In this thesis, the seminal work of Stokes concerning the ow of a Navier-Stokesuid due to a suddenly accelerated or oscillating plate and the ow due to torsionaloscillations of an innitely long rod in a Navier-Stokes uid is extended to a uid withpressure dependent viscosity. The viscosity of many uids varies signicantly withpressure, a fact recognized by Stokes; and Barus, in fact, conducted experiments thatshowed that the variation of the viscosity with pressure was exponential. Given sucha tremendous variation, we study how this change in viscosity aects the nature of thesolution to these problems. We nd that the velocity eld, and hence the structureof the vorticity and the shear stress at the walls for uids with pressure dependentviscosity, are markedly dierent from those for the classical Navier-Stokes uid.

In this paper, we discuss the viscosity solutions of the weakly coupled systems of fully nonlinear second order degenerate parabolic equations and their Cauchy-Dirichlet problem. We prove the existence, uniqueness and continuity of viscosity solution by combining Perron's method with the technique of coupled solutions. The results here generalize those in [2] and [3].

The objective of this study is to synthesize nanomaterials by mixing molten salt (alkali nitrate salt eutectics) with inorganic nanoparticles. The thermo-physical properties of the synthesized nanomaterials were characterized experimentally. Experimental results allude to the existence of a distinct compressed phase even for the solid phase (i.e., in the nanocomposite samples). For example, the specific heat capacity of the nanocomposites was observed to be enhanced after melting and re-solidification - immediately after their synthesis; than those of the nanocomposites that were not subjected to melting and re-solidification. This shows that melting and re-solidification induced molecular reordering (i.e., formation of a compressed phase on the nanoparticle surface) even in the solid phase - leading to enhancement in the specific heat capacity. Numerical models (using analytical and computational approaches) were developed to simulate the fundamental transport mechanisms and the energy storage mechanisms responsible for the observed enhancements in the thermo-physical properties. In this study, a simple analytical model was proposed for predicting the specific heat capacity of nanoparticle suspensions in a solvent. The model explores the effect of the compressed phase – that is induced from the solvent molecules - at the interface with individual nanoparticles in the mixture. The results from the numerical simulations indicate that depending on the properties and morphology of the compressed phase – it can cause significant enhancement in the specific heat capacity of nanofluids and nanocomposites. The interfacial thermal resistance (also known as Kapitza resistance, or “Rk”) between a nanoparticle and the surrounding solvent molecules (for these molten salt based nanomaterials) is estimated using Molecular Dynamics (MD) simulations. This exercise is relevant for the design optimization of nanomaterials (nanoparticle size, shape, material, concentration, etc.). The design trade-off is between maximizing the thermal conductivity of the nanomaterial (which typically occurs for nanoparticle size varying between ~ 20-30nm) and maximizing the specific heat capacity (which typically occurs for nanoparticle size less than 5nm), while simultaneously minimizing the viscosity of the nanofluid. The specific heat capacity of nitrate salt-based nanomaterials was measured both for the nanocomposites (solid phase) and nanofluids (liquid phase). The neat salt sample was composed of a mixture of KNO3: NaNO3 (60:40 molar ratio). The enhancement of specific heat capacity of the nanomaterials obtained from the salt samples was found to be very sensitive to minor variations in the synthesis protocol. The measurements for the variation of the specific heat capacity with the mass concentration of nanoparticles were compared to the predictions from the analytical model. Materials characterization was performed using electron microscopy techniques (SEM and TEM). The rheological behavior of nanofluids can be non-Newtonian (e.g., shear thinning) even at very low mass concentrations of nanoparticles, while (in contrast) the pure undoped (neat) molten salt may be a Newtonian fluid. Such viscosity enhancements and change in rheological properties of nanofluids can be detrimental to the operational efficiencies for thermal management as well as energy storage applications (which can effectively lead to higher costs for energy conversion). Hence, the rheological behavior of the nanofluid samples was measured experimentally and compared to that of the neat solvent (pure molten salt eutectic). The viscosity measurements were performed for the nitrate based molten salt samples as a function of temperature, shear rate and the mass concentration of the nanoparticles. The experimental measurements for the rheological behavior were compared with analytical models proposed in the literature. The results from the analytical and computational investigations as well as the experimental measurements performed in this proposed study – were used to formulate the design rules for maximizing the enhancement in the thermo-physical properties (particularly the specific heat capacity) of various molten salt based inorganic nanomaterials. The results from these studies are summarized and the future directions are identified as a conclusion from this study.

