L'objectif de cette thèse est de fournir une analyse de la transition vers la turbulence d'un fluide rhéofluidifiant (fluide de Carreau) dans une conduite cylindrique. Pour cela, un code pseudo-spectral de type Petrov-Galerkin a été développé. Une analyse linéaire de stabilité de l'écoulement laminaire est effectuée, montrant que cet écoulement est linéairement stable. Ensuite, des perturbations sous la forme des rouleaux longitudinaux contra-rotatifs sont utilisées comme condition initiale. Les termes non linéaires d'inertie et visqueux créent un écoulement secondaire avec des points d'inflexion, linéairement instable vis-à-vis de perturbations 3D. Une analyse linéaire de stabilité de ce nouvel écoulement de base bidimensionnelle est réalisée. La forme des vecteurs propres critiques est analysé. Enfin, une analyse non linéaire de stabilité de rouleaux vis-à-vis des perturbations tridimensionnelles de faible amplitude est effectuée, obtenant un retard pour la transition vers la turbulence des fluides rhéofluidifiants par rapport au cas Newtonien et une tendance à l'asymétrie du profil de vitesse axiale / The main objective of this thesis is to provide a description of the transition to turbulence of a shear thinning fluid in pipe flow. A linear stability analysis of the base flow is done. Results show that the flow is linearly stable and the optimal perturbation is given by a pair of counter rotating vortex. This kind of perturbation is used as an initial condition of a computational code which integrates the governing equations. Inertial and viscous non linear terms generate a secondary base flow with inflection points, which is linearly unstable to 3D perturbations. A secondary instability analysis is done, regarding the shape of unstable eigenvectors. Depending the rheological parameters and the size of the primary perturbation, the unstable mode might be near the wall or the center of the pipe. Finally, a non linear stability analysis of the streaks to 3D perturbations of weak amplitude, obtaining a delay in the transition to turbulence due to shear thinning

Cette thèse est une étude expérimentale de la formation et de la maturation d’un anneau tourbillonnaire. Elle porte sur les écoulements faiblement inertiels (Reynolds : 5 à 500) en fluide newtonien puis non newtonien. Les anneaux sont générés par un système cylindre-piston. Ils sont analysés par visualisation et par vélocimétrie par images de particules (PIV). La dynamique en fluide newtonien à faible nombre de Reynolds se révèle plus complexe que celle à grands Reynolds avec l’apparition d’un anneau secondaire contrarotatif. Les résultats obtenus en fluide rhéofluidifiant montrent l’influence de l’indice de comportement ainsi que les zones de comportement rhéofluidifiant et newtonien. Les explorations en fluides viscoplastique et viscoélastique montrent la formation d’un ou plusieurs anneaux secondaires contrarotatifs, qui diffèrent dans leur formation et leur dynamique des anneaux observés en fluide newtonien et que l’on associe aux propriétés physiques intrinsèques du fluide. / The present work is an experimental study of the generation and the maturation of vortex rings, in order to characterize their structure and their global dynamics for small to moderate Reynolds numbers (between 5 and 500) in Newtonian and non-Newtonian fluids. The experimental set-up consists of a vertical cylindrical piston-tube system with the lower part immersed in a filled tank. Measurement campaigns have been carried out using dye visualization and Particle Image Velocimetry (PIV). A first part of the work is focussed on Newtonian fluid and allows the dynamics at low Reynolds numbers to be investigated qualitatively and quantitatively. This dynamics turns out to be more complex than the one classically observed at high Reynolds numbers, and is characterized by the production of a counter-rotating secondary vortex ring. The results obtained for shear thinning fluids show the influence of the power-law index on the development and the propagation of the ring. The computation of the shear rate field allows the results to be analyzed in terms of shear thinning and Newtonian regions. Finally a preliminary investigation for viscoplastic and viscoelastic fluids has been performed. In both cases, it is shown that one (for viscoplastic fluids) or several (for viscoelastic fluids) counter-rotating secondary vortex rings are generated, a phenomenon that can be associated with the intrinsic physical properties of the fluid. All these results provide several perspectives of study in the field of vortex rings dynamics in the weakly inertial regimes.

