Dans ce travail, nous étudions le comportement rhéologique de suspensions concentrées de fibres non-browniennes. Dans un premier temps, nous avons élaboré de nouvelles méthodes expérimentales en géométrie torsionnelle plan-plan, pour mesurer la viscosité, les deux différences de contraintes normales, ainsi que les contraintes normales d'origine particulaire. Nous avons été en mesure d'apporter des résultats originaux qui ont été interprétés en termes d’évolution de la microstructure des suspensions de fibres. Les mesures de la viscosité en régimes stationnaire et transitoire ont permis de mettre en évidence l'importance de l'orientation et de l'effet du confinement sur la viscosité. Par ailleurs, nous avons obtenu pour la première fois des mesures indépendantes des deux différences de contraintes normales en géométrie torsionnelle plan-plan. Les mesures de la pression dans le fluide interstitiel nous ont donné accès aux contraintes normales particulaires et apporté une première mise en évidence expérimentale du phénomène de migration des fibres dans les suspensions non-browniennes. Dans un deuxième temps, nous avons établi deux modèles théoriques qui tentent d'expliquer la rhéofluidification des suspensions de fibres concentrées par une compétition entre des forces adhésives entre fibres et les forces hydrodynamiques et qui proposent un scénario de formation et de destruction d'agrégats. Les résultats de ces modèles sont alors confrontés aux mesures expérimentales et rendent bien compte du comportement de la viscosité sur une large gamme de taux de cisaillement. / In this manuscript we investigate, both experimentally and theoretically, the rheological behavior of concentrated non-Brownian fiber suspensions. The experiments consist in developing new methods for measuring the viscosity, the two normal stress differences as well as the particle normal stresses, in torsional plate-plate geometry. We were able to bring original results that have been interpreted by the evolution of the microstructure of the fiber suspensions during the flow. The experiments in stationary and transient regime highlight the importance of fiber orientation and the effect of the confinement on the viscosity measurement. For the first time, the first and the second normal stress differences have been measured separately in a torsional flow. Furthermore, thanks to the measurement of the pore pressure in the suspensions, an estimation of the particle normal stresses has been carried out and, for the first time the phenomenon of fiber migration in non-Brownian suspensions has been evidenced. From a theoretical point of view, we developed two complementary models that tend to explain shear-thinning behavior in concentrated fiber suspensions by a balance between adhesive and hydrodynamic forces and propose a scenario for the formation and the destruction of aggregates. These models are then tested against experimental measurements in a wide range of shear rates.

A numerical study of dilute suspensions based on a non-Newtonian matrix fluid and rigid spheroidal particles is performed. A Carreau fluid describes the non-Newtonian matrix. The special case of rigid spherical particles is considered. Here, a uniaxial elongational flow around a sphere is simulated and numerical homogenization is used to obtain the bulk viscosity of the dilute suspension for different applied rates of deformation and different thinning exponents. In the Newtonian regime the well-known Einstein result for the viscosity of a dilute suspension of rigid spherical particles is obtained. In the power-law regime it is found that the intrinsic viscosity depends only on the thinning exponent. Utilizing the simulation results a modification of the Carreau model for dilute suspensions with a non-Newtonian matrix fluid is proposed. To investigate the influence of the particle shape another numerical study is performed. In particular, different flows around spheroidal particles with different orientations are simulated and numerical homogenization is used to obtain the intrinsic viscosity of the suspension as function of applied rate of deformation, thinning exponent and aspect ratio. From the results it is possible to extract the rheological coefficients of the Lipscomb model. In the Newtonian regime the simulation results coincide with Lipscomb’s predictions. In the power-law regime the rheological coefficients depend strongly on the thinning exponent. Furthermore, simulation