Heavy oil is characterized by its high viscosity, which is a major obstacle to both logging and recovery. Due to the loss of T 2 information shorter than the echo spacing ( TE ), estimation of heavy oil properties from NMR T 2 measurements is usually problematic. In this work, a new method has been developed to overcome the echo spacing restriction of NMR spectrometer during the measurement of heavy oil. A FID measurement supplemented the CPMG in an effort to recover the lost T 2 data. Constrained by the initial magnetization ( M 0 ) estimated from the FID and Curie's law and assuming lognormal distribution for bitumen, the corrected T 2 of bitumen can be obtained. This new method successfully overcomes the TE restriction of the NMR spectrometer and is nearly independent on the TE applied in the measurement. This method was applied in the measurement of systems at elevated temperatures (8 ∼ 90 °C) and some important petrophysical properties of Athabasca bitumen, such as hydrogen index ( HI ), fluid content and viscosity were evaluated by using the corrected T 2 . Well log NMR T 2 measurements of bitumen appear to be significantly longer than the laboratory results. This is likely due to the dissolved gas in bitumen. The T 2 distribution depends on oil viscosity and dissolved gas concentration, which can vary throughout the field. In this work, the viscosity and laboratory NMR measurements were made on the recombined live bitumen sample and the synthetic Brookfield oil as a function of dissolved gas concentrations. The effects of CH 4 , CO 2 , and C 2 H 6 on the viscosity and T 2 response of these two heavy oils at different saturation pressures were investigated. The investigations on live oil viscosity show that, regardless of the gas type used for saturation, the live oil T 2 correlates with viscosity/temperature ratio on a log-log scale. More importantly, the changes of T 2 and viscosity/temperature ratio caused by solution gas follows the same trend of those caused by temperature variations on the dead oil. This conclusion holds for both the bitumen and the synthetic Brookfield oil. This finding on the relationship between the oil T 2 and its corresponding viscosity/temperature ratio creates a way for in-situ viscosity evaluation of heavy oil through NMR well logging.

More often consumers demand instant dry soup that can be prepared with a water temperature below 100o C, which is currently not possible, because the dry soup becomes too thin when using water with a lower temperature. In this study, various kinds of starch studies were made to optimize the starch used in the existing product to make it more viscous at both high and low temperatures. The result was that one of the two starches present in the existing product was retained by change in quantity as it contributed to important flavor parameters. The second was removed and replaced with a starch that made the product more viscous at lower temperatures. To find out if the new product differed from the existing product a viscosity measurement and a sensory paired preference test were made. The viscosity measurement contributed objective data that clarified whether differences existed or not. The sensory paired preference test provided insight into which of the two product variants the consumers preferred. The new starch contributes to higher viscosity at temperatures below 100 ° C and is significantly different from the existing product and is preferred by consumers when prepared at lower temperatures. The exclusion of one of the existing starches resulted in lack of mouth feel at 100oC which consumers perceive as negative. In order for this result to be possible to use to optimize the existing product it requires further product development for the company to gain customer satisfaction. / Fler och fler konsumenter efterfrågar Varma Koppen som kan tillagas med vatten vid lägre temperaturer än kokande vatten, vilket i nuläget inte är möjligt då pulversoppan blir för tunn vid tillsats av kallare vatten. I denna studie har olika sorters stärkelse arbetats med för att optimera det stärkelseinnehåll som finns i den befintliga produkten för att göra den viskös vid både höga och låga temperaturer. Resultatet blev att en av de två stärkelser som förekom i den befintliga produkten behölls men förändrades i mängd då den bidrog till viktiga smakparametrar. Den andra plockades bort och ersattes med en stärkelse som gjorde produkten mer viskös vid lägre temperaturer. För att ta reda på om den nya produkten skiljde sig ifrån den befintliga utfördes en viskositetsmätning och ett sensoriskt parvist preferenstest. Viskositetsmätningen bidrog med objektiv data som klargjorde ifall skillnader fanns eller inte. Det sensoriskt parvisa preferenstestet gav en inblick i vilken av de två produktvarianterna som konsumenterna föredrog. Den nya stärkelsen bidrar till högre viskositet vid temperaturer under 100oC och skiljer sig signifikant från den befintliga produkten och föredras av konsumenterna vid lägre temperaturer. Uteslutandet av en av de befintliga stärkelserna har dock bidragit till en försämrad munkänsla vid 100o C som konsumenterna ser som negativ. För att detta resultat ska kunna användas för att ge en optimerad pulversoppa krävs därför vidare produktutveckling på företaget.

