Blood is a dense suspension of flexible red blood cells. In response to a background flow, these cells distribute themselves non-uniformly throughout the vessel. As a result, material properties that are well defined in homogeneous fluids, such as viscosity, are no longer so, and depend upon the flow geometry along with the particle properties. Using a simple model that accounts for the steady-state particle distribution in vessel flow, we derive an expression for the effective viscosity of blood and the suspension flow velocity field in a pressure-driven tube flow. <br /><br /> We derive the steady-state particle distribution from a conservation equation with convective flux arising from particle deformation in the flow. We then relate the particle microstructure to the overall flow through a generalized Newtonian stress-tensor, with the particle volume fraction appearing in the expression for the local viscosity. Comparing with experimental data, we show that the model quantitatively reproduces the observed rheology of blood in tube flow. <br /><br /> We reconsider the problem in an alternate geometry corresponding to the flow between two concentric cylinders. The steady-state particle distribution, suspension velocity field and the measured effective viscosity are all very different from their counterparts in tube flow, casting serious doubt upon the practice of using data from a Couette viscometer to parameterize constitutive models applied to vascular blood flow. <br /><br /> Finally, we calculate the effect of random fluctuations in the particle velocity on the averaged behaviour of the particle conservation equation. Using a smoothing method for linear stochastic differential equations, we derive a correction to the free Einstein-Stokes diffusion coeffcient that is due to the interaction of the particles with their neighbours.

Magnetohydrodynamic (MHD) flows in annular channels are of great current interest due to experimental search for the so-called magnetorotational instability (MRI) which is important for astrophysical applications (accretion disk physics, magnetic dynamo effect). <p>The main point of MRI experiments is to study the stability of liquid metal rotating in an external magnetic field. Two different types of fluid rotation are proposed: Taylor-Couette flow between rotating coaxial cylinders and electrically driven flow in transverse magnetic field. The implementation of MRI experiments and explanation of experimental results requires a theoretical study of the equilibrium and the stability of MHD flow in an annular channel. This is one of the main tasks of present thesis.<p>For study of equilibrium Taylor-Couette and electrically driven flows, a numerical code is developed which is based on the finite difference scheme with Jacobi iterations. The structure of flows is calculated for different parameters of the experiment. Effect of the inertia on the rotation profiles is investigated in detail. The approximate analytical expressions are obtained for radial profiles of rotation that can be used for optimization of the experimental device for MRI investigation. Equilibrium Taylor-Couette and electrically driven flows are compared from the perspective of experimental studies of MRI.<p>The spectral stability of electrically driven flow is studied by solving the eigen-value problem. This study is performed in the frames of both ideal and dissipative MHD models. It is shown that electrically driven flow can be destabilized through the mechanism of MRI if fluid velocity exceeds some instability threshold, which is determined by non-axisymmetric modes. The obtained results are compared with available experimental data.<p>A general variational method is developed for the stability study of MHD flows of ideal compressible fluids. It is shown that the linearized dynamics of such fluids has an infinite set of invariants. A necessary and sufficient stability criterion can be obtained after inclusion of one or several such invariants in analysis. An analytical example is presented to confirm the fruitfulness of the developed method.

Mixing is a common feature of stratified fluids. In stratified fluids the density varies with the height. This is true for the most fluids in geophysical environments, like lakes, the atmosphere or the ocean. Turbulent mixing plays a crucial role for the overall energy budget of the earth and has therefore an huge impact on the global climate. By introducing the mixing efficiency, it is possible to quantify mixing. It is defined as the ratio of gain of potential energy to the injection of mechanical energy. In the ocean energy provided by tidal forces leads to turbulence and thus highly dense water is lifted up from the deep sea to the surface. For this process, a mixing efficiency of 0.2 is estimated. Until now it is not completely understood how this high value can be achieved. Thus we measured the mixing efficiency by using a Couette-Taylor system, which can produce steady-state homogeneous turbulence. This is similar to what we find in the ocean. The Couette-Taylor system consists of two concentric cylinders that can be rotated independently. In between a stratified fluid is filled using salt as a stratifying agent. In the laboratory experiment, we obtained mixing efficiencies in the order of 0.001 as a result. Moreover we found that the mixing efficiency decreases with decreasing stratification like previous laboratory experiments have shown. As this value is two orders of magnitude smaller than what we find in the ocean, further studies will be necessary. / text

Zugl.: Cottbus, Techn. University, Diss.