results indicate that the rheological coefficients additionally depend on the particle orientation in the non-linear regime. / Une étude numérique sur des suspensions diluées à base d’un fluide non newtonien et de particules sphéroïdales rigides est réalisée. Le comportement de la matrice est décrit par un fluide de type Carreau. De particules sphériques et rigides est considéré en premier. Un écoulement en élongation uniaxiale autour d’une sphère est simulée. Ensuite, l’homogénéisation numérique est utilisée pour déterminer la viscosité apparente de la suspension pour différents taux de déformation et d’indices pseudoplastiques. Dans le domaine newtonien, le résultat d’Einstein donnant la viscosité d’une suspension diluée de particules sphériques et rigides est obtenu. Dans le régime en loi de puissance on constate que la viscosité intrinsèque dépend uniquement de l’indice pseudoplastique. Une autre étude numérique est effectuée pour investiguer l’influence de la forme des particules. Plusieurs écoulements autour d’une particule sphéroïdale sont simulés pour différentes orientations. Une homogénéisation numérique est ensuite utilisée pour obtenir la viscosité intrinsèque de la suspension en fonction du taux de déformation appliqué, de l’indice d’écoulement et du rapport de forme de la particule. A partir de ces résultats, il est possible d’exprimer les coefficients rhéologiques du modèle de Lipscomb. Dans le régime newtonien, les résultats coïncident avec les prédictions de Lipscomb. Dans le domaine en loi de puissance, les coefficients rhéologiques deviennent fortement dépendent de l’indice pseudoplastique. En outre, les résultats des simulations montrent que ces coefficients rhéologiques dépendent également de l’orientation des particules dans le régime non linéaire. / Numerische Untersuchung zu verdünnten Suspensionen basierend auf einer nicht Newtonschen Matrixflüssigkeit und harten spheroidalen Partikeln wurde durchgeführt. Ein Carreau Fluid beschreibt die nicht Newtonsche Matrix. Zuerst wird der Spezialfall harter Kugeln betrachtet. Hierzu wird eine uniaxiale Dehnströmung um eine Kugel simuliert und numerische Homogenisierung wird verwendet um die effektive Viskosität der Suspension für verschieden aufgebrachte Deformationsgeschwindigkeiten und Verdünnungsexponenten zu bestimmen. Im Newtonschen Bereich wird die bekannte Lösung Einsteins für die Viskosität einer verdünnten Suspension harter Kugeln erhalten. Im power-law Bereich ist die intrinsische Viskosität einzig eine Funktion des Verdünnungsexponenten. Unter Nutzung der Simulationsergebnisse wird eine Modifikation des Carreau Modells vorgeschlagen. Um den Einfluss der Partikelform auf die nichtlinearen Eigenschaften zu untersuchen wird eine weitere numerische Simulationen durchgeführt. Dabei werden verschiedene Strömungen um spheroidale Partikel mit unterschiedlicher Orientierung simuliert und numerische Homogenisierung wird verwendet um die intrinsische Viskosität als Funktion der aufgebrachten Deformationsgeschwindigkeit, des Verdünnungsexponenten und des Partikelaspektverhältnisses zu bestimmen. Es ist möglich die rheologischen Parameter des Lipscomb Modells aus den Simulationsergebnissen zu bestimmen. Im Newtonschen Bereich stimmen die numerisch bestimmten Werte mit der Vorhersage Lipscomb‘s überein. Im power-law Bereich hängen die rheologischen Parameter stark vom Verdünnungsexponenten ab. Weiter kann man aus den Ergebnissen auf eine zusätzliche Abhängigkeit der rheologischen Parameter von der Partikelorientierung schließen.

In Abhängigkeit von der Suspensionszusammensetzung und der jeweiligen Scherrate können konzentrierte Kaolinsuspensionen ungewöhnliche rheologische Phänomene wie Oszillationen der scheinbaren Viskosität oder eine negative 1.~Normalspannungsdifferenz zeigen. In dieser Arbeit wurde die Abhängigkeit der 1.~Normalspannungsdifferenz, des Speicher- und des Verlustmoduls im linear-viskoelastischen Bereich sowie der Fließgrenze von der Oberflächenbeladung des Kaolins, von der Kaolinfeststoffkonzentration, vom pH-Wert und von der Ionenstärke untersucht. Weiterhin wurde eine Methode entwickelt, die die Fixierung der scherinduzierten Mikrostruktur der Suspensionen und deren anschließende Charakterisierung mittels Röntgenbeugung gestattet. Außerdem wurde ein rheologisches Modell abgeleitet, das den Zusammenhang zwischen den Aussagen zur scherinduzierten Mikrostruktur und dem Auftreten negativer 1.~Normalspannungsdifferenzen herstellt.