Food packaging plays a crucial role in protecting and storing food to keep the products fresh and reduce waste. There is a need to increase the number of paper packages in the food industry to meet the growing demand. Therefore, barrier coatings are an essential aspect of the paper industry since they have good resistance to grease and moisture, which protects the food. The development and improvement of these barrier coatings have the potential to contribute to the advancement of environmentally friendly food packaging. This work aims to examine the impact of rheological behavior and properties on the runnability and barrier performance of barrier coating formulations containing two different kaolin clays, Speswhite (K1) and Capim NP (K2), with the addition of nanoclay in varying amounts. Different formulations were tested as multilayer barrier coatings on lab- and pilot-scale in order to determine the effect of various nanoclay concentrations on runnability, water retention, and rheology properties. Various measurement techniques have been used to obtain a wide range of information on the rheological properties, including the viscosity, under varied shear rate ranges. Also studied are runnability, grease and moisture barrier performance, water retention, and high shear testing for rheology to determine flow behavior. The results show that the viscosity was higher on the lab scale than on the pilot scale due to the poor nanoclay dispersion at the pilot scale. As expected for this type of barrier coating, the KIT-test revealed that the grease barrier was highly effective. Measurements of water retention were good for the low amounts of nanoclay content. Lastly, the shear testing gave very similar results between all the different barrier coating formulas. It was determined that a low nanoclay content gave a good barrier coating performance. However, a higher nanoclay content resulted in decreased water resistance compared to a coating with a low nanoclay content. / Livsmedelsförpackningar spelar en avgörande roll för att skydda och lagra mat för att hålla produkterna fräscha och minska avfallet. Det finns ett behov av att öka antalet pappersförpackningar inom livsmedelsindustrin för att möta den växande efterfrågan. Därför är barriärbestrykningar en väsentlig del av pappersindustrin eftersom de har god motståndskraft mot fett och fukt, vilket skyddar maten. Utvecklingen och förbättringen av dessa barriärbestrykningar har potential att bidra till utvecklingen av miljövänliga livsmedelsförpackningar. Detta arbete syftar till att undersöka inverkan av reologiskt beteende och egenskaper på körbarheten och barriärprestandan hos barriärbestryknings-formuleringar som innehåller två olika kaolinleror, Speswhite (K1) och Capim NP (K2), med tillsats av nanolera i varierande mängder. Olika formuleringar testades som flerskiktsbarriärbestrykningar i laboratorie- och pilotskala för att bestämma effekten av olika nanolerakoncentrationer på körbarhet, vattenretention och reologiska egenskaper. Olika mättekniker har använts för att erhålla bred information om de reologiska egenskaperna, inklusive viskositeten under varierande skjuvhastighets-intervall. Körbarhet, fett- och fuktbarriärprestanda, vattenretention och högskjuvningstestning för reologi har studeras för att bestämma flödesbeteende. Resultaten visar att viskositeten var högre på laboratorieskalan än på pilotskalan på grund av den dåliga nanolerdispergeringen på pilotskalan. Som förväntat för denna typ av barriärbestrykning visade KIT-testet att fettbarriären var mycket effektiv. Mätningar av vattenretention var bra för de låga värdena på nanolerainnehåll. Slutligen gav skjuvprovningen mycket likartade resultat mellan alla olika barriärbestryknings-formuleringar. Det fastställdes att ett lågt nanolerainnehåll gav en bra barriärbestryknings-prestanda. En högre halt av nanolera resulterade dock i minskad vattenbeständighet jämfört med en beläggning med låg nanolerhalt.

