We study the convergence of a nonlinear approximation method introduced in the engineering literature for the numerical solution of a high-dimensional Fokker--Planck equation featuring in Navier--Stokes--Fokker--Planck systems that arise in kinetic models of dilute polymers. To do so, we build on the analysis carried out recently by Le~Bris, Leli\`evre and Maday (Const. Approx. 30: 621--651, 2009) in the case of Poisson's equation on a rectangular domain in $\mathbb{R}^2$, subject to a homogeneous Dirichlet boundary condition, where they exploited the connection of the approximation method with the greedy algorithms from nonlinear approximation theory explored, for example, by DeVore and Temlyakov (Adv. Comput. Math. 5:173--187, 1996). We extend the convergence analysis of the pure greedy and orthogonal greedy algorithms considered by Le~Bris, Leli\`evre and Maday to the technically more complicated situation of the elliptic Fokker--Planck equation, where the role of the Laplace operator is played out by a high-dimensional Ornstein--Uhlenbeck operator with unbounded drift, of the kind that appears in Fokker--Planck equations that arise in bead-spring chain type kinetic polymer models with finitely extensible nonlinear elastic potentials, posed on a high-dimensional Cartesian product configuration space $\mathsf{D} = D_1 \times \dotsm \times D_N$ contained in $\mathbb{R}^{N d}$, where each set $D_i$, $i=1, \dotsc, N$, is a bounded open ball in $\mathbb{R}^d$, $d = 2, 3$. We exploit detailed information on the spectral properties and elliptic regularity of the Ornstein--Uhlenbeck operator to give conditions on the true solution of the Fokker--Planck equation which guarantee certain rates of convergence of the greedy algorithms. We extend the analysis to discretized versions of the greedy algorithms.

Dans le cadre de cette thèse, nous nous intéressons aux différents comportements de fluides structurés (solutions aqueuses de polymères, suspensions), sous écoulements cisaillés. Dans la première partie, nous donnons une description globale des objets constituant le matériau en utilisant une modélisation structurelle, d'une part et en effectuant des mesures de biréfringence pour qualifier l'anisotropie des objets, d'autre part. A travers la loi tentio-optique, nous montrons que le comportement des objets ne dépend que de la contrainte appliquée. En outre, nous étudions les conditions de mesures objectives pour mener une caractérisation rigoureuse, en comparant des mesures de fluage et d'oscillations et en utilisant une approche analytique. Ce qui va permettre de développer une méthode d'identification des paramètres viscoélastiques et leurs évolutions sous cisaillement, dans le régime linéaire et non linéaire. La deuxième partie concerne les écoulements bidimensionnels de ces fluides dans une géométrie de cylindres coaxiaux centrés et excentrés, à grand entrefer. Le dispositif expérimental est validé par des mesures sur un fluide newtonien. L'objectif est d'étudier le comportement local de différents fluides en utilisant la technique de la PIV. Pour cela, nous réalisons un dispositif expérimental fiable et suffisamment précis pour accéder au champs de vitesse instantané dans tous l'entrefer. Les mesures nous permettent d'accéder à la loi de comportement locale de chaque matériau que nous comparons avec la loi de comportement globale donnée par le rhéomètre dans le cas de la géométrie centrée. De plus, des simulations numériques sur Fluent, ont été effectuées pour compléter notre étude. Les résultats obtenus pour des écoulements laminaires, de différents fluides: newtonien, peu rhéofluidifiant, très rhéofluidifiant, montrent qu'il est possible de décrire et prédire le comportement des fluides newtoniens et faiblement rhéofluidifiants mais les modèles classiques existants dans Fluent ne sont pas capables de décrire le comportement des fluides très rhéofluidifiant qui présentent une très forte hétérogénéité des gradients de vitesse dans l'entrefer / Under this thesis, we look at the different behaviors of structured fluids (aqueous solutions of polymers, suspensions) under sheared flow. In the first part, we give a comprehensive description of the items constituting the material using a structural modeling, on the one hand and carrying out birefringence measures to qualify anisotropy objects on the other. Through the tentio-law, we show that the behavior of objects depends only on the applied stress. In addition, we study the conditions of objective measures to conduct a rigorous characterization, comparing creep and oscillations measures, and using an analytical approach. This will help develop a method for identifying viscoelastic parameters and their developments under shear, in both a linear and a no linear regime. The second part concerns the two-dimensional flows of fluids in a coaxial cylinder geometry centered and eccentred, in a wide gap. The objective is to study the local behavior of different fluids using the PIV technic. To do this, we realize an experimental reliable and accurate enough, in all the gap. The experimental device is validated by measurements on a Newtonian fluid. The measures allow to access the local law behavior of each material that we compare with the overall behavior of law given by the rheometer in the case of centered geometry . In addition, digital simulations on Fluent, were made to complement our study. The results for laminar flow, for different fluids: newtonian, little rhéofluidifiant and very rhéofluidifiant, show that it is possible to describe and predict the behavior of some fluid but the existing model in Fluent can not describe the behavior of very rheofluidifiant fluids which have a very strong heterogeneity gradients speed in the gap.