Globale Megatrends erfordern immer flexiblere analytische Messmethoden und Assays. Insbesondere im Umwelt-, Agrar-, Lebensmittel- und Gesundheitssektor sind chemische Assays hier eine geeignete Wahl. Eine Vielzahl solcher Assays steht in akademischen und industriellen Bereichen zur Verfügung. Die Anpassung an neue Verbindungen hingegen ist oft schwierig zu realisieren, da der einzelne Test meist für einen spezifischen Analyten konzipiert ist. Eine modulare, analytische Plattform für die Entwicklung chemischer Assays ist daher sehr wünschenswert. Ein solches System sollte die Möglichkeit einer schnellen und flexiblen Implementierung verschiedener Erkennungstypen für neue Analyten und die Möglichkeit einer Multiparameter-(Multiplex-)Bestimmung in einem robusten und portablen Auslesegerät beinhalten. Einzelpartikel-basierte, chemische Assays haben sich hier als geeignete Lösung erwiesen. In dieser Arbeit stelle ich Polystyrol-Kern-Silikat-Schale-Partikel als modulare, hybride Plattform für die flexible Konfiguration von Einzelpartikel-basierten chemischen Assays vor. Zunächst wurde ein Verfahren entwickelt, das den Zugang zu verschiedenen-Partikelarchitekturen ermöglicht. Diese Partikel wurden für den DNA-Nachweis bis in den fmol-Bereich getestet (Kapitel 2). Ein neues Werkzeug zur Bestimmung der Rauheit der Partikel aus elektronenmikroskopischen Bildern wurde entwickelt und auf das breite Spektrum der im Projekt hergestellten SiO2@PS-Partikel angewendet (Kapitel 3). Damit soll die Grundlage zur Vergleichbarkeit zwischen zukünftigen Partikelcharakterisierungen geschaffen werden. Schließlich wurde ein Multiplex-Assay mit farbstoffkodierten, Protein-abweisenden Partikeln entwickelt, um kleine Moleküle durch immunochemische Reaktionen in einem waschfreien Verfahren nachzuweisen (Kapitel 4). Letzteres verdeutlicht, dass eine hohe analytische Leistung mit neuem Potenzial an flexibler Funktionalität durch die Verwendung hybrider SiO2@PS-Partikel kombiniert werden kann. / Global megatrends such as demographic change, personalization, climate change or urbanization demand for increasingly flexible and mobile analytical measurement methods and assays. Especially in the environmental, agricultural, food and health sectors, chemical assays are a suitable choice. A large variety of such assays is available in the academic and industry area. However, their modification to measure new compounds is time-consuming and laborious, because they are typically designed to detect a specific single analyte. A modular platform for chemical assay development is thus highly desirable. Such a system should include the possibility for fast, easy and flexible implementation of various recognition types towards emerging analytes and the possibility for multi-parameter (multiplexed) detection in a potentially portable fashion. Single particle-based assays have proven to be an adequate solution here. In this work, I present hybrid polystyrene core-silica shell (SiO2@PS) particles as new spherical substrates for the flexible configuration of single particle-based chemical assays. First, a procedure to control the surface topology of the beads was developed, giving access to smooth, raspberry-like or multilayer-like CS structures. These particles were used for DNA detection down to the fmol-level (Chapter 2). A new tool to extract the roughness of the particles from electron microscopy images was developed next and applied to the wide range of CS beads prepared throughout the project (Chapter 3). This general protocol provides the basis for the comparability of future CS particle characterization. Finally, a multiplex assay with dye-encoded beads with non-fouling surfaces was developed to detect small molecules via immunochemical reactions in a wash-free procedure (Chapter 4). The latter ultimately proves that hybrid CS particles can combine high analytical performance and unmatched potential for flexible functionality. / Suspension Array Technology

No description available.