Techn. Universiẗat, Diss., 2003--Berlin.

Este trabajo es un estudio sobre una transición de onda de gravedad que ocurre en un flujo en régimen turbulento. Esta bifurcación fue descubierta recientemente y hay muchas preguntas abiertas respecto de ella. En particular, no se conoce el mecanismo de la inestabilidad ni se tiene claridad respecto del rol de la turbulencia en ella. En el capítulo 1, además de describirse el fenómeno estudiado, se presentan brevemente los aspectos conocidos de la mecánica de fluidos que son más pertinentes al estudio realizado. Posteriormente se plantean los objetivos. En el segundo capítulo se da una descripción detallada del montaje tipo Taylor-Couette desarrollado durante este trabajo. También se explican los protocolos de medición utilizados. En el capítulo 3 se presentan los resultados experimentales obtenidos. El hallazgo más importante es el hecho de que el número de Froude es, dentro de los parámetros adimensionales considerados, el que mejor describe la bifurcación. Esto resulta evidente al comparar los diagramas de bifurcación de este experimento con el previamente existente. Por otro lado se obtiene la dependencia de las frecuencias propias de algunos modos fundamentales. En esa dependencia es posible observar que la zona en que se desarrolla la inestabilidad coincide con el encuentro de las frecuencias de dos modos propios de superficie. Finalmente, es importante mencionar que se registraron efectos asociados al desgaste del montaje que, junto con algunas diferencias entre estos resultados y los datos experimentales previos, se pueden interpretar como producto de la influencia de ruido en la transición, ruido asociado tanto a las fluctuaciones turbulentas como a las vibraciones mecánicas del montaje. Este aspecto requiere mayor caracterización que permita aislar de mejor manera el rol de la turbulencia. En el capítulo 4 se realiza un análisis teórico que busca determinar la dependencia con la intensidad del flujo de los modos propios de onda de gravedad de la superficie libre. Esto busca determinar la aparición de alguna inestabilidad lineal en los modos a medida que incrementa la intensidad del flujo. Pese a no poderse determinar la estabilidad de los modos, los resultados para la dependencia de las frecuencias propias presentan un buen ajuste a las medidas. Finalmente, en el capítulo 5 se presentan las conclusiones. Entre ellas se menciona una posibilidad respecto de cuál puede ser el mecanismo. Ese mecanismo estaría determinado por la colisión de las frecuencias de dos modos, lo que se sugiere tanto de los resultados experimentales como de los teóricos. Adicionalmente se proponen algunos aspectos que podrían abordar investigaciones futuras.

The purpose of this thesis is to design a physical microchannel model for micro-Couette blood flow that provides constant and controlled conditions to study and analyze Red Blood Cell (RBC) aggregation. The innovation of this work is that the Couette blood flow is created by the motion of a second fluid with different properties, thereby entraining the blood. The experimental work is coupled with three-dimensional numerical simulations performed using a research Computational Fluid Dynamic (CFD) Solver, Nek5000, based on the spectral element method, while the experiments are conducted using a micro Particle Image Velocimetry (μPIV) system with a double frame CCD camera and an inverted laser imaging microscope. The design of the channel (150 × 33 μm and 170 × 64 μm microchannels) is based on several parameters determined numerically, such as the velocity and viscosity ratios and the degree of miscibility between the fluids, and the resulting configurations are fabricated in the laboratory using standard photolithography methods. The microchannel designed numerically is then tested experimentally, first, with a Newtonian fluid (glycerol), then with RBC suspensions to be compared to the simulations results. It was found that, numerically, using a velocity ratio of 4 between the two fluids, a third of the channel thickness corresponds to the blood layer. Within that range, it can be concluded, that the velocity profile of the blood layer is approximately linear as confirmed by experimental tests, resulting in the desired profile to study RBC aggregation in controlled conditions. The effect of several parameters, such as the hematocrit and the shear rate, on the RBC aggregates and the velocity profile is investigated, through experiments on the RBC suspensions. The final goal of this research is to ensure the compatibility of the results between the experiments and the Newtonian numerical model for several ranges of shear rate with the future intention of finding an accurate method to be able to quantitatively analyze aggregates and determine the number of RBC in each aggregate depending on the flow conditions (the shear rate).

