The study of turbulence has been dominated historically by a bottom-up approach, with a much stronger emphasis on the physical structure of flows than on that of the dynam- ical state space. Turbulence has traditionally been described in terms of various visually recognizable physical features, such as waves and vortices. Thanks to recent theoretical as well as experimental advancements, it is now possible to take a more top-down approach to turbulence. Recent work has uncovered non-trivial equilibria as well as relative periodic orbits in several turbulent systems. Furthermore, it is now possible to verify theoretical results at a high degree of precision, thanks to an experimental technique known as Particle Image Velocimetry. These results squarely frame moderate Reynolds number Re turbulence in boundary shear flows as a tractable dynamical systems problem. In this thesis, I intend to elucidate the finer structure of the state space of moderate Re wall-bounded turbulent flows in hope of providing a more accurate and precise description of this complex phenomenon. Computation of new undiscovered equilibria, relative equilibria, and their heteroclinic connections provide a skeleton upon which a numerically accurate description of turbulence can be framed. The behavior of the equilibria under variation of Reynolds number and cell aspect ratios is also examined. It is hoped that this description of the state space will provide new avenues for research into nonlinear control systems for shear flows as well as quantitative predictions of transport properties of moderate Re fluid flows.

Cette thèse s’articule autour de trois projets principaux indépendants les uns des autres. En premier lieu, nous avons développé une méthode de résolution chirale innovante reposant sur l’écoulement de Taylor-Couette et ne nécessitant donc pas l’utilisation d’une phase stationnaire. Les résultats de cette étude sont présentés dans le chapitre 2. En parallèle, nous nous sommes également investis en chimie supramoléculaire et avons notamment commencé à explorer l’effet d’un faible champ magnétique (< 2 T) sur le processus d’auto-assemblage de motifs moléculaires paramagnétiques. Nos efforts expérimentaux sont consignés dans le chapitre 3, chapitre à la fin duquel nous discutons de l’intérêt des états hors-équilibre dissipatifs, en particulier en chimie supramoléculaire. Ces derniers sont d’ailleurs (encore aujourd’hui) une branche énigmatique de la thermodynamique dans la mesure où de tels systèmes ne sont encore décrits par aucun principe thermodynamique (à l’inverse des systèmes à l’équilibre, parfaitement décrits par la thermodynamique classique) rendant leur prédiction compliquée. Dans le chapitre 4, nous exposons notre tentative de description d’un système dissipatif (un oscillateur de pH tout organique) au moyen de mesures calorimétriques à flux continu. Ces trois projets, bien que très différents, s’articulent néanmoins tous autour d’une philosophie commune : l’auto-assemblage loin de l’équilibre. / This thesis deals with three main projects, which are loosely related to one another. Chapter one introduces the progress made in the field of mechanical chiral resolution. The second chapter of this thesis shows the development of a resolution method based on Taylor-Couette flow, and how nonequilibrium self-assembly amplifies the resolution process. The third chapter describes our efforts to control non-equilibrium self-assembly by using weak magnetic fields (<2T). Finally, in chapter four, we show our attempts to describe non-equilibrium dissipative states using continuous-flow calorimetry. All chapters contain elements of non-equilibrium self-assembly or non-equilibrium systems, hence the title: “Non-equilibrium self-assembly: from shear flows to magnetic fields”

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Une « boue » est constituée de particules submillimétriques immergées dans un fluide. Nous étudions des boues concentrées (ou « pâtes granulaires »), où la concentration en particules est proche du maximum réalisable. Les particules peuvent être plus denses que le fluide, et sédimenter, ou être équilibrées en densité. Ces deux cas sont examinés, à l’aide d’une boue modèle. Nous étudions les écoulements de ces boues dans une cellule de Couette. Les expériences utilisent des méthodes innovantes, permettant de mesurer les vitesses des grains individuellement et collectivement, et les profils de concentration sous cisaillement. Les expériences apportent des informations nouvelles sur les écoulements, comme l’existence de courants de re-circulation. Les résultats sur les vitesses azimutales et concentrations sont en accord avec la théorie de Morris et Boulay d’équilibre des forces normales, pour un rapport convenable des coefficients viscométriques des forces tangentielle et normales. / Wet granular materials are made of solid particles in high concentration, immersed in a viscous fluid. We investigated particle dynamics in a model granular suspension in Couette geometry, at low Reynolds/Taylor numbers for density and non density matched suspension. We used innovated techniques such as: Single Particle Tracking (SPT), Multi Particles Video Trajectography (MPVT) and Concentration Photometry (CP). These experiments allow us to provide information about single and collective motion of grains as well as particle repartition (local volume fraction). We investigated fully 3D velocity profiles in concentrated suspensions, diffusion coefficients, particle fluctuations and recirculation motion, also differential flows. We observe that the flow of non density matched suspensions is localized near the inner cylinder in the low shear rate regime, resulting in a sheared layer only a few particle diameters in thickness, in a way very similar to sheared dry granular materials. At high enough angular velocity, the initially localized flow crosses over to full fluidization: in this regime the granular suspension nearly behaves as a density-matched suspension. Dependence between particles’ velocity and associated fluctuation amplitude is evidenced. Experiments as velocity and concentration profiles were compared with theoretical prediction based on the force balance model and different viscometric laws were investigated for normal and shear forces.