Roterugnar är cylindriska kärl som används för att höja materials temperaturer i en kontinuerlig process som kallas för kalcinering. Roterugnar kan tillämpas i olika processer såsom reduktion av oxidmalm samt återvinning av farligt avfall. Fördelen med roterugnar ligger i dess förmåga att hantera råmaterial som sträcker sig från slam till granulära material med en mängd olika partikelstorlekar, och därigenom upprätthålla distinkta miljöer såsom en bädd av fasta partiklar som samexisterar med ett oxiderande fribord. Sex olika bäddbeteende har dokumenterats med avseende på fyllningsgrad samt Froude nummer. Syftet med denna studie var att utveckla en tvådimensionell suspensions modell med CFD genom att använda den kommersiella mjukvaran COMSOL 5.5 för att simulera de två faser, gas och fast, som en blandad fas efter verk av Philips et. al., Physics of Fluids A: Fluid Dynamics 4.1 (1992) 30-40 och Acrivos & Zhang., International Journal Multiphase Flow 20.3 (1994) 579-591. Denna modell undersöktes genom att jämföra den med de dokumenterade flödesregimerna samt genom parameter som partikelstorlek, partikeldensitet och viskositeten hos gas i flödesregimen känd som rullande läge. Dessutom undersöktes temperaturprofilen för den roterande ugnen genom att utforska hur blandningsvariationer av den fasta bädden i den roterande ugnen påverkas av värmeöverföringen när värme tillförs från väggen under rullande läge. Resultaten av den tvådimensionella suspension modellen visade att det var bara möjligt att simulera glidläge korrekt; andra lägen kunde inte beskrivas som dokumenterat i litteraturen. Det indikeras att vilovinkeln och viskösa krafter i den roterande ugnen var låga vilket resulterade i att suspensions modellen inte kunde avbilda exakt de återstående flödesregimerna som dokumenterat. Till exempel avbildades rullningsläget mer likt forsandeläge då partiklarna fall fritt efter höjning av bädden. Partikelstorlek och partikeldensitet har visat sig ha en betydande påverkan på suspensions modellen eftersom de viskösa krafterna blir låga för en partikelstorlek och partikeldensitet under 0,4 mm respektive 1500 kg/m3. Angående gasens viskositet visades det sig att ju närmare värdet 2.055e-3 (Pa*s) den blev desto större blev sedimentationsflödet vilket resulterade i att bäddpartiklarna dras ner och förblir där. Suspensions modellen kunde således simulera en fast och flytande fas och inte en gasfas som avsett. Slutligen visade temperaturanalysen att påverkan av den termiska konduktiviteten var mer signifikant än den specifika värmekapaciteten i intervallet 1 - 50 (W/(m*K)) respektive 300 - 800 (J/(kg*K)) på grund av den tid det tog att nå en homogen temperaturprofil. / Rotary kilns are cylindrical vessels used to raise materials temperature in a continuous process known as calcination. Rotary kilns find application in various processes such as reduction of oxide ore and hazardous waste reclamation. The advantage of the rotary kiln lies in its ability to handle feedstock ranging from slurries to granular materials with a variety of particle size, thereby maintaining distinct environments such as a bed of solid particles coexisting with an oxidising freeboard. Six different bed behaviours within the kiln have been documented with respect to the filling degree and Froude number. The aim of this study was to develop a two-dimensional suspension model with CFD by using the commercial software COMSOL 5.5 to simulate the two phases, gas and solid, as a mixed phase, following the works of Philips et. al., Physics of Fluids A:  Fluid Dynamics 4.1 (1992) 30-40 and Acrivos & Zhang., International Journal Multiphase Flow 20.3 (1994) 579-591. This model was investigated by comparing it against the documented flow regimes as well as through parameters such as particle size, particle density and viscosity of gas in the flow regime known as rolling mode. In addition, the temperature profile of the rotary kiln was investigated by exploring how the mixture variation of the solid bed within the rotary kiln affects the heat transfer when heat is supplied from the wall during a rolling mode. The results of the two-dimensional suspension model showed that it was only possible to simulate the slipping mode accurately; others mode could not be described as documented in literature. It is indicated that the angle of repose and viscous forces within the rotary kiln were low resulting in the suspension model not being able to accurately depict the remaining flow regimes as documented. For instance, the rolling mode was depicted more as a cataracting mode due to the free fall of particles after elevation of the bed. The particle size and the particle density were found to have a significant impact on the suspension model as the viscous forces became low for a particle size and particle density below 0.4 mm and 1500 kg/m3 respectively. As for the viscosity of gas it was found that the closer it got to the value 2.055e-3 (Pa*s) the sedimentation flux became too large resulting in the bed particles being pulled down and remaining there. Thus, the suspension model could simulate a solid and liquid phase and not a gas phase as intended. Lastly, the temperature analysis revealed that the impact of the thermal conductivity was more significant than the specific heat capacity in the range of 1 - 50 (W/(m*K)) and 300 - 800 (J/(kg*K)) respectively, due to the time it took to reach a homogeneous temperature profile.