L'étude théorique de la transition vers la turbulence d'écoulements en tuyau de fluides non newtoniens rhéofluidifiants (fluides de Carreau) est menée, avec l'approche consistant à calculer des «~structures très cohérentes~» sous la forme d'«~ondes non linéaires~». Pour cela un code pseudo-spectral de type Petrov-Galerkin, permettant de suivre des solutions ondes non linéaires tridimensionnelles dans l'espace des paramètres par continuation, est développé. Ce code est validé par comparaison à des résultats existants en fluide newtonien, et grâce à un test de consistance en fluide non newtonien. Une convergence spectrale exponentielle est obtenue dans tous les cas. Ce code est utilisé pour chercher (guidé par des résultats expérimentaux récents) de nouvelles solutions de nombre d'onde azimutal fondamental égal à 1, sans succès pour l'instant. Par contre des solutions de nombre d'onde azimutal fondamental égal à 2 ou 3 sont obtenues par continuation à partir du cas newtonien. La rhéofluidification induit, en termes de nombres de Reynolds critiques, un retard à l'apparition de ces ondes par rapport au cas newtonien. Ce retard est caractérisé, et le parallèle est fait avec divers résultats expérimentaux qui montrent un retard à l'apparition de bouffées turbulentes en fluides non newtoniens / The transition to turbulence in pipe flows of shear-thinning fluids is studied theoretically. The method used is the computation of `exact coherent structures' that are tridimensional nonlinear waves. For this purpose a pseudo-spectral Petrov-Galerkin code is developped, which also allows to follow solution branches in the parameter space with continuation methods. This code is validated by recovering already published results in the Newtonian case, and by a consistency test in the non-Newtonian case. A spectral exponential convergence is obtained in all cases. This code is used to seek (guided by recent experimental results) new solutions of fundamental azimuthal wavenumber equal to 1,without success at the time being. On the contrary solutions with a fundamental azimuthal wavenumber equal to 2 and 3 are obtained by continuation from the Newtonian case. The shear-thinning effects induce, in terms of critical Reynolds numbers, a delay for the onset of these waves, as compared with the Newtonian case. This delay is characterized. An analogy is made with various experimental results that show a delay in the transition to turbulence, more precisely, in the onset of `puffs', in non-Newtonian fluids

L'objectif de cette thèse est d'analyser l'influence des non linéarités, du comportement rhéologique des fluides rhéofluidifiants, sur les conditions de stabilité et de transition vers la turbulence. Dans un premier temps, une analyse linéaire de stabilité avec une approche modale a été réalisée. Les résultats obtenus mettent clairement en évidence l'effet stabilisant de la rhéofluidification. Ensuite, une analyse faiblement non linéaire de stabilité a été menée en vue d'examiner l'influence de la perturbation de la viscosité sur la stabilité vis à vis de perturbations d'amplitude finie. L'analyse de la contribution des termes non linéaires d'inertie et visqueux montre que, contrairement aux termes d'inertie, les termes non linéaires visqueux ont tendance à accélérer l'écoulement et favoriser une bifurcation sur-critique. Les effets rhéofluidifiants tendent à réduire la dissipation visqueuse. Finalement, une analyse fortement non linéaire de stabilité a été conduite en utilisant les techniques de suivi de branches de solutions par des méthodes de continuation. Pour pouvoir traiter les termes visqueux fortement non linéaires, un code de calcul pseudo-spectral a été développé. Des solutions non linéaires d'équilibre ont été obtenues et caractérisées pour différentes valeurs des paramètres rhéologiques / The aim of this study is to understand the influence of the nonlinear rheological behaviour of the shear-thinning fluids on the flow stability and transition to turbulence. First, a linear stability analysis using modal approach was carried out. Results clearly highlight the stabilizing effect of shear-thinning. Then, as a first approach to take into account nonlinear effects of viscosity perturbation on the flow stability, a weakly nonlinear stability analysis is performed in the neighbourhood of the critical conditions. Results indicate that shear-thinning reduces the viscous dissipation and, in contrast to inertial terms, the nonlinear viscous terms tend to accelerate the flow and act in favour of supercritical bifurcation. Finally, a nonlinear stability analysis is done by following solution branches in the parameter space using continuation techniques. To deal with highly nonlinear viscous terms, a pseudo-spectral code is developed. Nonlinear equilibrium solutions was found and characterized for various values of the rheological parameters