La thèse porte sur l'étude de la réduction de traînée par injection de bulles. La réduction de traînée présente un intérêt pour les applications navales puisqu'elle est issue d'une modification des structures cohérentes qui contribuent le plus à la résistance à l'avancement. Le but de cette étude est d'analyser les mécanismes à l'origine de cette diminution du frottement pariétal. L'approche utilisée dans le cadre de cette étude est numérique, elle emploie le code JADIM par une approche Euler-Lagrange : la phase continue est simulée par Simulation Numérique Directe et la phase dispersée est simulée en suivant individuellement chaque bulle. La configuration retenue dans le cadre de cette étude est celle de l'écoulement de Taylor-Couette (écoulement compris entre deux cylindres en rotation). La première partie de la thèse vise à adapter l'outil numérique employé, afin de pouvoir prendre en compte le retour de la phase dispersée via des termes de forçage dans les équations bilan de matière et de quantité de mouvement. La deuxième partie de la thèse vise à étudier l'écoulement porteur en configuration monophasique, afin de disposer d'une référence sur l'écoulement non perturbé. La troisième partie de la thèse a pour objectif d'étudier la dispersion passive des bulles dans le système, afin d'analyser les mécanismes de migrations mis en jeu. Enfin la dernière partie de la thèse vise à étudier l'influence des bulles sur l'écoulement porteur en analysant l'effet de certains paramètres, notamment le taux de vide et la flottabilité. / The study deals with drag reduction induced by bubble injection, its application concerns naval transport. The aim of the study is to shed more light on mechanisms that are involved in this wall friction reduction. The study is based on a numerical approach, and use the JADIM code with an Euler-Lagrange approach: the continuous phase is solved by Direct Numerical Simulation, and the disperse phase by a tracking of each bubble. Within the framework of this study we consider the Taylor-Couette flow configuration (flow between two concentric cylinders in rotation). The first part of the study deals with the modification of the numerical tool, in order to take into account the influence of the disperse phase on the continuous one through forcing terms in the mass and momentum balance equations. The aim of the second part is to study de Taylor-Couette flow in its monophasic configuration, for the purpose of providing a reference of the undisturbed flow. The third part deals with the passive dispersion of bubble in Taylor-Couette flow, in order to analyze the migration mechanisms involved. And the aim of the last part is to study the effects of the disperse phase on the continuous one, by analyzing the influence of bubbly phase parameters (like void fraction and buoyancy).

Les biofilms bactériens se développent sur toute interface liquide-solide dès que les conditions sont favorables. Ils correspondent à des assemblages de microcolonies qui baignent dans une matrice extracellulaire polymérique. Parmi les facteurs contrôlant le développement des biofilms, l’hydrodynamique est un paramètre clé qui affecte la morphologie et la composition du biofilm. Nous nous intéressons plus particulièrement dans cette thèse à l'influence du gradient de vitesse pariétal sur la formation du biofilm. Pour cela, nous utilisons un réacteur Couette-Poiseuille qui permet de travailler sous écoulement laminaire stable dans différentes conditions d'écoulement. Les biofilms obtenus après circulation d'eaux usées, sont prélevés sur des coupons et visualisés par microscopie confocale à balayage laser. Différents paramètres caractérisant la morphologie du biofilm sont déterminés après reconstruction 3D de leur structure à l'aide du modeleur GOCAD. Nous montrons que le transport convectif constitue une étape essentielle dans la formation initiale du biofilm, et qu'un gradient pariétal nul permet d'inhiber le développement de celui-ci / Bacterial biofilms develop on any solid-liquid interface whenever conditions are appropriate. They correspond to microcolony assemblages embedded in an extracellular matrix. Among the factors controlling biofilm growth, hydrodynamics is a key parameter affecting both biofilm morphology and composition. In this thesis we investigate the influence of hydrodynamics, and more precisely the wall shear rate effect on biofilm development. For this purpose, a Couette-Poiseuille reactor, allowing to work under stable laminar flow with different flow velocities, was used. Biofilms grown from urban wastewater on coupon surfaces were observed with confocal scanning microscopy. A 3D modeling using GOCAD software was established, thus allowing the determination of various biofilms structural characteristics. The results show the essential role of convective mass transport in biofilm formation, actually a zero wall shear rate inhibited bacterial deposition, and hence biofilm growth