Le polymer flooding est une des techniques de récupération assistée des hydrocarbures (RAH) ; elle consiste à injecter une solution de polymères de forte masse moléculaire afin de déplacer plus efficacement le pétrole emprisonné dans la roche. Cependant, une limite importante de cette technique est la possible dégradation mécanique des polymères au cours de l'injection et dans le réservoir, due à une scission des chaînes macromoléculaires induite par l’écoulement. Ce travail de thèse a pour objectif de mieux comprendre les mécanismes et scénarios de scission, mais aussi leur impact sur le procédé de polymer flooding. Nous nous sommes intéressés au seuil de dégradation mécanique de solutions de poly(oxyde d’éthylène) et de de polyacrylamide partiellement hydrolysé, pour différents régimes de concentration (solutions diluées et semi-diluées) en régime laminaire et inertiel, et pour des solvants de différentes qualités. L’étude de la dégradation mécanique des solutions et de leur impact sur les propriétés rhéologiques a été menée à l’aide de différents dispositifs de dégradation et de différents rhéomètres, dont un dispositif microfluidique en élongation ; ces techniques de mesure ont été combinées à des mesures de distribution de masses moléculaires par chromatographie d’exclusion stérique couplée à la diffusion de lumière. L’étude montre en premier lieu qu’une composante élongationnelle est indispensable pour dégrader les chaînes macromoléculaires en solution. Les résultats mettent aussi clairement en évidence que les mécanismes de dégradation sont très différents en régime dilué et semi-dilué. En régime dilué, la dégradation mécanique des solutions de polymères est indépendante du régime d’écoulement et affecte préférentiellement les macromolécules de fortes masses, avec une scission en milieu de chaîne. En revanche, en régime semi-dilué, la dégradation mécanique dépend du régime de l’écoulement : en écoulement laminaire, la dégradation est gouvernée par le réseau d’enchevêtrements et la scission des chaînes est aléatoire, tandis qu’en régime inertiel, les chaînes se dégradent comme en régime dilué, avec le même scénario de scission en milieu de chaîne. Par ailleurs, les résultats montrent que les propriétés rhéologiques en élongation peuvent être très fortement impactées par la dégradation mécanique. Enfin, les résultats de l’étude préliminaire des propriétés d’injectivité dans un milieu poreux d’une solution de polymère semi-diluée faiblement dégradée montrent que la dégradation mécanique améliore l’injectivité du polymère aux abords du puits. / Polymer flooding is a technique used in enhanced oil recovery; it consists in injecting high molecular weight polymer solutions in order improve oil sweep efficiency in the reservoir. However, polymer flooding is challenged by possible mechanical degradation of polymer solutions during injection and in the reservoir, due to the flow induced scission of macromolecules. This work aims at better understanding the scission mechanisms and scenarios, but also their impact on polymer flooding. We investigated the onset of mechanical degradation of poly(ethylene oxide) and partially hydrolysed polyacrylamide solutions, for different concentration regimes (dilute and semi-dilute regimes), under laminar or inertial conditions, but also under good or bad solvent conditions. The study of mechanical degradation of polymer solutions and their impact on the rheological properties was performed using different degradation devices and different rheometers, including a microfluidic extensional device; these investigation techniques were combined with measurements of the molecular weight distributions using size exclusion chromatography coupled with light scattering experiments. The study first shows that an extensional component is needed to get a mechanical degradation of polymer chains. The results also clearly show that the degradation mechanisms are very different in dilute and semi-dilute regime. In dilute regime, the mechanical degradation of polymer solutions does not dependent on flow regime and mainly affects the macromolecules with high molecular weights, with a mid-chain scission scenario. On the other hand, in semi-dilute regime, mechanical degradation depends on flow regime: in laminar flows, degradation is governed by the entanglement network and chain scission is random, whereas in inertial flows, chain degradation is similar to that observed in dilute regime, with the same mid-chain scission scenario. Besides, the results show that the extensional rheological properties can be very strongly affected by mechanical degradation. At last, the results of a preliminary study of the injectivity of a slightly degraded semi-dilute polymer solution in porous media show that mechanical degradation improves polymer injectivity near the wellbore.