The linear stability of high speed-viscous plane Couette and Couette-Poiseuille flows are investigated numerically. The conservation equations along with Sutherland&amp / #65533 / s viscosity law are studied using a second-order finite difference scheme. The basic velocity and temperature distributions are perturbed by a small-amplitude normalmode disturbance. The small-amplitude disturbance equations are solved numerically using a global method using QZ algorithm to find all the eigenvalues at finite Reynolds numbers, and the incompressible limit of these equations is investigated for Couette-Poiseuille flow. It is found that the instabilities occur, although the corresponding growth rates are often small. Two families of wave modes, Mode I (odd modes) and Mode II (even modes), were found to be unstable at finite Reynolds numbers, where Mode II is the dominant instability among the unstable modes for plane Couette flow. The most unstable mode for plane Couette &amp / #65533 / Poiseuille flow is Mode 0, which is not a member of the even modes. Both even and odd modes are acoustic modes created by acoustic reflections between a will and a relative sonic line. The necessary condition for the existence of such acoustic wave modes is that there is a region of locally supersonic mean flow relative to the phase speed of the instability wave. The effects of viscosity and compressibility are also investigated and shown to have a stabilizing role in all cases studied. Couette-Poiseuille flow stability is investigated in case of a choked channel flow, where the maximum velocity in the channel corresponds to sonic velocity. Neutral stability contours were obtained for this flow as a function if the wave number,Reynolds number and the upper wall Mach number. The critical Reynolds number is found as 5718.338 for an upper wall Mach number of 0.0001, corresponding to the fully Poiseuille case.

