Three different models, relating to the study of microswimmers immersed in a low Reynolds number fluid, are presented. The underlying, mathematical concepts employed in each are developed using singularity methods of Stokes flow. The first topic concerns the motility of an artificial, three-sphere microswimmer with prescribed, non-reciprocal, internal forces. The swimmer progresses through a low Reynolds number, nonlinear, viscoelastic medium. The model developed illustrates that the presence of the viscoelastic rheology, when compared to a Newtonian environment, increases both the net displacement and swimming efficiency of the microswimmer. The second area concerns biological microswimming, modelling a sperm cell with a hyperactive waveform (vigorous, asymmetric beating), bound to the epithelial walls of the female, reproductive tract. Using resistive-force theory, the model concludes that, for certain regions in parameter space, hyperactivated sperm cells can induce mechanical forces that pull the cell away from the wall binding. This appears to occur via the regulation of the beat amplitude, wavenumber and beat asymmetry. The next topic presents a novel generalisation of slender-body theory that is capable of calculating the approximate flow field around a long, thin, slender body with circular cross sections that vary arbitrarily in radius along a curvilinear centre-line. New, permissible, slender-body shapes include a tapered flagellum and those with ribbed, wave-like structures. Finally, the detailed analytics of the generalised, slender-body theory are exploited to develop a numerical implementation capable of simulating a wider range of slender-body geometries compared to previous studies in the field.

Cette thèse traite de la dynamique de cellules sanguines dans la microcirculation. Cette appellation regroupe les deux thématiques de mon travail. La première est l'étude du mouvement de globules rouges soumis à un écoulement de cisaillement. Prenant la suite des travaux réalisés par Manouk Abkarian, Magalie Faivre et Annie Viallat, nous avons étudié le mouvement de cellules dans un flux oscillant et mis en évidence l'apparition de chaos (Dupire J. et al, PRL 104,168101 (2010)). Nous avons ensuite repris l'étude sous écoulement constant pour comprendre les régimes de mouvement encore non étudiés (article accepté à PNAS). Tous ces travaux se basent sur un modèle à forme ellipsoïdale constante (type Keller & Skalak) auquel a été rajouté un terme tenant compte de l'élasticité de la membrane. Pour mieux modéliser la mémoire de forme, nous avons recalculé les équations du modèle en tenant compte d'une nouvelle forme non contrainte du cytosquelette élastique. Elle nous permet entre autres d'ajuster le modèle aux données expérimentales en utilisant des valeurs de viscosité et de module élastique de cisaillement compatibles avec la littérature. Le deuxième partie traite de l'étude du mouvement de globules blancs dans un réseau de canaux microfluidiques. Ce réseau est régulier et possède des dimensions biomimétiques. Nous étudions comment la rhéologie des cellules influe sur leur mouvement à travers le dispositif. Nous montrons que l'entrée des cellules, et donc leur première déformation, peut être utilisée pour obtenir des informations sur leur rhéologie (viscosité, élasticité, tension). / This thesis deals with dynamics of blood cells in microflow. This title regroups two aspects of my work. The first one studies the movement of red blood cells (RBC) under flow. Continuing the work done by M. Abkarian, M. Faivre and A. Viallat, we looked at RBCs in an oscillating shear flow and showed the presence of chaos in the motion (Dupire J. et al, PRL 104,168101 (2010) ). Then we continued the study of RBC under constant flow to understand the regime of motion that were still to elucidate (PNAS, accepted for publication). These works use a ellipsoidal fixed shape model (based on Keller and Skalak's) to which we add an elastic membrane term. To take into account the shape memory, we calculated again the equations of motion considering a new stress-free shape of the elastic cytoskeleton. It allows us to fit the model on the experimental data using viscosity and elasticity coefficient compatible with the litterature. The second part deals with the motion of white blood cell (WBC) in a microfluidic channel network. The device has a regular geometry and has biomimetic shape characteristics matching the human lung mean values. We aim to study how the cell's rheology is related to their motion through the device. We show how the entry of the cell, and thus their first deformation, can be used to obtain information about a single cell rheology (viscosity, elasticity, tension). The motion is then decomposed in 2 phases : a transient regime right after the entrance and a final stationary regime. We study these regimes in terms of cellular deformation and wall friction.