The hydrophobicity of a surface is an important property in many areas of science and engineering. This is especially the case in mineral processing, where differences in surface hydrophobicity lie at the heart of the separation process of flotation. Chemicals are used to increase and decrease the natural hydrophobicity of minerals to attain a better separation between valuable and worthless material. Polymers are often used to reduce mineral surface hydrophobicity. Decades of empirically based decision making have produced a list of effective depressants. However the detailed study of how these polymer depressants affect surface hydrophobicity and mineral recovery lags behind applied investigations. The aim of this thesis was to study the adsorption of commonly used depressants on model surfaces and to interrogate the action of these polymers in reducing surface hydrophobicity. We have modelled the degree of hydrophobicity of common minerals in order to study polymer depressants with methods not commonly used in studies of surface characterisation in flotation. The model surfaces (self-assembled monolayers, SAMs) allowed us to use the quartz crystal microbalance with dissipation monitoring (QCM-D) to study the adsorption of polymers. The QCM-D can be used to obtain adsorption isotherms, adsorption kinetics, water content of adsorbed layers, and information on the conformation of the adsorbed polymer. The results from the QCM-D were correlated with the contact angle data from the captive bubble measurements, with which we assessed the hydrophobicity of the surface before and after polymer adsorption. Three of the polymers layers were probed with dynamic dewetting studies, in order to test other modes of depressant action. Three types of polymers were studied - a polyacrylamide (Polymer-H), a polyelectrolyte CMC (carboxymethyl cellulose) and a group of dextrins (Dextrin-TY, a phenyl succinate substituted dextrin (PS Dextrin) and a styrene oxide substituted dextrin (SO Dextrin)). These polymers are commonly used or have potential to be used in the depression of talc and graphite. Polymer-H was used to investigate the hydrophobic bonding between a non-ionic polymer depressant and chemically inert and non charged surfaces by probing the influence of substrate hydrophobicity on polymer adsorption and reduction of contact angle. Three different model surfaces were used (mixed self-assembled 0.5 SAM, 0.7 SAM or single self-assembled 1.0 SAM monolayers) with advancing contact angles between 75?? and 119??. The study of Polymer-H found that the substrate hydrophobicity is an important factor in adsorption of this polymer and the change in contact angle upon adsorption depends on adsorbed amount. The effectiveness of Polymer-H to reduce surface hydrophobicity was established to correlate with its conformation and morphology. CMC was investigated to find out how a stimulus responsive polymer depressant can be used in flotation. It was established that the adsorbed amount and rate of adsorption of CMC increase with decreasing of pH or increasing of ionic strength. It was shown that the surface hydrophobicity of a CMC pre-adsorbed layer changes with the environment and these alterations are fully reversible. A switch of ionic strength (from 10-2 M KCl to 10-1 M KCl) caused partial dehydration of the adsorbed layer and a decrease of the receding contact angle by 20??. A pH switch (pH = 9 to pH = 3) resulted in a 40?? change in receding contact angle. The CMC investigation showed that the use of a stimulus responsive polymer presents opportunities for exploiting solution conditions as a means to effect a better mineral separation in flotation The adsorption of three dextrin-based polymers on a model hydrophobic surface has been characterized using the quartz crystal microbalance with dissipation monitoring (QCM-D). The three polymers (one standard dextrin and two dextrins with different aromatic group substitutions) exhibited varying affinities and capacity for adsorption on the hydrophobic substrate. The effect of the three polymers on the static contact angle of the surface was studied using captive bubble contact angle measurements. The three polymers were seen to reduce the receding contact angle by similar amounts (approximately 14 degrees) in spite of having varying adsorbed amounts and differences in adsorbed layer water content. Although no differences were observed in the ability of the polymers to reduce the static contact angle, measurements of the dewetting dynamics between a rising air bubble and the polymer covered substrate yielded stark differences between the polymers, with one polymer slowing the dewetting dynamics by an order of magnitude more than the other two polymers. The differences in dewetting behaviour correlate with the adsorbed layer characteristics determined by QCM-D. / Thesis (PhD)--University of South Australia, 2010

This thesis reports on an experimental study of slow viscoelastic flow through models of fibrous porous media. The models were square arrays of parallel cylinders, with solid volume fractions or ‘solidities’ of 2.5%, 5.0%, and 10%. An initial study using a Newtonian fluid provided a baseline for comparison with results for two Boger fluids, so that the effects of fluid elasticity could be determined. Boger fluids are elastic fluids that have near constant viscosities and can be used in experiments without having to account for shear-thinning effects. The experimental approach involved measurements of pressure loss through the three arrays and interior velocity measurements using particle image velocimetry (PIV). For the Newtonian flows, pressure loss measurements were in good agreement with the analytical predictions of Sangani and Acrivos (1982). PIV measurements showed velocity profiles which were symmetrical and independent of flow rate. Pressure loss measurements for the Boger fluid flows revealed that the onset of elastic effects occurred at a Deborah number of approximately 0.5, for both fluids and the three arrays. Flow resistance data collapsed for the two Boger fluids, and increased with solidity. For all three models, the flow resistance increased monotonically with Deborah number, reaching values up to four times the Newtonian resistance for the 10% model. PIV measurements showed that the transverse velocity profiles for the Newtonian and Boger fluids were the same at Deborah numbers below the elastic onset. Above onset, the profiles became skewed. The skewness, like the flow resistance, was observed to increase with both Deborah number and solidity. In the wake regions between cylinders in a column, periodic flow structures formed in the spanwise direction. The structures were staggered from column to column, consistent with the skewing. As either Deborah number or solidity increased, the flow structures became increasingly three-dimensional, and the stagger became more symmetric. An analysis of fluid stresses reveals that the elastic flow resistance is attributed to additional normal stresses caused by shearing, and not by extension.