Molding is a simple manufacturing process whereby fluid fills a master tool and then solidifies in the shape of the tool cavity. The precise nature of material flow during molding has long allowed fabrication of plastic components with sizes 1 mm 1 m. Polymer molding with precise critical dimension control could enable scalable, inexpensive production of micro- and nanostructures for functional or lithographic use. This dissertation reports experiments and simulations on molding of polymer micro- and nanostructures at length scales 1 nm 1 mm. The research investigates two main areas: 1) mass transport during micromolding and 2) polymer mechanical properties during nanomolding at length scales 100 nm. Measurements and simulations of molding features of size 100 nm 1 mm show local mold geometry modulates location and rate of polymer shear and determines fill time. Dimensionless ratios of mold geometry, polymer thickness, and bulk material and process properties can predict flow by viscous or capillary forces, shape of polymer deformation, and mold fill time. Measurements and simulations of molding at length scales 100 nm show the importance of nanoscale physical processes distinct from bulk during mechanical processing. Continuum simulations of atomic force microscope nanoindentation accurately model sub-continuum polymer mechanical response but highlight the need for nanoscale material property measurements to accurately model deformation shape. The development of temperature-controlled nanoindentation enables characterization of nanoscale material properties. Nanoscale uniaxial compression and squeeze flow measurements of glassy and viscoelastic polymer show film thickness determines polymer entanglement with cooperative polymer motions distinct from those observed in bulk. This research allows predictive design of molding processes and highlights the importance of nanoscale mechanical properties that could aid understanding of polymer physics.

Title: Flows of incompressible fluids with pressure-dependent viscosity (and their application to modelling the flow in journal bearing) Author: Martin Lanzendörfer Department: Mathematical Institute of Charles University Supervisor: prof. RNDr. Josef Málek, DSc. Abstract: The viscosity of the fluids involved in hydrodynamic lubrication typically depends on pressure and shear rate. The thesis is concerned with steady isothermal flows of such fluds. Generalizing the recent results achieved in the case of homogeneous Dirichlet boundary conditions, the existence and uniqueness of weak solutions subject to the boundary conditions employed in practical applications will be established. The second part is concerned with numerical simulations of the lubrication flow. The experiments indicate that the presented finite element method is successful as long as certain restrictions on the constitutive model are met. Both the restrictions involved in the theoretical results and those indicated by the numerical experiments allow to accurately model real-world lubricants in certain ranges of pressures and shear rates. The last part quantifies those ranges for three representative lubricants. Keywords: existence and uniqueness of weak solutions, finite element method, pressure- thickening, shear-thinning, incompressible fluids,...

La production d’éthanol à partir de biomasse lignocellulosique est reconnue comme une des voies possibles de réduction des émissions de gaz à effet de serre et de remplacement partiel des énergies fossiles. Pour être compétitif, la production d'enzymes à bas coûts est nécessaire. Ces enzymes sont produites par le champignon filamenteux Trichoderma reesei, qui présente, à forte concentration, un comportement fortement rhéofluidifiant pouvant entrainer des limitations de mélange et de transfert de matière lors du changement d'échelle. Dans ce travail, il est proposé de compléter les données de la littérature concernant le temps de mélange, la puissance dissipée et le transfert de matière gaz-liquide (global et local) par des mesures à plusieurs échelles dans des fluides modèles de rhéologie similaire aux milieux biologiques visés. Les modèles et corrélations développés qui en résultent sont directement exploitables pour le design des fermenteurs industriels. Afin d’étudier plus en détail le mélange, le taux de cisaillement et la turbulence, une étude par PIV a été menée sur des milieux transparents. La caractérisation fine de l'hydrodynamique repose sur la dissociation des différentes composantes du mouvement à l’aide de la POD. L'évolution des grandeurs mesurées avec les conditions opératoires permet de fournir des indications précieuses pour l'extrapolation des fermenteurs mettant en œuvre des micro-organismes potentiellement sensibles au cisaillement / Ethanol made from cellulosic biomass is recognized as a promising substitute for fossil fuel and thus as a way to reduce greenhouse gas emissions. To be competitive, low cost cellulosic enzymes produced by the filamentous fungus Trichoderma reesei are required. At high biomass concentration, the culture broth becomes so highly shear-thinning that mixing and mass transfer limitations may be encountered when the process is scaled up.In this study, we propose to complete data available in the literature for mixing times, power draw, and mass transfer (local and global) with measurements at several scales in model fluids (shear thinning) that mimic the rheology of biological media. Models and correlations that derive from this work can be used directly for industrial fermentor design. In order to study mixing, local shear rate and turbulence in detail, PIV is performed in transparent model fluids. The refined hydrodynamic characterisation relies on the dissociation of instantaneous velocity by means of the POD method. The change of key parameters with operating conditions gives relevant information for the scale-up of shear-sensitive micro-organisms.