Copper losses to slag are generally between 0.7-2.3% during the copper matte smelting stage. In this study, the aim was to reduce these losses in the slag phase. For this purpose, usage of some additives (especially calcined colemanite labeled as CC, boric oxide-B2O3 and calcium oxide-CaO as well) as flux material was investigated. The flash furnace matte-slag (FFM-FFS) obtained from Eti Copper Inc. and a master matte-slag (MM-MS) produced synthetically were used as starting materials. Additives were tested in various amounts under two different atmospheres (N2 and low Po2 obtained by mixture of CO2/CO gases). Temperature and duration were also used as experimental variables. Experimental results have indicated that 2 hours was sufficient to obtain a low copper content in slag about 0.3% and 0.4% for FFS and MS, respectively. It was also seen that the copper content in slag decreased with increasing CC addition at all oxygen partial pressures and at all temperatures. Furthermore, the addition of all additives up to 4% had great influence in lowering the copper content in the final slags (~0.3%Cu). From FactSage calculations, it could be concluded that the colemanite addition decreased the liquidus temperature which led to early melting of slag and allowed enough duration for settling of matte particles within the slag without substantial changing its viscosity, which resulted in less mechanical copper losses to the slag. By using colemanite in copper production, it was possible that a new application area for boron compounds which are produced in Turkey could be created.

Scientific evidence shows that dietary intake of the omega-3 polyunsaturated fatty acids is beneficial to human health. Fish oil is a rich source of omega-3 fatty acids. However, fish oil with high levels of omega-3 PUFA is very susceptible to oxidative deterioration during storage. The objective of this study was to investigate the effect of xanthan gum (XG)-locust bean gum (LBG) mixtures on the physicochemical properties of whey protein isolate (WPI) stabilized oil-in-water (O/W) emulsions containing 20% v/v menhaden oil. The O/W emulsions containing XG/LBG mixtures were compared to emulsions with either XG or LBG alone. The emulsions were prepared using a sonicator by first mixing menhaden oil into the WPI solution and then either XG, LBG or XG/LBG mixtures were added. WPI solution (2 wt%) and gum solutions (0.0,0.05, 0.1, 0.15, 0.2 and 0.5 wt%) were prepared separately by dissolving measured quantities of WPI in distilled water. XG and LBG gums were blended in a synergistic ratios of 50:50 for the mixture. The emulsions were evaluated for apparent viscosity, microstructure, creaming stability and oxidative stability. Addition of 0.15, 0.2 and 0.5 wt% XG/LBG mixtures greatly decreased the creaming of the emulsion. The emulsion with 0.15, 0.2 and 0.5 wt% XG/LBG mixtures showed no visible serum separation during 15 d of storage. The apparent viscosity of the emulsions containing XG/LBG mixtures was significantly higher (p < 0.05) than the emulsions containing either XG or LBG alone. The viscosity was sharply enhanced at higher concentrations of XG/LBG mixtures. Microstructure images showed depletion flocculation for LBG (0.05-0.5 wt%), XG (0.05- 0.2 wt%) and XG/LBG mixtures (0.05 and 0.1 wt%) emulsions. Flocculation was decreased with the increased biopolymer concentration in the emulsion. The decrease in flocculation was much pronounced for the emulsion containing XG/LBG mixtures. The rate of lipid oxidation for 8 week storage was significantly (p < 0.05) lower in emulsions containing XG/LBG mixtures than in emulsions containing either of the biopolymer alone. The results suggested that the addition of XG/LBG mixtures greatly enhanced the creaming and oxidative stability of the WPI-stabilized menhaden O/W emulsion as compared to either XG or LBG alone.