This thesis reports on an experimental study of slow viscoelastic flow through models of fibrous porous media. The models were square arrays of parallel cylinders, with solid volume fractions or ‘solidities’ of 2.5%, 5.0%, and 10%. An initial study using a Newtonian fluid provided a baseline for comparison with results for two Boger fluids, so that the effects of fluid elasticity could be determined. Boger fluids are elastic fluids that have near constant viscosities and can be used in experiments without having to account for shear-thinning effects. The experimental approach involved measurements of pressure loss through the three arrays and interior velocity measurements using particle image velocimetry (PIV). For the Newtonian flows, pressure loss measurements were in good agreement with the analytical predictions of Sangani and Acrivos (1982). PIV measurements showed velocity profiles which were symmetrical and independent of flow rate. Pressure loss measurements for the Boger fluid flows revealed that the onset of elastic effects occurred at a Deborah number of approximately 0.5, for both fluids and the three arrays. Flow resistance data collapsed for the two Boger fluids, and increased with solidity. For all three models, the flow resistance increased monotonically with Deborah number, reaching values up to four times the Newtonian resistance for the 10% model. PIV measurements showed that the transverse velocity profiles for the Newtonian and Boger fluids were the same at Deborah numbers below the elastic onset. Above onset, the profiles became skewed. The skewness, like the flow resistance, was observed to increase with both Deborah number and solidity. In the wake regions between cylinders in a column, periodic flow structures formed in the spanwise direction. The structures were staggered from column to column, consistent with the skewing. As either Deborah number or solidity increased, the flow structures became increasingly three-dimensional, and the stagger became more symmetric. An analysis of fluid stresses reveals that the elastic flow resistance is attributed to additional normal stresses caused by shearing, and not by extension.

This thesis reports the results of light-scattering measurements and visual investigations of critical phenomena in the complex mixture 1-propanol (1P) + water (W) + potassium chloride (KCl) which has a special critical point (or a special thermodynamic state) known as the double critical point (DCP). The main theme of the thesis is the critical behavior on approaching a special critical point (i.e., the DCP) in a complex or associating mixture in contrast with that in simple, nonassociating mixtures. The asymptotic critical behavior in complex or associating fluids, such as polymer solutions and blends, ionic and nonionic micellar solutions, microemulsions, aqueous and nonaqueous electrolyte solutions, protein solutions, etc., is now commonly accepted to belong to the 3D-Ising universality class. However, the temperature range of the asymptotic regime in these fluids, with universal behavior, has a nonuniversal width and is, in general, smaller than that in simple or nonassociating fluids. In complex mixtures, which are made up of relatively large molecules or particle clusters of mesoscopic range, the coupling between the conventional correlation length of the critical fluctuations ( ξ) and an additional length scale associated with the mesoscale structures (ξD) is known to modify the approach towards the universal nonclassical critical behavior near their critical points. Nevertheless, the generality of this approach needs to be confirmed. There are also instances of a pure classical or close to classical behavior being observed in the critical domain of complex mixtures, although recent experimental results contradict the earlier observations. Therefore, further experimental evidences than that presently available are necessary before one can say how far the analogy between simple and complex fluids can be pushed. Variations in the effective dielectric constant of a mixture have been known to affect the critical behavior. Furthermore, we anticipate the presence of special critical points in complex mixtures to cause nontrivial modifications in the approach towards the universal asymptotic critical behavior. Special thermodynamic states are characterized by critical fluctuations with exceptionally large correlation length, and are displayed by multicomponent liquid mixtures, in which there are a multitude of thermodynamic paths by which a critical point can be approached, and offers rich information about the critical phenomena. These issues are being addressed in this research work. This thesis is organized into 7 Chapters. Chapter 1 begins with an account of the historical development of the field of critical point phenomena with a brief introduction to critical phenomena in simple fluids. Critical phenomena observed in various complex systems such as aqueous and nonaqueous ionic fluids, polymer solutions and blends, micellar and microemulsion systems, etc., are discussed, with particular attention to investigations into crossover from Ising to mean-field critical behavior observed in these systems, which are relevant to the present work. Theoretical attempts at modeling ionic criticality are cited and summarized. This is followed by a discussion of re-entrant phase transitions in multicomponent liquid systems. An account of the various types of special critical points, such as double critical point, critical double point, critical inflection point, quadruple critical point, etc., highlighting the critical behavior on approaching these special critical