Les contacteurs centrifuges, basés sur les écoulements de Taylor-Couette, sont bien adaptés pour la mise en œuvre de réactions chimiques ou biochimiques, y compris en milieu polyphasique. Ils possèdent particulièrement plusieurs propriétés favorables à la mise en œuvre des opérations d'extraction liquide-liquide. Un dispositif expérimental a été conçu avec cette idée en tête. Il est constitué de deux cylindres concentriques avec le cylindre intérieur entraîné en rotation et l'externe fixe. L’écoulement de Taylor-Couette se produit dans l’espace annulaire entre eux. Il présente la particularité d’évoluer vers la turbulence par apparition successive d’instabilités. La dispersion axiale ainsi que le mélange, sont extrêmement sensibles à ces structures d’écoulement, ce qui rend difficile la modélisation du couplage entre l’hydrodynamique et le transfert de matière. Ce point particulier a été étudié expérimentalement et numériquement. L’écoulement et le mélange ont été caractérisés par des mesures simultanées de PIV (Vélocimétrie par Imagerie de Particules) et PLIF (Fluorescence Induite par Laser). Les champs de concentration PLIF ont permis d’identifier les différents mécanismes de transport intra et inter-vortex. Pour les régimes ondulatoires (WVF et MWVF), le mélange intra-vortex est contrôlé par l’advection chaotique, directement lié aux caractéristiques du champ de vitesse, qui confère aux vortex une capacité plus importante à convecter et à étirer les filets de fluide. En revanche, l’apparition des vagues brisent les frontières qui séparent les vortex ce qui favorise le transport inter-vortex. La combinaison de ces deux mécanismes contrôle principalement la dispersion axiale. Nous avons également mis en évidence le comportement non monotone des propriétés de mélange en fonction de l’histoire de l’écoulement. Notamment l’état d’onde (la longueur d’onde axiale et l’amplitude de la vague). Nous avons calculé le coefficient de dispersion axiale Dx à l’aide des mesures de distribution de temps de séjour (DTS) et de suivi Lagrangien de particules (DNS). Les deux résultats numériques et expérimentaux ont confirmé l’effet significatif des structures de l’écoulement et de l’histoire sur la dispersion axiale. / Taylor-Couette flows between two concentric cylinders have great potential applications in chemical engineering. They are particularly convenient for two-phase small scale devices enabling solvent extraction operations. An experimental device was designed with this idea in mind. It consists of two concentric cylinders with the inner one rotating and the outer one fixed. Taylor-Couette flows take place in the annular gap between them, and are known to evolve towards turbulence through a sequence of successive instabilities. Macroscopic quantities, such as axial dispersion and mixing index, are extremely sensitive to these flow structures, which may lead to flawed modelling of the coupling between hydrodynamics and mass transfer. This particular point has been studied both experimentally and numerically. The flow and mixing have been characterized by means of flow visualization and simultaneous PIV (Particle Imaging Velocimetry) and PLIF (Planar Laser Induced Fluorescence) measurements. PLIF visualizations showed clear evidences of different transport mechanisms including « intravortex mixing » and « inter-vortex mixing ». Under WVF and MWVF regimes, intra-vortex mixing is controlled by chaotic advection, due to the 3D nature of the flow, while inter-vortex transport occurs due to the presence of waves between neighbouring vortices. The combination of these two mechanisms results in enhanced axial dispersion. We showed that hysteresis may occur between consecutive regimes depending on flow history and this may have a significant effect on mixing for a given Reynolds number. The axial dispersion coefficient Dx evolution along the successive flow states was investigated thanks to dye Residence Time Distribution measurements (RTD) and particle tracking (DNS). Both experimental and numerical results have confirmed the significant effect of the flow structure and history on axial dispersion. Our study confirmed that the commonly used 1-parameter chemical engineering models (e.g. the « well-mixed stirred tanks in serie » model) are not valid for Taylor-Couette reactors modelling : two parameters are at least required for an efficient description of mixing in Taylor-Couette flows.

In some species, including humans, red blood cells (RBCs) under low shear stress tend to clump together and form into regular stacks called rouleaux. These stacks are not static, and constantly move and break apart. This phenomenon is referred to as red blood cell aggregation and disaggregation. When modelled as a single liquid, blood behaves as a non-Newtonian fluid. Its viscosity varies, mainly due to the aggregation of RBCs. The aim of this research is to develop a mesoscale computational model for the simulation of RBCs in plasma. This model considers RBC interaction and aggregation to predict blood-flow characteristics such as viscosity, rouleaux size and velocity distribution. In this work, the population-balance modelling (PBM) approach is utilized to model the RBC aggregation process. The PBM approach is a known method that is used for modelling agglomeration and breakage in two-phase flow fluid mechanics to find aggregate size. The PBM model is coupled to the incompressible Navier-Stokes equations for the plasma. Both models are numerically solved simultaneously. The population-balance equation has been used previously in a more restricted form, the Smoluchowski equation, to model blood viscosity, but it has never been fully coupled with the Navier-Stokes equation directly for the numerical modelling of blood flow. This approach results in a comprehensive model which aims to predict RBC aggregate size and their velocities for different flow configurations, as well as their effects on the apparent macro-scale viscosity. The PBM approach does not treat the microscopic physics of aggregation directly but rather uses experimental correlations for aggregation and disaggregation rates to account for the effects of aggregation on the bulk. To find the aggregation rate, a series of experiments on RBC sedimentation due to gravity is designed. In these tests, aggregated RBCs (rouleaux) tend to settle faster than single RBCs and, due to low shear stresses, disaggregation is very low and can be neglected. A high-speed camera is used to acquire video-microscopic pictures of the process. The size of the aggregates and their velocities are extracted using image processing techniques. For image processing, a general Matlab program is developed which can analyze all the images and report the velocity and size distribution of rouleaux. An experimental correlation for disaggregation rate is found using results from a previous steady-state Couette flow experiment. Aggregation and disaggregation rates from these experiments are used to complete the PBM model. Pressure-driven channel flow experiments are then used for the final validation of the model. Comparisons of the apparent viscosity of whole blood in previous experiments show reasonable agreement with the developed model. This model fills a gap between micro-scale and macro-scale treatments and should be more accurate than traditional macro-scale models while being cheaper than direct treatment of RBCs at the micro-scale.