In day to day life we encounter many different materials which are intermediate between crystalline solids and simple liquids that include paints , glues , suspensions, polymers, surfactants, food and cosmetic products and so on. ‘Soft condensed matter’ is an emerging field of science that aims to generalize the flow and various deformation mechanisms in this apparent diverse class of materials from a ‘mesoscopic’ point of view (important length scales for these systems is usually 10nm-1μm) where the actual atomic and molecular details governed by various quantum mechanical laws are not very important. These soft systems are held together by weaken tropic forces and therefore can be perturbed easily (the typical elastic modulus of these materials is many orders of magnitude lower compared to metallic solids). Moreover, very long relaxation times in these systems(∼10−3 to 1 s) have made them ideal candidates to study non-equilibrium physics. The present Thesis is an endeavor to understand linear and non-linear flow behavior and low Reynolds number instabilities in various soft matter systems like suspensions of flocculated carbon nanotubes and carbon black, surfactant gels, colloidal glasses, Langmuir monolayers etc probed mainly by bulk and interfacial rheology, in-situ light scattering, particle image velocimetry(PIV) techniques and Fourier transform rheology. We also use dynamic light scattering techniques for particle sizing and characterization of Brownian systems. Chapter 1 gives a general introduction to soft condensed matter, particularly, the important length and time scales, various interactions and the rich phase behavior emerged from the delicate balance between energy and entropy in these systems. In this context, We describe the detailed phase behavior of two such systems studied in this thesis. We next describe briefly a few important concepts which motivate the main problems studied in the present thesis like the shear-thickening in suspensions of Brownian and non-Brownian particles, non-equilibrium steady state fluctuation relations in driven systems, elasticity driven instabilities in complex fluids, jamming transitions and aging behavior. This is followed by a discussion of the experimental techniques like linear and nonlinear rheology, including the Fourier transform rheology. Chapter 2 discusses the experimental techniques used by us in detail. We first describe the different components and mode of operations of the MCR-300 stress-controlled rheometer (Paar Physica, Germany) and various experimental geometries. Next we discuss the set up for two dimensional rheological measurements. The homebuilt imaging set up for in-situ polarized light scattering and direct imaging studies is described along with the in-situ particle image velocimetry (PIV) to map out the exact spatially resolved velocity profiles in 2D systems. We give a brief account of the techniques of Fourier transform rheology. At the end of this chapter, we briefly describe the angle resolved dynamic light scattering (DLS) set up (Brookhaven Instruments, USA). In Chapter 3, we study colossal discontinuous shear-thickening transition in confined suspensions of fractal clusters formed by multi-wall carbon nanotubes (MWNT) by rheology and in-situ imaging experiments. Monotonic decrease in viscosity with increasing shear stress, known as shear thinning, is a known rheological response to shear flow in complex fluids in general and for flocculated suspensions in particular. In the present experiments we demonstrate a discontinuous shear thickening transition where the viscosity jumps sharply above a critical shear stress by four to six orders of magnitude in flocculated suspensions of MWNT even at very low weight fractions(∼0.5%). Rheo-optical observations reveal the shear-thickened state as a percolated structure of MWNT flocs spanning the system size. We present a dynamic phase diagram of the non-Brownian MWNT dispersions revealing a starting jammed state followed by shear-thinning and shear-thickened states. The present study further suggests that the shear-thickened state obtained as a function of shear stress is likely to be a generic feature of fractal clusters under flow, albeit under confinement. An understanding of the shear thickening phenomena in confined geometries is pertinent for flow controlled fabrication techniques in enhancing the mechanical strength and transport properties of thin films and wires of nanostructured composites as well as in lubrication issues. We try to understand the flow of jammed and shear-thickened states under constant applied strain rate by studying the building up and relaxation of individual