points, and some of the models of reentrant miscibility are briefly given. The Chapter ends with a statement on the goals of the present research work. Chapter 2 describes the instrumentation developed and the data acquisition procedures adopted for the study. Details of the thermostats and precision temperature controllers used for visual and light-scattering measurements are provided. The important design considerations relating to the achievement of a high degree of temperature stability (~ ±1 mK in the range 293-383 K) are elucidated clearly. The temperature sensors used in the present experiments and their calibration procedures are discussed. The light-scattering instrumentation is discussed in depth. The problems associated with the light-scattering techniques when it is used to study critical point phenomena, and the strategies adopted to overcome them are discussed. The sample cells used for visual investigations and light- scattering experiments, along with the procedure adopted for cleaning and filling of sample cells are also described. Chapter 3 essentially deals with the characterization of the system 1P + W + KCl. It begins with a brief introduction to the critical behavior in complex mixtures, and the motivation behind choosing the present system. The phase behavior in the present mixture, the generation of the coexistence curves and the line of critical points in the mixture, and the method used for preparation of the samples are described. The criticality of the samples is judged by the equal volume phase separation criterion through visual investigations. Addition of a small amount of salt (i.e., KCl) to the 1P + W solution induces phase separation in the mixture as a result of a salting-out process. Decreasing the salt concentration has the same effect as that of increasing pressure on the liquid-liquid demixing of this mixture. Therefore, KCl may be considered as an appropriate field variable analogous to pressure in this mixture. The mixture 1P + W + KCl exhibits reentrant phase transitions and has an array of lower (TL) and upper (TU) critical solution temperatures. It is found that the line of TL’s and TU’s, known as the line of critical points, merge (TU - TL = ΔT → 0) to form a special thermodynamic state known as the DCP. The DCP is approached as close as 509 mK (i.e., ΔT ~ 509 mK) in this work. An analysis of the critical line shows that it is roughly parabolic in shape, which is in consonance with the predictions of the lattice models and the Landau-Ginzburg theory of phase transition. In addition to the presence of a special critical point, various structure probing techniques like small angle X-ray scattering (SAXS), small angle neutron scattering (SANS), etc., indicate the presence of large-scale density inhomogeneities or clusters in 1P + W solution and its augmentation on adding small amount of KCl. Therefore, the present mixture provides a unique possibility to investigate the combined effects of molecular structuring as well as a special critical point on the critical behavior. Only a section of the coexistence surface of the mixture could be generated, owing to various experimental limitations and other problems inherent to the system. This limited further studies on the coexistence curves in the mixture. Chapter 4 reports the critical behavior of osmotic susceptibility in the present mixture. The behavior of the susceptibility exponent is deduced from static light-scattering measurements, on approaching the lower critical solution temperatures (TL’s) along different experimental paths by varying t [ =| (T - T TL)/ TL|] from the lower one-phase region. The light-scattering data analysis emphasizes the need for correction-to-scaling terms for a proper description of the data over the investigated t range. Renormalization of the critical exponents is observed as the critical line is approached along certain special paths. Experimental evidence for the doubling of the extended scaling exponent Δ1 near the DCP is shown. There is no signature of Fisher renormalization in the values of the critical exponents. The data analysis yields very large magnitudes for the correction amplitudes A1 and A2, with the first-correction amplitude A1 being negative, signifying a nonmonotonic crossover behavior of the susceptibility exponent in the mixture. The magnitudes of the correction amplitudes are observed to increase gradually as TL approaches the DCP. The increasing need for extended scaling in the neighborhood of special critical points has been noted earlier in several aqueous electrolyte solutions, in polymer-solvent systems, etc. However, the magnitudes of the correction amplitudes were not as large as that in the present case. Analysis of the effective susceptibility exponent γeff in terms of t indicate that, for the TL far away from the DCP, γeff displays a nonmonotonic crossover from its single limit 3D Ising value (~ 1.24) towards its mean-field value with increase in t. While for that closest to the DCP, γeff displays a sharp, nonmonotonic crossover from its nearly doubled 3D-Ising value (~ 2.39) towards its nearly doubled mean-field value (~ 1.84) with increase in t. For the in-between TL’s, the limiting value of γeff in the asymptotic as well as nonasymptotic regimes gradually increases towards the DCP. The renormalized Ising regime extends over a relatively larger t range for the TL closest to the DCP, and a trend towards shrinkage in the renormalized Ising regime is observed as TL shifts away from the DCP. Nevertheless, the crossover behavior to the mean-field limit extends well beyond t > 10¯2 for the TL’s studied. The crossover behavior is discussed in terms of the