaire de type gradient, et nous étudions le problème dans un domaine non borné. Nous montrons que les équations sont bien posées et satisfont certaines propriétés de régularité. Nous sommes alors capables de relier les paramètres physiques avec le problème abstrait et de prouver des propriétés quantitatives de la solution. En particulier, nous montrons que la solution a un support compact, la limite de ce que nous appelons la frontière libre. Nous construisons également des solutions explicites d’une équation différentielle ordinaire qui peut estimer la frontière libre. Enfin, le troisième et dernier chapitre de la thèse est dédié aux solutions de l’équation de Boltzmann homogène avec molécules maxwelliennes et énergie infinie. Nous obtenons de nouveaux résultats d’existence de solutions éternelles pour cette équation dans un espace de mesures de probabilité d’énergie infinie (i.e. de moment d’ordre deux infini). Elles permettent de décrire le comportement asymptotique en temps d’autres solutions d’énergie infinie, mais elles apparaissent aussi comme des états asymptotiques intermédiaires dans l’étude des solutions d’énergie finie, mais arbitrairement grande. Les méthodes issues de l’analyse harmonique sont utilisées pour étudier l’équation de Boltzmann, où la variable de vitesse est exprimée en Fourier. Enfin, un changement d’échelle logarithmique en la variable temporelle permet de déterminer le bon comportement asymptotique à l’infini des solutions / This thesis consists of three different and independent chapters, concerning the mathematical study of three distinctive physical problems, which are modelled by three non- linear partial differential equations. These equations concern the level set method, the theory of incompressible flow of non-Newtonian materials and the kinetic theory of rare- fied gases. The first chapter of the thesis concerns the dynamics of moving interfaces and contains a rigorous justification of a numerical procedure called re-initialization, for which there are several applications in the context of the level set method. We apply these results for first order level set equations. We write the re-initialization procedure as a splitting algorithm and study the convergence of the algorithm using homogenization techniques in the time variable. As a result of the rigorous analysis, we are also able to introduce a new method for the approximation of the distance function in the context of the level set method. In the case where one only looks for a level set function with gradient bounded from below near the zero level, we propose a simpler approximation. In the general case where the zero level might present changes of topology we introduce a new notion of relaxed limits. In the second chapter of the thesis, we study a free boundary problem arising in the study of the flow of an incompressible non-Newtonian material with Drucker-Prager plasticity on an inclined plane. We derive a subdifferential equation, which we reformulate as a variational problem containing a term with linear growth in the gradient variable, and we study the problem in an unbounded domain. We show that the equations are well posed and satisfy some regularity properties. We are then able to connect the physical parameters with the abstract problem and prove some quantitative properties of the solution. In particular, we show that the solution has compact support and the support is the free boundary. We also construct explicit solutions of an ordinary differential equation, which we use to estimate the free boundary. The last chapter of the thesis is dedicated to the study of infinite energy solutions of the homogeneous Boltzmann equation with Maxwellian molecules. We obtain new results concerning the existence of eternal solutions in the space of probability measure with infinite energy (i.e. the second order moment is infinite). These solutions describe the asymptotic behaviour of other infinite energy solutions but could also be useful in the study of intermediate asymptotic states of solutions with finite but arbitrarily large energy. We use harmonic analysis tools to study the equation, where the velocity variable is expressed in the Fourier space. Finally, a logarithmic scaling of the time variable allows to determine the correct asymptotic scaling of the solutions

Radial basis function methods exhibit several very attractive properties such as a high order convergence of the approximated solution and flexibility to the domain geometry. However the method in its classical formulation becomes impractical for problems with relatively large numbers of degrees of freedom due to the ill-conditioning and dense structure of coefficient matrix. To overcome the latter issue we employ a localisation technique, namely a partition of unity method, while the former issue was previously addressed by several authors and was of less concern in this thesis. In this thesis we develop radial basis function partition of unity methods for partial differential equations arising in financial mathematics and glaciology. In the applications of financial mathematics we focus on pricing multi-asset equity and credit derivatives whose models involve several stochastic factors. We demonstrate that localised radial basis function methods are very effective and well-suited for financial applications thanks to the high order approximation properties that allow for the reduction of storage and computational requirements, which is crucial in multi-dimensional problems to cope with the curse of dimensionality. In the glaciology application we in the first place make use of the meshfree nature of the methods and their flexibility with respect to the irregular geometries of ice sheets and glaciers. Also, we exploit the fact that radial basis function methods are stated in strong form, which is advantageous for approximating velocity fields of non-Newtonian viscous liquids such as ice, since it allows to avoid a full coefficient matrix reassembly within the nonlinear iteration. In addition to the applied problems we develop a least squares radial basis function partition of unity method that is robust with respect to the node layout. The method allows for scaling to problem sizes of a few hundred thousand nodes without encountering the issue of large condition numbers of the coefficient matrix. This property is enabled by the possibility to control the coefficient matrix condition number by the rate of oversampling and the mode of refinement.

Le couchage rideau est un procédé d'enduction sans contact qui permet un couchage « contour » d'une feuille de papier dont le point clé est la stabilité du rideau. Ce procédé semble devoir se développer dans les années à venir pour la production de papiers impression-écriture et de papiers et cartons d'emballages. Néanmoins, il existe aujourd'hui un écart important entre la stabilité théorique du rideau et les observations. Nous avons donc analysé par CFD l'écoulement interne dans un dispositif de couchage pilote avec différents fluides Newtoniens et Non-Newtoniens ainsi que l'écoulement externe sur le plan incliné de l'appareil. L'étude de l'écoulement interne par CFD a permis de faire ressortir la cause de vortex pouvant apparaître dans le dispositif. Pour avoir un écoulement sans vortex, le nombre de Reynolds à l'entrée doit être inférieur à une valeur critique égale à 20 pour la géométrie étudiée quel que soit le fluide utilisé. De plus la présence d'une seconde cavité permet de filtrer les perturbations pour des fluides peu rhéofluidifiants, ce qui est le cas des sauces de couchages pour des papiers WFC. Ces résultats ont été validés expérimentalement à l'aide de traceurs et de PIV en utilisant une réplique exacte en Plexiglas de la coucheuse rideau. Enfin en ce qui concerne l'étude de l'écoulement externe sur le plan incliné, l'utilisation de la CFD a permis de conclure que, pour les dispositifs de couchage utilisés et les conditions opératoires de nos industries, certains problèmes présentés dans la littérature ne devraient pas exister. / Curtain coating is a contactless coating process which permits a contour coating of the paper and the key parameter of this process is a perfect stable curtain. This technology is expected to spread widely for graphic paper grades and boards in the next few years. Nevertheless, many experimental works revealed some differences between stability theory and results observed on the curtain. In this work, we performed CFD simulations both for Newtonian and Non-Newtonian fluids on the internal flow in a pilot curtain coater and on the flow down the inclined plane. The CFD study of the internal flow revealed the cause of vortex creation into the coater. To maintain vortex-free operation, the Reynolds number at the inlet must remain below a critical value whatever the fluid, which is equal to 20 with the studied geometry whatever the studied fluid. Moreover, a second cavity is useful since instabilities coming from the first cavity could be filtered for low shear-thinning fluids, which is the case of the WFC coating colours. These simulation results were validated thanks to flow visualization experiments with tracers and PIV using a transparent replica of the coater. Finally CFD simulations on the inclined plane were carried out and permitted to conclude that for the range of operating conditions used on the pilot curtain coater, some issues presented in literature should not exist industrially.

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.