An aluminum NACA 0018 airfoil testbed was constructed with 95 static pressure taps and 25 embedded microphones to enable novel time-resolved measurements of surface pressure. The main objective of this investigation is to utilize time-resolved surface pressure measurements to estimate salient flow characteristics in the separated flow region over the upper surface of an airfoil. The flow development over the airfoil was examined using hot wire anemometry and mean surface pressure for a range of Reynolds numbers from 80x103 to 200x103 and angles of attack from 0° to 18°. For these parameters, laminar boundary layer separation takes place on the upper surface and two flow regimes occur: (i) separation is followed by flow reattachment, so that a separation bubble forms and (ii) separation occurs without subsequent reattachment. Measurements of velocity and mean surface pressure were used to characterize the separated flow region and its effect on airfoil performance using the lift coefficient. In addition, the transition process and the evolution of disturbances were examined. The lift curve characteristics were found to be linked to the rate of change of the separation, transition, and reattachment locations with the angle of attack. For both flow regimes, transition was observed in the separated shear layer. Specifically, the amplification of disturbances within a band of frequencies in the separated shear layer resulted in laminar to turbulent transition. Validation of time-resolved surface pressure measurements was performed for Rec = 100x103 at α = 8° and α = 12°, corresponding to regimes of flow separation with and without reattachment, respectively. A comparative analysis of simultaneous velocity and time-resolved surface pressure measurements showed that the characteristics and development of velocity fluctuations associated with disturbances in the separated shear layer can be extracted from time-resolved surface pressure measurements. Specifically, within the separated flow region, the amplitude of periodic oscillations in the surface pressure signal associated with disturbances in the separated shear layer grew in the streamwise direction. In addition, the frequency at the spectral peak of the amplified disturbances in the separated shear layer was identified. Based on the results of the validation analysis, time-resolved surface pressure measurement analysis techniques were applied for a Reynolds number range from 60x103 to 130x103 and angles of attack from 6° to 16°. Within the separated flow region, the streamwise growth of surface pressure fluctuations is distinctly different depending on the flow regime. Specifically, within the separation bubble, the RMS surface pressure fluctuations increase in the streamwise direction and reach a peak just upstream of the reattachment location. The observed trend is in agreement with that observed for other separating-reattaching flows on geometries such as the forward and backward facing step and splitter plate with fence. In contrast to the separation bubble formation, when the separated shear layer fails to reattach to the airfoil surface, RMS surface pressure fluctuations increase in the streamwise direction with no maximum and the amplitude is significantly lower than those observed in the separation bubble. Surface pressure signals were further examined to identify the frequency, convective velocity, and spanwise uniformity of disturbances in the separated shear layer. Specifically, for both flow regimes, the fundamental frequency and corresponding Strouhal number exhibit a power-law dependency on the Reynolds number. Based on the available data for which velocity measurements were obtained in the separated flow region, the convective velocity matched the mean velocity at the wall-normal distance corresponding to the maximum turbulence intensity. A distinct increase in the convective velocity of disturbances in the separated shear layer was found when the airfoil was stalled in comparison to that found in the separation bubble. From statistical analysis of surface pressure signals in the spanwise direction, it was found that disturbances are strongly two-dimensional in the laminar portion of the separated shear layer and become three-dimensional through the transition process.

An aluminum NACA 0018 airfoil testbed was constructed with 95 static pressure taps and 25 embedded microphones to enable novel time-resolved measurements of surface pressure. The main objective of this investigation is to utilize time-resolved surface pressure measurements to estimate salient flow characteristics in the separated flow region over the upper surface of an airfoil. The flow development over the airfoil was examined using hot wire anemometry and mean surface pressure for a range of Reynolds numbers from 80x103 to 200x103 and angles of attack from 0° to 18°. For these parameters, laminar boundary layer separation takes place on the upper surface and two flow regimes occur: (i) separation is followed by flow reattachment, so that a separation bubble forms and (ii) separation occurs without subsequent reattachment. Measurements of velocity and mean surface pressure were used to characterize the separated flow region and its effect on airfoil performance using the lift coefficient. In addition, the transition process and the evolution of disturbances were examined. The lift curve characteristics were found to be linked to the rate of change of the separation, transition, and reattachment locations with the angle of attack. For both flow regimes, transition was observed in the separated shear layer. Specifically, the amplification of disturbances within a band of frequencies in the separated shear layer resulted in laminar to turbulent transition. Validation of time-resolved surface pressure measurements was performed for Rec = 100x103 at α = 8° and α = 12°, corresponding to regimes of flow separation with and without reattachment, respectively. A comparative analysis of simultaneous velocity and time-resolved surface pressure measurements showed that the characteristics and development of velocity fluctuations associated with disturbances in the separated shear layer can be extracted from time-resolved surface pressure measurements. Specifically, within the separated flow region, the amplitude of periodic oscillations in the surface pressure signal associated with disturbances in the separated shear layer grew in the streamwise direction. In addition, the frequency at the spectral peak of the amplified disturbances in the separated shear layer was identified. Based on the results of the validation analysis, time-resolved surface pressure measurement analysis techniques were applied for a Reynolds number range from 60x103 to 130x103 and angles of attack from 6° to 16°. Within the separated flow region, the streamwise growth of surface pressure fluctuations is distinctly different depending on the flow regime. Specifically, within the separation bubble, the RMS surface pressure fluctuations increase in the streamwise direction and reach a peak just upstream of the reattachment location. The observed trend is in agreement with that observed for other separating-reattaching flows on geometries such as the forward and backward facing step and splitter plate with fence. In contrast to the separation bubble formation, when the separated shear layer fails to reattach to the airfoil surface, RMS surface pressure fluctuations increase in the streamwise direction with no maximum and the amplitude is significantly lower than those observed in the separation bubble. Surface pressure signals were further examined to identify the frequency, convective velocity, and spanwise uniformity of disturbances in the separated shear layer. Specifically, for both flow regimes, the fundamental frequency and corresponding Strouhal number exhibit a power-law dependency on the Reynolds number. Based on the available data for which velocity measurements were obtained in the separated flow region, the convective velocity matched the mean velocity at the wall-normal distance corresponding to the maximum turbulence intensity. A distinct increase in the convective velocity of disturbances in the separated shear layer was found when the airfoil was stalled in comparison to that found in the separation bubble. From statistical analysis of surface pressure signals in the spanwise direction, it was found that disturbances are strongly two-dimensional in the laminar portion of the separated shear layer and become three-dimensional through the transition process.