emergence of a new lengthscale ξD associated with the enhanced ion-induced clustering seen in the mixture, as revealed by various structure probing techniques, while the observed unique trend in the crossover is discussed in terms of the varying influence of the DCP on the critical behavior along the TL line. The discussion is extended to explain the observed critical behavior in various re-entrant systems having other special critical points. The extended renormalized Ising regime towards the DCP is also reflected in a decrease in the correlation length amplitude (ξ0) as TL approaches the DCP. It is observed that the first-correction amplitude A1 corresponding to fit using two correction terms becomes more negative as TL approaches the DCP, implying an increase in the value of the parameter ū of the crossover model [by Anisimov et al., Phys. Rev. Lett. 75, 3146 (1995)] as the DCP is approached. This increase in reflected in a trend towards a relatively sharp crossover behavior of γeff as TL shifts towards the DCP, i.e., towards the high temperature critical points. The significance of the field variable tUL in understanding different aspects of reentrant phase transitions is manifested in the present system as well. Analysis of the data in terms of tUL led to the retrieval of universal values of the exponents for all TL’s. The effective susceptibility exponent as a function of tUL displays a nonmonotonic crossover from its asymptotic 3D-Ising value towards a value slightly lower than its nonasymptotic mean-field value of 1. The limited (TL _ T) range restricted such a behavior of the effective exponent (in terms of t as well as tUL) for the lowest TL. This feature of the effective susceptibility exponent is interpreted in terms of the possibility of a nonmonotonic crossover to the mean-field value from lower values in the nonasymptotic, high tUL region, as foreseen earlier in micellar systems. The effective susceptibility exponent in terms of tUL also indicates an increase in the sharpness of crossover towards the high temperature TL’s. An increase in the sharpness of crossover with polymer chain length has been observed in polymer solutions. Therefore, our results suggest the need for further composition and temperature-dependent study of molecular structuring in the present mixture. There is also a large decrease in the dielectric constant of the mixture towards the high temperature TL’s. In Chapter 5 the light-scattering measurements are performed on approaching the DCP along the line of the upper critical solution temperatures (i.e., TU’s), by varying t [ = (T - TU )/ TU ] from the high temperature one-phase region in the mixture. A trend towards shrinkage in the simple scaling region is observed as TU shifts away from the DCP. Such a trend was not visible in the data analysis of the TL’s using the correction terms, due to the varying (TL - T) ranges. The light-scattering data analysis substantiates the existence of a nonmonotonic crossover behavior of the susceptibility exponent in the mixture. As with the TL’s, for the TU closest to the DCP, γeff displays a nonmonotonic crossover from its 3D-Ising value towards its nearly doubled mean-field value with increase in t. While for that far away from the DCP, γeff displays a nonmonotonic crossover from its single limit Ising value towards a value slightly lower than its mean-field value of 1 with increase in t. The limited (TL – T) range restricted such a behavior of γeff for the TL far away from the DCP, This feature of γeff in the nonasymptotic, high t region is yet again interpreted in terms of the possibility of a nonmonotonic crossover to the mean-field value from below. Unlike TL’s, the crossover behavior in the present case is pronounced and more sharp for all TU’s. However, the variation in the width of the renormalized Ising regime on approaching the DCP along the TU line is quite similar to that observed along the TL line. The crossover behavior is attributed to the strong ion-induced structuring seen in the mixture, while the observed trend in the crossover as TU shifts towards/away from the DCP is attributed to the varying influence of the DCP. The influence of the DCP on the critical behavior along the TU (or TL) line decreases as TU (or TL) shifts away from the DCP. Our observations indicate an increase in the sharpness of crossover as the critical temperature shifts from TL towards TU, or in other words, as the critical point shifts towards higher temperatures. SANS measurements on the present mixture indicate no difference in the growth of mesoscale clusters in the lower and upper one-phase regions in the mixture. Hence, the observed increase in the sharpness of crossover towards the TU’s is very puzzling. The dielectric constant of the major constituent (i.e., water, ~ 62 %) of the present mixture decreases from around 80 to 63 as the critical temperature shifts from TL towards TU. Therefore, our results suggest the need to look at the crossover phenomena probably from two perspectives, namely, the solvent or dielectric effect and the clustering effect. The increase in the sharpness of the crossover behavior on approaching the high temperature critical points is probably related to the macroscopic property of the mixture, i.e., to the decrease in the dielectric constant of the mixture, while the actual nonmonotonic character of the crossover behavior is related to the microscopic property of the mixture, i.e., to the clustering effects, the extent of which determines the width of the asymptotic critical domain. However, this conclusion is somewhat subtle and calls for rigorous theoretical and experimental efforts to unravel the exact