Even though fluid mechanics is well developed as a science, there are many physical phenomena that we do not yet fully understand. One of these is the deformation rates and fluid stresses generated in a boundary layer for a non-Newtonian fluid. One such non-Newtonian fluid would be a waxy crude oil flowing in a centrifugal pump. This type of flow can be numerically modeled by a rotating disk system, in combination with an appropriate constitutive equation, such as the relation for a Bingham fluid. A Bingham fluid does not begin to flow until the stress magnitude exceeds the yield stress. However, experimental measurements are also required to serve as a database against which the results of the numerical simulation can be interpreted and validated. The purpose of the present research is to gain a better understanding of the behavior of a Bingham fluid in the laminar boundary layer on a rotating disk. For this project, two different techniques were employed: numerical simulation, and laboratory investigations using Particle Image Velocimetry (PIV) and flow visualization. Both methods were applied to the flow of a Bingham fluid over a rotating disk. In the numerical investigations, the flow was characterized by the dimensionless yield stress Bingham number, By, which is the ratio of the yield and viscous stresses. Using von Kármáns similarity transformation, and introducing the rheological behavior of the fluid into the conservation equations, the corresponding nonlinear two-point boundary value problem was formulated. A solution to the problem under investigation was obtained by numerical integration of the set of Ordinary Differential Equations (ODEs) using a multiple shooting method. The influence of the Bingham number on the flow behavior was identified. It decreases the magnitude of the radial and axial velocity components, and increases the magnitude of the tangential velocity component, which has a pronounced effect on the moment coefficient, CM, and the volume flow rate, Q. In the laboratory investigations, since the waxy crude oils are naturally opaque, an ambitious experimental plan to create a transparent oil that was rheologically similar to the Amna waxy crude oil from Libya was developed. The simulant was used for flow visualization experiments, where a transparent fluid was required. To fulfill the demand of the PIV system for a higher degree of visibility, a second Bingham fluid was created and rheologically investigated. The PIV measurements were carried out for both filtered tap water and the Bingham fluid in the same rotating disk apparatus that was used for the flow visualization experiments. Both the axial and radial velocity components in the (r-z) plane were measured for various rotational speeds. Comparison between the numerical and experimental results for the axial and radial velocity profiles for water was found to be satisfactory. Significant discrepancies were found between numerical results and measured values for the Bingham fluid, especially at low rotational speeds, mostly relating to the formation of a yield surface within the tank. Even though the flow in a pump is in some ways different from that of a disk rotating in a tank, some insight about the behavior of the pump flow can be drawn. One conclusion is that the key difference between the flow of a Bingham fluid in rotating equipment from that of a Newtonian fluid such as water relates to the yield surface introduced by the yield stress of the material, which causes an adverse effect on the performance and efficiency of such equipment.

Even though fluid mechanics is well developed as a science, there are many physical phenomena that we do not yet fully understand. One of these is the deformation rates and fluid stresses generated in a boundary layer for a non-Newtonian fluid. One such non-Newtonian fluid would be a waxy crude oil flowing in a centrifugal pump. This type of flow can be numerically modeled by a rotating disk system, in combination with an appropriate constitutive equation, such as the relation for a Bingham fluid. A Bingham fluid does not begin to flow until the stress magnitude exceeds the yield stress. However, experimental measurements are also required to serve as a database against which the results of the numerical simulation can be interpreted and validated. The purpose of the present research is to gain a better understanding of the behavior of a Bingham fluid in the laminar boundary layer on a rotating disk. For this project, two different techniques were employed: numerical simulation, and laboratory investigations using Particle Image Velocimetry (PIV) and flow visualization. Both methods were applied to the flow of a Bingham fluid over a rotating disk. In the numerical investigations, the flow was characterized by the dimensionless yield stress Bingham number, By, which is the ratio of the yield and viscous stresses. Using von Kármáns similarity transformation, and introducing the rheological behavior of the fluid into the conservation equations, the corresponding nonlinear two-point boundary value problem was formulated. A solution to the problem under investigation was obtained by numerical integration of the set of Ordinary Differential Equations (ODEs) using a multiple shooting method. The influence of the Bingham number on the flow behavior was identified. It decreases the magnitude of the radial and axial velocity components, and increases the magnitude of the tangential velocity component, which has a pronounced effect on the moment coefficient, CM, and the volume flow rate, Q. In the laboratory investigations, since the waxy crude oils are naturally opaque, an ambitious experimental plan to create a transparent oil that was rheologically similar to the Amna waxy crude oil from Libya was developed. The simulant was used for flow visualization experiments, where a transparent fluid was required. To fulfill the demand of the PIV system for a higher degree of visibility, a second Bingham fluid was created and rheologically investigated. The PIV measurements were carried out for both filtered tap water and the Bingham fluid in the same rotating disk apparatus that was used for the flow visualization experiments. Both the axial and radial velocity components in the (r-z) plane were measured for various rotational speeds. Comparison between the numerical and experimental results for the axial and radial velocity profiles for water was found to be satisfactory. Significant discrepancies were found between numerical results and measured values for the Bingham fluid, especially at low rotational speeds, mostly relating to the formation of a yield surface within the tank. Even though the flow in a pump is in some ways different from that of a disk rotating in a tank, some insight about the behavior of the pump flow can be drawn. One conclusion is that the key difference between the flow of a Bingham fluid in rotating equipment from that of a Newtonian fluid such as water relates to the yield surface introduced by the yield stress of the material, which causes an adverse effect on the performance and efficiency of such equipment.

