This thesis is concerned with modelling natural convective flows and specifically with their role in electrochemistry. The studies described here demonstrate that many electroanalytical techniques are prone to non-negligible natural convective effects, thus making the standard assumption for purely diffusional mass transport inapplicable. The chosen approach focusses on investigating idealized systems and establishing orders of magnitude for the quantities of interest. The complexity of the observed natural convective flows and their strong dependence on factors such as container geometry serve as compelling arguments for rigorously excluding natural convection in experimental measurements. The text is structured as follows. Chapter 1 introduces the theoretical framework used in the rest of the text and gives an outline of the electrochemical techniques to which the results in later chapters apply. Chapter 2 surveys the literature on natural convection in electrochemistry and emphasizes recent developments. Chapter 3 studies the natural convection induced by the intrinsic heat of an electrochemical reaction, specifically its effect on mass transport in chronoamperometry and cyclic voltammetry. Chapters 4-6 deal exclusively with coupled heat and momentum transport. Chapter 4 considers the thermal convective flows that arise in an idealized cell for scanning electrochemical microscopy (SECM) and the surrounding air under conditions of imperfect thermostating. Chapter 5 is dedicated to thermal convection in an SECM cell that is being thermostated from below through a solid substrate. This chapter demonstrates the influence of the spatial distribution of substrate thermal conductivity on the observed flows and highlights this effect by using a simpler model of the SECM cell than Chapter 4. Chapter 6 investigates the thermal convection in a novel thermostated cell for electrochemical measurements. Chapter 7 contains the main conclusions from the studies described in the thesis. Appendices A, B and C provide additional data for Chapters 3, 5 and 6, respectively.

Mak Chung Ming = 多孔介質中的局部性與整體性漲落 / 麥仲明. / Thesis submitted in: July 2004. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2005. / Includes bibliographical references (leaves 116-123). / Text in English; abstracts in English and Chinese. / Mak Chung Ming = Duo kong jie zhi zhong de ju bu xing yu zheng ti xing zhang luo / Mai Zhongming. / Abstract (in English) --- p.i / Abstract (in Chinese) --- p.ii / Acknowledgements --- p.iii / Table of Contents --- p.iv / List of Figures --- p.vi / List of Tables --- p.ix / Chapters / Chapter 1. --- Introduction --- p.1 / Chapter 1.1 --- Motivation of research on porous medium --- p.1 / Chapter 1.2 --- Description of porous medium --- p.2 / Chapter 1.3 --- Brief history of research of thermal convection in porous medium --- p.5 / Chapter 2. --- Background --- p.7 / Chapter 2.1 --- Introduction --- p.7 / Chapter 2.2 --- Governing equations and parameters --- p.8 / Chapter 2.3 --- Review of literature --- p.15 / Chapter 2.4 --- Summary --- p.20 / Chapter 3. --- Instrumentation --- p.21 / Chapter 3.1 --- Experimental setup --- p.21 / Chapter 3.1.1 --- Porous medium --- p.21 / Chapter 3.1.2 --- Working fluid --- p.24 / Chapter 3.1.3 --- Container cell --- p.25 / Chapter 3.1.4 --- Top plate --- p.26 / Chapter 3.1.5 --- Bottom plate --- p.28 / Chapter 3.2 --- Thermistors and its calibration --- p.28 / Chapter 3.3 --- Other apparatuses --- p.31 / Chapter 4. --- Data analysis and results --- p.33 / Chapter 4.1 --- Measurement of global heat flux --- p.33 / Chapter 4.1.1 --- Heat transfer characteristic --- p.34 / Chapter 4.2 --- Local temperature measurements --- p.37 / Chapter 4.2.1 --- 3mm bead´ؤwater system (small cell) --- p.38 / Chapter 4.2.2 --- 6mm bead´ؤwater system (small cell) --- p.44 / Chapter 4.2.3 --- 6mm bead´ؤwater system (large cell) --- p.64 / Chapter 4.2.4 --- 10mm bead´ؤwater system (large cell) --- p.76 / Chapter 4.3 --- Correlation of the time series --- p.96 / Chapter 4.4 --- Thermal pulse experiment --- p.101 / Chapter 5. --- Conclusions --- p.111 / Appendix --- p.114 / Bibliography --- p.116