dependence of the crossover behavior on the dielectric constant. Analysis using the field variable tUL in lieu of the conventional variable t led to the retrieval of unique, universal exponents for all TU’s irrespective of the ΔT value. For all TU’s, the effective susceptibility exponent in terms of tUL displays a nonmonotonic crossover from its asymptotic 3D-Ising value towards a value slightly lower than its nonasymptotic mean-field value of 1, as that observed in the t analysis of the effective exponent for the TU far away from the DCP. Like with the TL’s, the crossover behavior extends over nearly the same tUL range for the TU’s studied. However, the crossover is again sharper when compared to the TL’s. Chapter 6 reports light-scattering measurements (by heating as well as cooling) on a non phase-separating 1P + W + KCl mixture in the vicinity of the DCP. The results indicate that despite the lack of phase-separation or critical points, critical-phenomena-like fluctuations can still occur in homogeneous mixtures if they reside in some other direction than temperature or composition (like, pressure or salt concentration) of the phase diagram. Unlike earlier studies on non phase-separating mixtures, our results indicate a crossover behavior of the effective susceptibility exponent, in addition to the power-law behavior. Chapter 7 sums up the major findings of the work reported in this thesis. It also presents a range of open problems that need to be explored further in order to fully understand the results that are reported in this thesis, especially, regarding the exact dependence of dielectric constant of the mixture on the character of the crossover behavior.

The hydrophobicity of a surface is an important property in many areas of science and engineering. This is especially the case in mineral processing, where differences in surface hydrophobicity lie at the heart of the separation process of flotation. Chemicals are used to increase and decrease the natural hydrophobicity of minerals to attain a better separation between valuable and worthless material. Polymers are often used to reduce mineral surface hydrophobicity. Decades of empirically based decision making have produced a list of effective depressants. However the detailed study of how these polymer depressants affect surface hydrophobicity and mineral recovery lags behind applied investigations. The aim of this thesis was to study the adsorption of commonly used depressants on model surfaces and to interrogate the action of these polymers in reducing surface hydrophobicity. We have modelled the degree of hydrophobicity of common minerals in order to study polymer depressants with methods not commonly used in studies of surface characterisation in flotation. The model surfaces (self-assembled monolayers, SAMs) allowed us to use the quartz crystal microbalance with dissipation monitoring (QCM-D) to study the adsorption of polymers. The QCM-D can be used to obtain adsorption isotherms, adsorption kinetics, water content of adsorbed layers, and information on the conformation of the adsorbed polymer. The results from the QCM-D were correlated with the contact angle data from the captive bubble measurements, with which we assessed the hydrophobicity of the surface before and after polymer adsorption. Three of the polymers layers were probed with dynamic dewetting studies, in order to test other modes of depressant action. Three types of polymers were studied - a polyacrylamide (Polymer-H), a polyelectrolyte CMC (carboxymethyl cellulose) and a group of dextrins (Dextrin-TY, a phenyl succinate substituted dextrin (PS Dextrin) and a styrene oxide substituted dextrin (SO Dextrin)). These polymers are commonly used or have potential to be used in the depression of talc and graphite. Polymer-H was used to investigate the hydrophobic bonding between a non-ionic polymer depressant and chemically inert and non charged surfaces by probing the influence of substrate hydrophobicity on polymer adsorption and reduction of contact angle. Three different model surfaces were used (mixed self-assembled 0.5 SAM, 0.7 SAM or single self-assembled 1.0 SAM monolayers) with advancing contact angles between 75?? and 119??. The study of Polymer-H found that the substrate hydrophobicity is an important factor in adsorption of this polymer and the change in contact angle upon adsorption depends on adsorbed amount. The effectiveness of Polymer-H to reduce surface hydrophobicity was established to correlate with its conformation and morphology. CMC was investigated to find out how a stimulus responsive polymer depressant can be used in flotation. It was established that the adsorbed amount and rate of adsorption of CMC increase with decreasing of pH or increasing of ionic strength. It was shown that the surface hydrophobicity of a CMC pre-adsorbed layer changes with the environment and these alterations are fully reversible. A switch of ionic strength (from 10-2 M KCl to 10-1 M KCl) caused partial dehydration of the adsorbed layer and a decrease of the receding contact angle by 20??. A pH switch (pH = 9 to pH = 3) resulted in a 40?? change in receding contact angle. The CMC investigation showed that the use of a stimulus responsive polymer presents opportunities for exploiting solution conditions as a means to effect a better mineral separation in flotation The adsorption of three dextrin-based polymers on a model hydrophobic surface has been characterized using the quartz crystal microbalance with dissipation monitoring (QCM-D). The three polymers (one standard dextrin and two dextrins with different aromatic group substitutions) exhibited varying affinities and capacity for