stress fluctuation events similar to the flow in dense granular materials. We also characterize the metastable shear thickened states by superposing a small sinusoidal stress component on a steady applied stress as well as by studying the a thermal entropy consuming fluctuations which are also observed for other jammed systems under an applied steady shear stress as described in the next chapter. Chapter 4 reports the study of non-equilibrium fluctuations in concentrated gels and glassy systems(in jammed state), the nature of fluctuations and their systemsize dependence in the framework of fluctuation relation and Generalized Gumbel distribution. In the first part, we show that the shear rate at a fixed shear stress in a micellar gel in a jammed state exhibits large fluctuations, showing positive and negative values, with the mean shear rate being positive. The resulting probability distribution functions (PDFs) of the global power flux to the system vary from Gaussian to non-Gaussian, depending on the driving stress and in all cases show similar symmetry properties as predicted by Gallavotti-Cohen steady state fluctuation relation. The fluctuation relation allows us to determine an effective temperature related to the structural constraints of the jammed state. We have measured the stress dependence of the effective temperature. Further, experiments reveal that the effective temperature and the standard deviation of the shear rate fluctuations increase with the decrease of the systemsize. In the second part of this chapter, we report a universal large deviation behavior of spatially averaged global injected power just before the rejuvenation of the jammed state formed by an aging suspension of laponite clay under an applied stress. The probability distribution function (PDF) of these entropy consuming strongly non-Gaussian fluctuations follow an universal large deviation functional form described by the Generalized Gumbel (GG) distribution like many other equilibrium and non-equilibrium systems with high degree of correlations but do not obey Gallavotti-Cohen Steady State Fluctuation Relation (SSFR). However, far from the unjamming transition (for smaller applied stresses) SSFR is satisfied for both Gaussian as well as non-Gaussian PDF. The observed slow variation of the mean shear rate with system size supports a recent theoretical prediction for observing GG distribution. We also establish the universality of the observations reported in this chapter in the light of other jammed systems under shear. We examine in the first part of Chapter 5, the shear-thinning behavior of a two dimensional yield stress bearing monolayer of sorbitan tristearate at air/water interface. The flow curve (stress vs shear rate) consists of a linear region at low shear stresses/shear rates, followed by a stress plateau at higher values. The velocity profile obtained from particle imaging velocimetry indicates that shear banding occurs showing coexistence of fluidized region near the rotor and solid region with vanishing shear-rate away from the rotor. In the fluidized region, the velocity profile which is linear at low shear rates becomes exponential at the onset of shear-thinning, followed by a time varying velocity profile in the plateau region. At low values of constant applied shear rates, the viscosity of the film increases with time, thus showing aging behavior like in soft glassy three-dimensional (3D) systems. Further, at the low values of the applied stress in the yield stress regime, the shear-rate fluctuations in time show both positive and negative values, similar to that observed in sheared 3D jammed systems. By carrying out a statistical analysis of these shear-rate fluctuations, we estimate the effective temperature of the soft glassy monolayer using the Galavatti-Cohen steady state fluctuation relation. In the second part of this chapter, we study in detail the non-linear viscoelastic behavior of Langmuir monolayers. Under oscillatory shear usually observed in many 3D metastable complex fluids with large structural relaxation times. At large strain amplitudes(γ), the storage modulus (G”) decreases monotonically whereas the loss modulus (G”) exhibits a peak above a critical strain amplitude before it decreases at higher strain amplitudes. The power law decay exponents of G” and G” are in the ratio 2:1. The peak in G” is absent at high temperatures and low concentration of sorbitan tristearate. Strain-rate frequency sweep measurements on the monolayers do indicate a strain-rate dependence of the structural relaxation time. The present study on sorbitan tristearate monolayers clearly indicates that the nonlinear