Dans cette thèse, nous nous intéressons à un modèle simplifié de corrosion issu du modèle ''Diffusion Poisson Coupled Model'' (DPCM). Nous analysons de manière approfondie le schéma numérique qui a été implémenté dans le code CALIPSO utilisé par l'ANDRA. Il est de type Euler implicite en temps et volumes finis en espace, avec des flux de Scharfetter-Gummel. Nous étudions notamment la convergence de ce schéma ainsi que son comportement asymptotique en différentes limites de paramètres. Enfin, nous explorons différentes possibilités pour augmenter l'ordre en temps. / In this PhD thesis, we are interested in a simplified corrosion model derived from the Diffusion Poisson Coupled Model (DPCM). We analyze the numerical scheme implemented in the CALIPSO code used by the French nuclear waste management agency ANDRA. It is a backward Euler scheme in time and a finite volume scheme in space, with Schafetter-Gummel approximation of the convection-diffusion fluxes. We study the convergence of this scheme and its asymptotic behavior for different limits of parameters. Finally, we compare several higher order schemes in time.

La convection thermique dans les objets naturels de grande taille est associée à de fortes variations de la pression, hydrostatique au premier ordre. C’est le cas pour l’atmosphère de la Terre (et d’autres planètes), les planètes gazeuses géantes, les étoiles, mais aussi l’intérieur des planètes telluriques. De part l’importance des effets de compressibilité, l’approximation de Boussinesq n’y est pas vérifiée et d’autres modèles, comportant également des approximations, sont utilisés : les modèles anélastiques. Toutefois, peu d’expériences ont été réalisées pour les vérifier. Cette thèse présente une expérience dont les paramètres ont été optimisés afin d’obtenir des effets de compressibilité importants en laboratoire. Pour ce faire, une gravité apparente forte est obtenue à l’aide d’une centrifugeuse et du xénon gazeux est utilisé, nous permettant d’atteindre un nombre de dissipation significatif. Ces expériences ont permis l’observation en laboratoire d’un gradient adiabatique de 3 K/cm et d’un exposant de 0,3 pour la loi de puissance caractérisant le transfert thermique turbulent entre le nombre de Nusselt et le nombre de Rayleigh superadiabatique.L’étude des fluctuations de pression et de température montrant que l’écoulement est quasi-geostrophique dû à la forte rotation imposée par la centrifugeuse, un modèle anélastique quasi-géostrophique est développé afin de réaliser des simulations numériques bidimensionnelles relatives à l’expérience. / In large natural objects, thermal convection is associated with large pressure differences, mainly due to hydrostatic balance. This is true in the atmosphere of the Earth (and other planets), in gas giant planets, in stars, but also in the interior of telluric planets. Boussinesq approximation is not valid owing to large compressibility effects, and other approximate models can be used to model these objects, like the anelastic approximation. However, very few experiments have been performed to assess these models. In the present PhD thesis, an experiment is shown, with parameters designed to maximize compressibility effects in a laboratory. In this perspective, an enhanced apparent gravity is obtained using a centrifuge, and Xenon gas is used, allowing us to reach a significant dissipation parameter. In our experiments, we have observed an adiabatic gradient of 3~K/cm and the power law between the superadiabatic Rayleigh number and the Nusselt number measuring the turbulent heat transfer is characterized by an exponent 0.3.Measurements of temperature and pressure fluctuations show that the flow is quasi-geostrophic as a result of the strong rotation rate of the centrifuge. An anelastic, quasi-geostrophic model has then been developed and solved numerically in the same configuration as the experiments.

No description available.

Thesis (Ph. D.)--University of Washington, 2007. / Vita. Includes bibliographical references (leaves 105-110).