adsorption on the hydrophobic substrate. The effect of the three polymers on the static contact angle of the surface was studied using captive bubble contact angle measurements. The three polymers were seen to reduce the receding contact angle by similar amounts (approximately 14 degrees) in spite of having varying adsorbed amounts and differences in adsorbed layer water content. Although no differences were observed in the ability of the polymers to reduce the static contact angle, measurements of the dewetting dynamics between a rising air bubble and the polymer covered substrate yielded stark differences between the polymers, with one polymer slowing the dewetting dynamics by an order of magnitude more than the other two polymers. The differences in dewetting behaviour correlate with the adsorbed layer characteristics determined by QCM-D. / Thesis (PhD)--University of South Australia, 2010

The goal of this thesis has been to throw light on a selection of open problems in chemical and biological physics using the general principles of statistical mechanics. These problems are all broadly concerned with the role of fluctuations in the dynamics of macromolecular systems. More specifically, they are concerned with identifying the microscopic roots of a number of interesting and unusual effects, including fractional viscoelasticity, anomalous chain cyclization dynamics in crowded environments, subdifffusion in hair bundles, symmetries in the work distributions of stretched polymers, heterogeneities in the geometries of reptation channels in polymer melts, and non-Gaussianity in the distributions of the end products of gene expression. I have shown here that all these effects are expressions of essentially the same underlying process of stochasticity, which can be described in terms of the dynamics of a point particle or a continuous curve that evolves in simple potentials under the action of white or colored Gaussian noise [8]. I have also shown that this minimal model of time-dependent behavior in condensed phases is amenable to analysis, often exactly, by path integral methods [13-15], which are naturally suited to the treatment of random processes in many-body physics. The results of such analyses are theoretical expressions for various experimentally measured quantities, comparisons with which form the basis for developing physical intuition about the phenomena under study. The general success of this approach to the study of stochasticity in biophysics and molecular biology holds out hopes of its application to other unsolved problems in these fields. These include electrical transport in DNA [143], quantum coherence in photosynthesis [144], power generation in molecular motors [145], cell signaling and chemotaxis [146], space dependent diffusion [147], and self-organization of active matter [148], to name a few. Most of these problems are characterized by non-linearities of one kind or another, so they add a new layer of complexity to the problems considered in this thesis. Although path integral and related field theoretic methods are equipped to handle such complexities, the attendant calculations are expected to be non-trivial, and the challenge to theory will be to devise effective approximation schemes for these methods, or to develop new and more sophisticated methods altogether.

Ce travail de thèse porte sur l'étalement de fluides complexes. Il met en évidence la riche phénoménologie d'un acte simple : celui d'étaler avec un racloir (rigide ou souple) une émulsion ou une solution de polymères sur un substrat. Pour chacun des fluides modèles étudiés, nous nous sommes focalisés expérimentalement sur l'observation de l'écoulement au cours de l'entraînement de la solution. Dans des conditions données d'étalement, il apparaît qu'une émulsion o/w peut s'inverser via plusieurs mécanismes de déstabilisation, ou encore, dans le cas d'une solution de polymères, exhiber une instabilité de sa ligne de contact, donnant naissance à des filaments de tailles et de longueurs d'ondes spécifiques. Nous montrons que les différents paramètres d'étalement, comme par exemple la hauteur du racloir, la vitesse d'étalement, les propriétés du substrat ou encore la rhéologie des solutions, doivent être pris en compte pour construire des diagrammes de phase d'étalement séparant les domaines d'existence des instabilités observées (régime de recouvrement partiel), des domaines où la solution transite vers le recouvrement total du substrat. D'autre part, nous tirons l'avantage de ces instabilités pour nous permettre de déposer de façon contrôlée des structures variées, offrant d'intéressantes perspectives en termes d'applications. / This study shows the rich phenomenology of a simple act : spreading complex solutions such as emulsion and polymer solution on a plate, by using a rigid and flexible blade respectively. Here, we experimentally study the flow of the solution over the course of its spreading. During the spreading and in certain conditions, different phenomena occur, namely, emulsion inversion in the case of o/w emulsion or a contact line instability in the case of the polymer solution, which gives rise to the formation of polymer filaments with a well-defined wavelength and characteristic sizes. We showed, thanks to spreading phase diagrams, that the the existence of the instability (partial wetting regime) is separated to a domain where the solution cover the substrate. Spreading parameters such as the height of the scraper, spreading velocity or properties of the fluids turns out to be crucial. Finally, we take advantage of the instabilities to print a variety of interesting patterns for further applications.