In industrial practice greases are mainly used as lubricants in hydrodynamic plain bearings and roller bearings. The use in hydrostatic bearings is avoided due to the difficult controllability. One reason is the complex non-Newtonian flow behavior of greases. The motivation for this paper is the use of greases to increase the efficiency of hydrostatic bearings. The assumption is that the so-called yield stress of consistent greases can lead to self-sealing behavior in the bearing under stationary operation conditions. Assuming a volume-flow-free operation of the bearing, a concept for the active control of the sealing gap height and thus the bearing stiffness was developed. The concept idea is the use of a second medium with Newtonian characteristic for pressure transfer. The grease and the pressure control fluid are structurally separated. The grease is induced in the shortest possible way into the bearing pocket to keep the pressure losses as low as possible. The results of test bench investigations indicate the feasibility of a gap height control with very high bearing stiffness under use of highly consistent greases and initiate further investigation on non-stationary operation.

In the first chapter of the thesis we present an introduction to the visco- plasticity and overview of the presented problems. The constitutive relation for Bingham fluid is derived and in the second chapter. Further there is demon- strated a procedure of proving existence and uniqueness with classical varia- tional method. This method is compared with the same process using modern implicit theory. The last chapter starts with summary of used problem formu- lations and used software. It is then followed by the main part with results of numerical simulations, both for the purpose of used formulations comparison and then verification of the preferred one in more complicated simulations. We expect a possible application of tested approaches on different materials. 1

La technologie du béton progresse très rapidement, principalement en ce qui concerne l'amélioration de ses propriétés mécaniques. Au cours des dernières années, de grands efforts ont été faits pour améliorer l'apparence de la surface du béton. L'amélioration de la surface du béton améliore non seulement l'aspect esthétique du béton, mais protège également le béton contre les agressions provenant de l'environnement. La surface du béton brut présente généralement de nombreux défauts de surface. Ces défauts sont visibles à l'œil nu par des variations de couleur ou de texture. Selon la littérature, l'ensemble de tous ces défauts est dû à la composition initiale du béton, aux formes de remplissage et enfin, aux conditions de conservation après démoulage. Au travers de ma thèse j'ai travaillé sur l'influence de la composition des matériaux cimentaires sur l'aspect final de la surface une fois durcie, et notamment en analysant le rapport E/C. Les essais ont tous été effectués sur de ciment CEM I. Pour la partie expérimentale, nous avons fabriqué des pâtes de ciment et des mortiers avec différents rapports E/C dans des moules métalliques de 4x4x16 $cm^3$. Nous avons utilisé un spectre colorimètre pour mesurer l'intensité de la lumière réfléchie en termes de luminance et un microscope numérique pour mesurer la rugosité des surfaces en termes de surface développée. A partir de nos résultats, nous avons observé que l'augmentation du rapport E/C engendre l'éclaircissement des surfaces et une diminution de la rugosité de la surface des matériaux cimentaires. Nous avons également effectué des essais rhéologiques sur des pâtes et des mortiers frais. Pour les pâtes, un rhéomètre rotatif de l'IRC (Institut de Recherche en Constructibilité) -ESTP Paris a été utilisé, tandis que pour les mortiers, le rhéomètre de CERIB (à Épernon) a été privilégié. Par nos résultats, nous avons observé que l'augmentation de l'eau dans la composition des matériaux cimentaires engendre considérablement la diminution du seuil de cisaillement et de la viscosité. Les modèles mathématiques pour décrire l'écoulement de matériaux cimentaires utilisés étaient les modèles classiques (Bingham, Herschel Bulkley et Casson) et modifiés par Papanastasiou. A partir de la régression numérique, nous avons observé que la loi de Herschel Bulkley et tous les autres modèles modifiés sont bien adaptés pour décrire le comportement des pâtes de ciment. Pour les mortiers, les modèles Bingham, Herschel Bulkley et tous les modèles modifiés sont bien adaptés pour les mortiers fluides. Enfin, la loi de Bingham-Papanastasiou a été choisie pour modéliser l'écoulement des pâtes de ciment via COMSOL multiphysics. Les résultats numériques sont comparés avec ceux d’expérimentation / This thesis deals with the study of the influence of the water variations in the concrete-formwork interface. The proposed approach is intended to analyze two aspects. • The role of the concrete mixing formulation, and the casting procedures on the finished mortar surface. • The movement of water in concrete formwork interface. Firstly, we search to confirm the phenomenological results on the relationship between the luminance of the concrete surface and its roughness, this last being governed by the local W/C ratio in the formwork interface. This relationship will be established for compositions of modern concrete. After, we will examine the role of operational factors on the granular segregation on the mortar surface and their consequences on the bleeding of the specimens, on the water movements as well as on the color of the surface. Parameters : Formulation parameters : granular composition, G/S, S/G, W/C ratio and admixtures Parameters of implementation: Temperature and relative humidity, vibration, waiting time, type of formwork, release agents. Maturation parameters: temperature, relative humidity, form release deadline and carbonation

We study a system of differential-algebraic equations, describing motions of a mass-spring-dashpot oscillator by three different forms of implicit constitu- tive relations. For some problems with fully implicit but linear constitutive laws for combined force, we find conditions for solution stability. Assuming monotone relationship between the displacement, velocity and the respective forces, we prove global existence of the solutions. For a linear spring and a dashpot with maximal monotone relationship between the damping force and the velocity, we prove the global existence and uniqueness result. We also solve this problem numerically for Coulomb-like damping term.

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.