Small wind turbines that operate in low-wind environments are prone to suffer performance degradation as they often fail to accelerate to a steady, power-producing condition. The behaviour during this process is called “starting behaviour” and it is the subject of this present work. This thesis evaluates potential benefits that can be obtained from the improvement of starting behaviour, investigates, in particular, small wind turbine starting behaviour (both horizontal- and vertical-axis), and presents aerofoil performance characteristics (both steady and unsteady) needed for the analysis. All of the investigations were conducted using a new set of aerodynamic performance data of six aerofoils (NACA0012, SG6043, SD7062, DU06-W-200, S1223, and S1223B). All of the data were obtained at flow conditions that small wind turbine blades have to operate with during the startup - low Reynolds number (from 65000 to 150000), high angle of attack (through 360◦), and high reduced frequency (from 0.05 to 0.20). In order to obtain accurate aerodynamic data at high incidences, a series of CFD simulations were undertaken to illustrate effects of wall proximity and to determine test section sizes that offer minimum proximity effects. A study was carried out on the entire horizontal-axis wind turbine generation system to understand its starting characteristics and to estimate potential benefits of improved starting. Comparisons of three different blade configurations reveal that the use of mixed-aerofoil blades leads to a significant increase in starting capability. The improved starting capability effectively reduces the time that the turbine takes to reach its power-extraction period and, hence, an increase in overall energy yield. The increase can be as high as 40%. Investigations into H-Darriues turbine self-starting capability were made through the analogy between the aerofoil in Darrieus motion and flapping-wing flow mechanisms. The investigations reveal that the unsteadiness associated with the rotor is key to predicting its starting behaviour and the accurate prediction can be made when this transient aerofoil behaviour is correctly modelled. The investigations based upon the analogy also indicate that the unsteadiness can be exploited to promote the turbine ability to self-start. Aerodynamically, this exploitation is related to the rotor geometry itself.

It is well known that when a flexible or flexibly-mounted structure is placed perpendicular to the flow of a Newtonian fluid, it can oscillate due to the shedding of separated vortices at high Reynolds numbers. If the same flexible object is placed in non-Newtonian flows, however, the structure's response is still unknown. The main objective of this thesis is to introduce a new field of viscoelastic fluid-structure interactions by showing that the elastic instabilities that occur in the flow of viscoelastic fluids can drive the motion of a flexible structure placed in its path. Unlike Newtonian fluids, the flow of viscoelastic fluids can become unstable at infinitesimal Reynolds numbers due to the onset of a purely elastic flow instability. This instability occurs in the absence of nonlinear effects of fluid inertia and the Reynolds number of the flows studied here are in the order of 10-4. When such an elastic flow instability occurs in the vicinity of a flexible structure, the fluctuating fluid forces exerted on the structure grow large enough to cause a structural instability which in turn feeds back into the fluid resulting in a flow instability. Nonlinear periodic oscillations of the flexible structure are observed which have been found to be coupled to the time-dependent growth and decay of viscoelastic stresses in the wake of the structure. Presented in this thesis are the results of an investigation of the interaction occurring in the flow of a viscoelastic wormlike micelle solution past a flexible rectangular sheet. The structural geometries studied include: flexible sheet inclinations at 20°, 45° and 90° and flexible sheet widths of 5mm and 2.5mm. By varying the flow velocity, the response of the flexible sheet has been characterized in terms of amplitude and frequency of oscillations. Steady and dynamic shear rheology and filament stretching extensional rheology measurements are conducted in order to characterize the viscoelastic wormlike micelle solution. Bright field images show the deformation of the flexible sheet during an unstable oscillation while flow-induced birefringence images highlight the viscoleastic fluid stresses produced in the wake of the flexible sheet.