NUMERICAL AND EXPERIMENTAL STUDY OF TRANSIENT LAMINAR NATURAL CONVECTION OF HIGH PRANDTL NUMBER FLUIDS IN A CUBICAL CAVITYObai Younis Taha ElaminLa convección natural en espacios cerrados, se encuentra ampliamente en sistemas naturales e industriales. El objetivo general de este trabajo es desarrollar y validar una herramienta de simulación capaz de predecir las tasas de enfriamiento de aceite en un tanque. Esta herramienta ha de tener en cuenta la variación de la viscosidad del aceite para dar información detallada de las tasas de enfriamiento del aceite bajo diferentes condiciones de contorno térmicas realisticas. En primer lugar, la influencia de diferentes condiciones de contorno térmicas en las paredes, la variación de la viscosidad y la conductividad de la pared en la convección natural del flujo laminar transitorio en una cavidad cúbica con seis paredes térmicamente activo están analizadas.Para analizar el efecto individual de las paredes laterales de la cavidad en el proceso de enfriamiento, la segunda parte de este estudio considera que, tanto numéricamente como experimentalmente, la transición de la convección natural laminar en una cavidad cúbica con dos paredes opuestas frías y verticales.Nuevas relaciones de escala que tengan en cuenta la variación de la viscosidad con la temperatura, no publicadas anteriormente en la literatura, se derivan de las velocidades de la capa límite, por el tiempo necesario para la capa límite para alcanzar el estado estacionario y para la velocidad y el espesor de las intrusiones horizontales.NUMERICAL AND EXPERIMENTAL STUDY OF TRANSIENT LAMINAR NATURAL CONVECTION OF HIGH PRANDTL NUMBER FLUIDS IN A CUBICAL CAVITYObai Younis Taha ElaminFree convection in enclosed spaces is found widely in natural and industrial systems. The general objective of this work is to develop and validate a simulation tool able to predict the cooling rates of oil in a tank. This tool has to take into account the variation of the oil viscosity to give detailed information of the cooling rates of the oil under different realistic thermal boundary conditions. First, the influence of different thermal wall boundary conditions, the variation of the viscosity and the wall conductivity on the transient laminar natural convection flow in a cubical cavity with the six walls thermally active is studied numerically. To analyze the individual effect of the side walls of the cavity on the cooling process, the second part of this study considers, numerically and experimentally, the transient laminar natural convection in a cubical cavity with two cold opposite vertical walls. The shadowgraph technique is employed to visualize the development of the transient convective flow. New scaling relations that take into account the viscosity variation with temperature, not reported previously in the literature, are derived for the boundary layer velocities, for the time needed for the boundary layer to reach the steady state and for the velocity and thickness of the horizontal intrusions.