The polymers are integral part of vast number of products used in day to day life due to their anomalous viscoelastic behaviour. The remarkable flow behaviour exhibited by the polymeric fluids including rod climbing, extrudate swell, tube-less siphon, viscoelastic jet, elastic recoil and sharkskin instability is attributed to the complex microstructures in the polymeric liquids that arise due to the interactions of long chain polymer molecules with each other and with the surrounding fluid particles. The significance of polymer in transportation, packaging, pharmaceutical, chemical, biomedical, textiles, food and polymer processing industries highlights the requirement to comprehend the complex rheology of polymeric fluids. First, we investigate the flow features exhibited by different shear thinning vis-coelastic fluids in rectangular cavities over a wide range of depth to width ratio. We have developed a viscoelastic flow solver in order to perform numerical simulations of highly elastic flow of viscoelastic fluids. In particular, we discuss the simulations of flows of constant viscosity Boger and shear thinning viscoelastic fluids in the complex flow problems using different constitutive equations. The effects of elasticity and inertia on the flow behaviour of two shear thinning vis-coelastic fluids modeled using Giesekus and linear PTT constitutive equations in rectangular cavities is studied. The size of the primary eddies and critical aspect ratio over which the corner eddies merge to yield a second primary eddy in deep cavities is discussed. We demonstrate that the flow in the shallow and deep cavities can be characterized using Weissenberg number, defined based on the shear rate, and Deborah number, specified based on the convective time scale, respectively. The study of flow in driven cavities is important in understanding of the mixing process during synthesis of blends and composites. Next, we study two phase polymeric flow in confined geometries. Nowadays, polymer processing industries prefer to develop newer polymer with the desired material properties mechanically by mixing and blending of different polymer components instead of chemically synthesizing fresh polymer. The microstructure of blends and emulsions following drop deformation, breakup and coalescence during mixing determines its macroscopic interfacial rheology. We developed a two phase viscoelastic flow solver using volume conserving sharp interface volume-of-fluid (VOF) method for studying the dynamics of single droplet subjected to the complex flow fields. We investigated the effects of drop and matrix viscoelasticity on the motion and deformation of a droplet suspended in a fully developed channel flow. The flow behaviour exhibited by Newtonian-Newtonian, viscoelastic-Newtonian, Newtonian-viscoelastic and viscoelastic-viscoelastic drop-matrix systems is presented. The difference in the drop dynamics due to presence of constant viscosity Boger fluid and shear thinning viscoelastic fluid is represented using FENE-CR and linear PTT constitutive equations, respectively. The presence of shear thinning viscoelastic fluid either in the drop or the matrix phase suppresses the drop deformation due to stronger influence of matrix viscoelasticity as compared to the drop elasticity. The shear thinning viscoelastic drop-matrix system further restricts the drop deformation and it displays non-monotonic de-formation. The constant viscosity Boger fluid droplet curbs the drop deformation and exhibits flow dynamics identical to the shear thinning viscoelastic droplet, thus indicating that the nature of the drop viscoelasticity has little influence on the flow behaviour. The matrix viscoelasticity due to Boger fluid increases drop deformation and displays non-monotonic deformation. The drop deformation is further enhanced in the case of Boger fluid in viscoelastic drop-matrix system. Interestingly, the pressure drop due to the presence of viscoelastic drop in a Newtonian matrix is lower than the single phase flow of Newtonian fluid. We also discuss the effects of inertia, surface tension, drop to matrix viscosity ratio and the drop size on these drop-matrix systems. Finally, we investigate the emulsion rheology by studying the motion of a droplet in the square lid driven cavity flow. The viscoelastic effects due to constant viscosity Boger fluid and shear thinning viscoelastic fluid are illustrated using FENECR and Giesekus rheological relations, respectively. The presence of viscoelasticity either in drop or matrix phase boosts the drop deformation with the drop viscoelasticity displaying intense deformation. The drop dynamics due to the droplet viscoelasticity is observed to be independent of the nature of vis-coelastic fluid. The shear thinning viscoelastic matrix has a stronger influence on the drop deformation and orientation compared to the Boger fluid matrix. The different blood components, cells and many materials of industrial importance are viscoelastic in nature. Thus, the present study has significant applications in medical diagnostics, drug delivery, manufacturing and processing industries, study of biological flows, pharmaceutical research and development of lab-on-chip devices.

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.