viscoelastic behavior in 2D Langmuir monolayers is very general and exhibits many of the features observed in 3D complex fluids. We report in the first part of Chapter 6 scattering dichroism experiments to quantify the spatio-temporal nematodynamics of shear-thinning worm like micellar gels of surfactant Cetyltrimethylammonium Tosylate (CTAT) in the presence of salt sodium chloride (NaCl) enroute to rheochaos. For shear rates past the plateau onset, we observe a presence of alternating bright and dark‘ intertwined’ birefringent structures along the vorticity direction. The orientational order corresponding to these structures are predominantly oriented at +45deg and−45deg to the flow (v) in the (v,∇v) plane. The orientational dynamics of the nematics especially at the interface between the structures, has a one-to-one correspondence with the temporal behavior of the stress. Experiments show that the spatial motion of the vorticity structures depend on the gap thickness of the Couette cell. We next discuss the random temporal flow behavior of this system at high values of applied shear rate/stress in the framework of elastic turbulence in the second part of this chapter. Here, we study the statistical properties of spatially averaged global injected power fluctuations for the worm-like micellar system described above. At sufficiently high Weissenberg numbers (Wi) the shear rate and hence the injected power p(t) at a constant applied stress shows large irregular fluctuations in time. The nature of the probability distribution function (PDF) of p(t) and the power-law decay of its power spectrum are very similar to that observed in recent studies of elastic turbulence for polymer solutions. Remarkably, these non-Gaussian pdf scan be well described by an universal large deviation functional form given by the Generalized Gumbel (GG) distribution observed in the context of spatially averaged global measures in diverse classes of highly correlated systems. We show by in-situ rheology and polarized light scattering experiments that in the elastic turbulent regime the flow is spatially smooth but random in time, in agreement with a recent hypothesis for elastic turbulence. In Chapter 7, we study the vorticity banding under large amplitude oscillatory shear (LAOS) in a dilute worm-like micellar gel formed by surfactant CTAT by Fourier transform rheology and in-situ polarized light scattering. Under LAOS we found the signature of a non-trivial order-disorder transition of Taylor vortices. In the non-linear regime, higher harmonicde composition of the resulting stress signal reveals that the third harmonic I3 shows a very prominent maximum at the strain value where the number density (nv) of the Taylor vortices is maximum for a wide range of angular frequencies both above and below the linear crossover point. Subsequent increase in applied strain results in distortions of the vortices and a concomitant decrease in nv when I3 also drops very sharply and acts like an order parameter for this order-disorder transition. We further quantify the transition by defining an independent order parameter like quantity from the spatial correlation function of the scattered intensity and equivalently its Fourier transform which essentially captures the non monotonous third harmonic behavior. Lissajous plots indicate an intra-cycle strain hardening for the values of γ corresponding to the peak of I3 similar to that observed for hard-sphere glasses. Our study is an important step forward to correlating the structures developed in the system under LAOS to the appearances of the higher harmonics in the non-linear regime. The Thesis concludes with a summary of the main results and a brief account on the scope of future work as described in Chapter 8.

Ce mémoire presente une synthèse de travaux de recherche consacrés à l'analyse de problèmes mathématiques issus de la mécanique des fluides. En particulier, par le mélange de modélisation, d'analyse théorique et numérique d' équations aux dérivées partielles ainsi que de calcul scientifique, les champs applicatifs de ces travaux ont porté essentiellement sur deux grandes thématiques : la mécanique des films minces et les biosciences. Cette synthèse s'articule autour de trois chapitres : 1) la lubrification hydrodynamique, 2) les lois de conservation scalaires sur un domaine borné et 3) la modélisation mathématique appliquée aux sciences du vivant qui présente, à son tour, deux axes distincts : la modélisation du système respiratoire et, en particulier, des échanges gazeux dans l'arbre bronchique et la simulation de suspensions biomimétiques actives ou passives dans un fluide de Stokes.