L’écoulement entre deux cylindres coaxiaux, appelé l’écoulement de Couette-Taylor, a été étudié lorsque le cylindre intérieur tourne. Quatre dispositifs ont été utilisés avec différentes tailles d’entrefer. Les visualisations montrent l’évolution des motifs avec le nombre de Reynolds, Re. La variation du couple sur le cylindre intérieur a été déterminée en utilisant le pseudo-nombre de Nusselt, qui est une mesure du taux de dissipation d’énergie.Pour des faibles valeurs de Re, l’écoulement est laminaire et azimutal, et le couple est proportionnel à Re. Au-delà d’une valeur critique de Re, les rouleaux de Taylor apparaissent et la pente de variation du couple change brutalement. Pour de grandes valeurs de Re, les rouleaux deviennent turbulents et la pente du couple augmente à cause de la dissipation d’énergie turbulente. Le couple a été mesuré jusqu’à Re=45.000 et montre une dépendance avec le rapport de rayons des cylindres et du nombre de vortex. Avant le régime ultime de la turbulence, les états avec plus de rouleaux présentent un couple plus grand et la situation est inversée dans le régime ultime.Une étude du couple agissant sur le cylindre intérieur a été menée en présence d’un liquide viscoélastique contenant des polymères de grande masse molaire. En appliquant des cycles d’accélération-décélération de la rotation du cylindre intérieur, le couple présente une boucle d’hystérèse dont l’aire augmente avec la concentration de polymère. Les statistiques des fluctuations de la turbulence élastique ont été analysées. Le couple exercé par les vortex solitaires obtenus lors de la phase de décélération, avant la relaminarisation complète de l’écoulement, a été étudié. / The flow between two concentric cylinders, i.e., the Couette-Taylor flow, has been investigated when only the inner cylinder rotates. Four set-ups have been employed with 4 values of the radius ratio. Flow visualisations have been performed to analyse the evolution of the flow patterns with the Reynolds number, Re. The variation of the torque acting on the inner cylinder with different parameters has been quantified using the pseudo-Nusselt number, which measures the rate of energy dissipation in the flow.At low Re, the flow is laminar and azimuthal, and the torque is proportional to Re. Above a critical value of Re, Taylor vortices emerge in the flow and the slope of the torque changes drastically. At high values of Re, the vortices become turbulent and the increase rate of torque is enhanced due to the energy dissipation of turbulence. The torque measured up to Re=45 000 depends on the radius ratio of the cylinders and on the number of vortices. Below the ultimate regime of turbulence, flows containing larger number of vortices exert larger levels of torque; above it, flows containing larger number of vortices exert lower levels of torque.A specific study of the torque exerted on the inner cylinder has been carried out with viscoelastic fluids made of large-weight-molecule polymers. If acceleration-deceleration cycles of the rotation of the inner cylinder are applied, the torque exhibits a hysteretic loop, which increases with the polymer concentration. The statistics of the elastic turbulence fluctuations have been analysed. A special focus was made on the torque induced by the solitary vortices obtained in the deceleration phase, before the flow relaminarisation.