No description available.

<div>Advances in modern research have unveiled numerous fundamental and practical benefits of studying the hydrodynamics of microorganisms. Many microorganisms, especially bacteria, actively search for nutrients via a process called chemotaxis. The physical constraints posed by hydrodynamics in the locomotion of microorganisms can combine with their chemotactic ability to significantly affect functions like colonization of nutrient sources. In this thesis, we investigate the interplay between hydrodynamics and chemotaxis toward dictating bacterial distribution around fluid-fluid interfaces, which often act as a source of nutrition. We approach our problem statements using mathematical models and numerical and/or semi-analytical tools. Our studies are particularly relevant in the context of hydrocarbon degradation after oil-spills.</div><div><br></div><div>We begin by showing that the flow generated by rising oil drops delocalizes dissolved nutrient patches in the ocean, and aids chemotactic bacteria in improving their nutrition (over non-chemotactic bacteria) by 45%. We then move from studying colonization of soluble nutrient patches to colonization around nutrient sources, e.g., oil drops, marine snow. Towards this, we first demonstrate the phenomenon of hydrodynamics-mediated 'trapping' of bacteria around oil drops and show that a surfactant-laden drop can retain an approaching bacterium on its surface for approximately 35% longer times than a clean drop. We also analyze hydrodynamic trapping of bacteria around settling marine snow particles and show how bacteria can collide with and colonize the marine snow, even when the latter moves 10 times faster than the former. In all the cases above, we show how the hydrodynamic interactions are complemented by chemotaxis to enable extremely effective bacterial foraging. We next explore how propulsion mechanisms of microorganisms affect their ability to form biofilms on fluid-fluid interfaces and unveil the hydrodynamic origins behind the tendency of flagellated bacteria to swim parallel to plane surfactant-laden interfaces. Finally, we summarize our results, identify further avenues of research and propose problem statements related to them.</div>

No description available.

Une étude expérimentale et numérique traitant de l'influence de structures tourbillonnaires sur la sédimentation de nuage de particules sphériques sous l'effet de la gravité est présentée dans une première partie de ce manuscrit. L'écoulement est créé par électro-convection, ce qui permet de générer un réseau de vortex contrôlés en vitesse et de taille constante qui imite un écoulement tourbillonnaire. Des techniques de PIV (Particle image-velocimetry) et de suivi de particules sont utilisés pour étudier la sédimentation du nuage.Le nuage est modélisé comme un ensemble de particules ponctuelles pour lesquelles les forces d'interaction hydrodynamiques entre particules sont prépondérantes. Le comportement du nuage est comparé aux prédictions obtenues avec des modèles numériques. Dans une seconde partie est présentée une étude expérimentale et numérique concernant la sédimentation à faible nombre de Reynolds de fibres flexibles dans un fluide visqueux au repos. L'état d'équilibre atteint par la fibre flexible est étudié. Nous identifions trois régimes ayant des signatures différentes sur l'état stationnaire de la fibre flexible: un régime de faibles déformations dans lequel la force de traînée est proportionnelle à celle d'une fibre sédimentant horizontalement par rapport à la gravité; un régime de grandes déformations dans lequel la force de traînée est aussi proportionnelle à la vitesse de la fibre, mais avec un coefficient de traînée qui est celui d'une fibre chutant parallèlement à la gravité; et un régime de reconfiguration élastique où le filament se déforme avec une traînée plus faible qui n'est plus proportionnelle à sa vitesse, mais à la racine carrée de celle-ci / In the first part, a jointed experimental and numerical study examining the influence of vortical structures on the settling of a cloud of solid spherical particles under the action of gravity at low Stokes numbers is presented. We use electro-convection to generate a two-dimensional array of controlled vortices which mimics a simplified vortical flow. Particle image-velocimetry and tracking are used to examine the motion of the cloud within this vortical flow. The cloud is modeled as a set of point-particles for which the hydrodynamic interaction is preponderant. The cloud behavior (trajectory, velocity, aspect ratio, break-up time …) is compared to the predictions of a two-way-coupling numerical simulation. In the second part, a jointed experimentally and numerical study on the dynamics of slender flexible filaments settling in a viscous fluid at low Reynolds number is presented. The equilibrium state of a flexible fiber settling in a viscous fluid is examined using a combination of macroscopic experiments, numerical simulations and scaling arguments. We identify three regimes having different signatures on this equilibrium configuration of the elastic filament: a weak deformation regime wherein the drag is proportional to the fiber velocity settling perpendicular to the gravity; a large deformation regime wherein the drag is proportional to the fiber velocity settling parallel to the gravity and an intermediate elastic reconfiguration regime where the filament deforms to adopt a shape with a smaller drag which is no longer linearly proportional to the velocity but to the square root of the velocity