A novel approach for the production of soy protein isolates was investigated integrating electroacidification and membrane ultrafiltration. The effect of electroacidification on the ultrafiltration performance and physicochemical properties of the soy protein extracts was obtained by comparing an electroacidified (pH 6) and a non-electroacidified (pH 9) soy protein extract. The effect of membrane fouling on the permeate flux decline was studied in a hollow fiber and a dead end ultrafiltration system. Due to more significant membrane fouling, the permeate flux was always lower for the electroacidified extract, resulting in at least 1.5-fold increase in the total fouling resistance compared to the non-electroacidified extract. The total amount of protein deposited on the membrane surface during unstirred dead-end ultrafiltration was comparable (about 7 mg/cm2) for both soy protein extracts. The discrepancy between the total fouling resistance and the protein deposition estimates was attributed to the formation of denser (less permeable) fouling deposit for the electroacidified extract, which was supported by scanning electron microscopy studies of fouled membranes. The removal of carbohydrates and minerals was evaluated for direct ultrafiltration and two-stage discontinuous diafiltration using a hollow fiber system. The carbohydrate removal results were always consistent with the theoretical predictions, indicating that the carbohydrates were freely permeable across the membrane. In contrast, the minerals were partially retained by the membrane, but to a higher extent for the non-electroacidified extract, which demonstrated that the electroacidification pretreatment enhanced the mineral removal during the ultrafiltration. Incorporation of the diafiltration step improved the ash (mineral) and carbohydrate removal. Stronger electrostatic interactions between soy proteins, calcium/magnesium, and phytic acid (antinutrient) at alkaline pH resulted in less efficient removal of calcium, magnesium, and phytic acid during the ultrafiltration of the non-electroacidified extract compared to the electroacidified extract. Consequently, the soy protein isolates produced by electroacidification and the hollow fiber ultrafiltration had a lower mineral and phytic acid content. The protein content was at least 88 % (dry basis), with or without the electroacidification pretreatment. The study of the viscosity revealed that the electroacidification pretreatment reduced the viscosity of the soy protein extract, which resulted in a lower axial pressure drop increase during the ultrafiltration of the electroacidified extract compared to the non-electroacidified extract. Adjusting the pH of the electroacidified extract to 9 and the pH of the non-electroacidified extract to 6 had a great impact on the particle size distribution but only a marginal effect on the viscosity of the pH adjusted extracts. This indicated that the pH and the particle size distribution were not responsible for the viscosity difference between the electroacidified and the non-electroacidified soy protein extracts. It was proposed that the electroacidification pretreatment had some impact on the water hydration capacity of the soy proteins, which consequently affected the viscosity.

This thesis explores numerical methods for solving nonlinear partial differential equations (PDEs) that arise in option pricing problems. The goal is to develop or identify robust and efficient techniques that converge to the financially relevant solution for both one and two factor problems. To illustrate the underlying concepts, two nonlinear models are examined in detail: uncertain volatility and passport options. For any nonlinear model, implicit timestepping techniques lead to a set of discrete nonlinear equations which must be solved at each timestep. Several iterative methods for solving these equations are tested. In the cases of uncertain volatility and passport options, it is shown that the frozen coefficient method outperforms two different Newton-type methods. Further, it is proven that the frozen coefficient method is guaranteed to converge for a wide class of one factor problems. A major issue when solving nonlinear PDEs is the possibility of multiple solutions. In a financial context, convergence to the viscosity solution is desired. Conditions under which the one factor uncertain volatility equations are guaranteed to converge to the viscosity solution are derived. Unfortunately, the techniques used do not apply to passport options, primarily because a positive coefficient discretization is shown to not always be achievable. For both uncertain volatility and passport options, much work has already been done for one factor problems. In this thesis, extensions are made for two factor problems. The importance of treating derivative estimates consistently between the discretization and an optimization procedure is discussed. For option pricing problems in general, non-smooth data can cause convergence difficulties for classical timestepping techniques. In particular, quadratic convergence may not be achieved. Techniques for restoring quadratic convergence for linear problems are examined. Via numerical examples, these techniques are also shown to improve the stability of the nonlinear uncertain volatility and passport option problems. Finally, two applications are briefly explored. The first application involves static hedging to reduce the bid-ask spread implied by uncertain volatility pricing. While static hedging has been carried out previously for one factor models, examples for two factor models are provided. The second application uses passport option theory to examine trader compensation strategies. By changing the payoff, it is shown how the expected distribution of trading account balances can be modified to reflect trader or bank preferences.