Pour ma thèse, j'ai étudié trois problèmes autour des propriétés de transport des suspensions actives. J'ai utilisé principalement des suspensions de bactéries Escherichia Coli mais aussi des systèmes de nageurs artificiels auto-propulsés. En premier lieu, j'ai étudié l'activation du mouvement Brownien de particules passives dans une suspension de bactéries, près d'une surface. En utilisant diverses solutions et diverses conditions expérimentales permettant de changer les conditions de nage des bactéries et le confinement, j'ai montré que la diffusivité des traceurs passifs augmente linéairement avec ce que j'ai défini comme le flux actif de la suspension; c'est à dire la concentration de nageurs actifs multipliée par leur vitesse moyenne de nage. De manière générale, le confinement entre deux parois ou par rapprochement d'une paroi, montre un meilleur transfert de la quantité de mouvement qui a pour conséquence une augmentation du facteur de couplage entre diffusivité et fluide actif. Le remplacement des bactéries par des nageurs artificiels comme des bâtonnets bi-métalliques en condition réductrice produit des résultats identiques. Deuxièmement, j'ai étudié la modification de la viscosité d'un fluide produite par la présence d'entités autopropulsées. Il a été montré théoriquement que la présence de nageurs du type "pousseurs" comme les bactéries, réduit la viscosité de la suspension à une valeur inférieure de celle du fluide porteur. Le manque de résultats expérimentaux qui mettent en évidence cet effet au sein d'une suspension (cela été montré pour des films liquides minces), nous a poussé à fabriquer un rhéomètre microfluidique en forme d'Y permettant d'étudier la réponse rhéologique d'une suspension d'E. Coli. Des résultats préliminaires révèlent un comportement non Newtonien de la suspension active avec une baisse de viscosité du liquide aux faibles taux de cisaillement et aux faibles fractions volumiques. Troisièmement, j'ai proposé d'étudier les effets de dispersion et de transport de solutions E. Coli dans un micro-canal rectangulaire possédant une constriction en son centre. Dans un tel milieu confiné, les interactions avec les parois ainsi que la géométrie du canal jouent un rôle essentiel sur les propriétés de transport. Mes résultats, de façon inattendue, montrent que l'écoulement dans un canal produit une re-concentration en bactéries après la constriction et que cet effet est contrôlé par l'écoulement même.

Diese Arbeit stützt sich auf die theoretische und experimentelle Untersuchung der Thermodiffusion im Magnetfeld. Bei magnetischen Flüssigkeiten als kolloidalen Suspensionen versteht man unter der Thermodiffusion einen durch einen Temperaturgradienten angestoßenen unidirektionalen Partikeltransport, der zur Separation des Fluids führt. Beschrieben wird die Thermodiffusion theoretisch über das Konzentrationsprofil der Partikel in Abhängigkeit von Zeit und Ort in einer Fluidschicht. Die Experimente detektieren die Separation des Fluids über die Konzentrationsdifferenz zwischen zwei Fluidkammern. Die Bestimmung des Soret-Koeffizienten erfolgt über einen Datenfit zwischen experimentellen und theoretischen Daten. Für das kerosinbasierte Ferrofluid EMG905 wurden zwei Effekte festgestellt. Bei kleinen Magnetfeldstärken wandern die Partikel zum kalten Rand der Schicht (ST>0), bei steigenden Feldstärken kehrt sich diese Richtung um (ST<0). Die Ergebnisse der Untersuchungen zur Thermodiffusion gehen dann in eine lineare Stabilitätsanalyse einer Ferrofluidschicht bei anliegendem Temperaturgradienten und Magnetfeld ein. Dabei wird festgestellt, dass die kritische Rayleigh-Zahl als charakteristische Größe zum Einsetzen von Konvektion von dem Soret-Koeffizienten abhängt. Ist letzterer positiv, wird das Einsetzen von Konvektion begünstigt, ist er wiederum negativ, so kann Konvektion vollständig unterdrückt werden.