In this thesis I investigate a number of problems in the nonlinear stability of density stratified plane Couette flow. I begin by describing the history of transient growth phenomena, and in particular the recent application of adjoint based optimisation to find nonlinear optimal perturbations and associated minimal seeds for turbulence, the smallest amplitude perturbations that are able to trigger transition to turbulence. I extend the work of Rabin et al. (2012) in unstratified plane Couette flow to find minimal seeds in both vertically and horizontally sheared stratified plane Couette flow. I find that the coherent states visited by such minimal seed trajectories are significantly altered by the stratification, and so proceed to investigate these states both with generalised Koopman mode analysis and by stratifying the self-sustaining process described by Waleffe (1997). I conclude with an introductory problem I considered that investigates the linear Taylor instability of layered stratified plane Couette flow, and show that the nonlinear evolution of the primary Taylor instability is not coupled to the form of the linearly unstable mode, in contrast to the Kelvin-Helmholtz instability, for example. I also include an appendix in which I describe joint work conducted with Professor Neil Balmforth of UBC during the 2015 WHOI Geophysical Fluid Dynamics summer programme, investigating stochastic homoclinic bifurcations.

Le projet e-MECA : electro-Mécanique Embarquée à Compacité Améliorée, dont l’objectif est de concevoir une machine ultra compacte et ultra rapide à une puissance utile de 12Kw, trouve son application dans les véhicules mild et full hybrides. Ce type de machine présente en effet un fort potentiel de déploiement industriel en très grandes séries à des prix abordables. Pour ces machines, les pertes de charge liées aux écoulements dans le jeu constituent des enjeux essentiels pour les constructeurs. La présente étude porte sur le moyen d’identifier de ces pertes des machines électriques ultra-compactes et ultra-rapides (50 000 rpm).Cette thèse a pour objet l’étude des pertes aérauliques dans l’espace entre le rotor et le stator d’une machine électrique ultra-rapide (≈ 250 m/s) et ultra-compacte (0,5mm - 2mm d’entrefer), en cherchant à répondre aux spécifications élaborées par nos partenaires dans le cadre du projet e-MECA. / The project e-MECA: electromechanical engineering Embarked in Improved Compactness, the objective of which is to design a machine with a small gap and high speed rotor with a useful power of 12Kw, finds its application in mild and hybrid vehicle. This type of machine indeed presents a high potential in the industrial deployment in very big series to affordable prices. The losses in these machines are linked to the flow in the gap has a significant importance for the manufacturers. This study aims to identify these losses for the ultra-compact and ultrafast electric machines (50 000 rpm).This thesis is a study of the air losses in the space between the rotor and the stator of an ultra-fast electric machine (≈ 250 m/s) and ultra-compact (0,5mm - 2mm of air-gap). This study was done to meet the specifications that had been elaborated by our partners in the e-MECA project.

Couette, pipe, channel, and zero-pressure gradient (ZPG) turbulent boundary layer (TBL) flows have classically been considered as canonical wall-bounded turbulent flows since their near-wall behavior is generally considered to be universal, i.e. invariant of the flow case and the Reynolds number. Nevertheless, the idea that large-scale motions, being dominant in regions further away from the wall, might interact with and influence small-scale fluctuations close to the wall has not been disregarded. This view was mainly motivated due to the observed failure of collapse of the Reynolds normal stresses in viscous scaling. While this top-down influence has been studied extensively over the last decade, the idea of a bottom-up influence (backward energy transfer) is less examined. One exception was the recent experimental work on a Couette flow by Kawata, T. &amp; Alfredsson, P. H. (Phys. Rev. Lett. 120, 244501, 2018). In the present work, a spectral representation of the Reynolds Stress transport equation is used to perform a scale-by-scale analysis of the terms in the equation. Two flow cases were studied: first, a Direct Numerical Simulation (DNS) of a Couette flow at a similar Reynolds number as Kawata and Alfredsson. The Reynolds number was ReT = 120, viscosity v. Second, a Large Eddy Simulation (LES) of a ZPG TBL at ReT = 730, 1270, and 2400. For both cases the classic interscale transport or turbulent kinetic energy was observed. However, also an inverse interscale transport of Reynolds shear stress was observed for both cases.