Two thermal convection problems of geophysical interest are examined, theoretically. First, convection in the earth's mantle is treated on the basis of a one-dimensional 'strip model'. This model results from further simplification of the well known 'Rayleigh model'. For homogeneous, Newtonian fluids, the strip model yields results similar to those obtained by the Rayleigh method. The strip model is used to determine the critical Rayleigh number for convection in an internally heated two-phase fluid. The critical number depends on the parameters of the phase transition, the physical properties of the fluid, and the depth of the fluid layer. Depending on these factors, a univariant phase transformation may either enhance or hinder convective instability. For the olivine-spinel and spinel-oxides transitions in (MgFe)₂SiO₄ which are thought to take place in the upper mantle, it is shown that the critical Rayleigh number is altered only slightly from the critical number for convection in a fluid with one phase. This result holds both for convection in the entire mantle or convection restricted to the upper mantle. Hence the phase changes are of minor importance regarding the existence of mantle convection in general. A method for estimating the order of magnitude of the displacement of the phase surface as a function of Rayleigh number is outlined for a fluid with only one phase transition. The strip model is also used to treat convection in non-Newtonian fluids obeying a power law rheological equation. If the mantle is governed by a flow law of this type, it appears that convection can take place. Lastly, the procedure for applying the strip model to fluids with variable viscosity and thermal conductivity is outlined. The second convection problem concerns some aspects of convection of fluids in thin vertical fractures in the crust. A steady state model is developed to estimate the magnitude of the mass flow as a function of fracture thickness. It is shown that fractures of the order of a millimeter thick or greater can carry a measurable convective flow. A time dependent model is used to estimate the rate of decay of the mass flow with time. The results indicate that in fractures of the order of a centimeter thick, a measurable decrease of the mass flow takes place after a period of the order of a day. This rapid decay rate suggests that the principal effect of sea water convection in extensive fracture systems which are expected on mid-ocean ridge crests is to cool a volume of crustal rock in the vicinity of the fractures. Circulation of sea water in vertical fractures in the upper crust may provide an explanation of 1) the relatively low conductive heat flow measured at some locations on ocean ridge axes and 2) the very 'noisy' data obtained in the axial zone. / Graduation date: 1972

The effect of unsteady thermocapillary convection on the mass transfer rate of a solute between two immiscible liquids within a rectangular microscale channel with differentially heated sidewalls was numerically investigated. A computational fluid dynamic code in Fortran77 was developed using the finite volume method with Marker and Cell (MAC) technique to solve the governing equations. The discrete surface tracking technique was used to capture the location of the moving liquid-liquid interface. The code produced results consistent with those reported in published literature. The effect of the temperature gradients, the aspect ratio, the viscosity of liquid, and the deformation of the interface on the mass transfer rate of a solute were studied. The mass transfer rate increases with increasing temperature gradient. The improvement of the mass transfer rate by the thermocapillary convection was found to be a function of the Peclet number (Pe). At small Pe, the improvement of the mass transfer rate increases with increasing Pe. At high Pe, increasing the Pe has no significant effect on increasing the mass transfer rate. Increasing the aspect ratio of the cavity up to 1 increases the mass transfer rate. When the aspect ratio is higher than 1, the vortex moves only near the interface, resulting in decreasing the mass transfer rate. By increasing the viscosity of the liquid in top phase, the maximum tangential velocity at the interface decreases. As a result, the improvement of the mass transfer rate decreases. The deformation of the interface has no significant effect on the improvement of the mass transfer rate. By placing the heating source at the middle of the cavity, two steady vortices can be induced in a cavity. As a result, the mass transfer rate is slightly enhanced than that in the system with one vortex. By reversing the direction of the temperature gradient, the mass transfer rate decreases due to the decrease in the velocity of bulk fluid. The thermocapillary convection also promotes the overall reaction process when the top wall of the cavity is served as a catalyst. / Graduation date: 2005

Described in this thesis is an investigation of the fully developed natural convection heat transfer in a vertical channel formed by two infinitely wide parallel plates maintained at a uniform wall temperature. Closed-form solutions for the velocity and temperature profiles are developed along with local and averaged Nusselt numbers. The local Nusselt number based on bulk temperature is found to be 3.77. This result is an analog corresponding to 7.60 for fully developed laminar forced convection in a parallel plate channel with uniform wall temperature boundary condition. The local Nusselt number based on the ambient temperature is deduced as a function of flowwise location. Results are compared with existing numerical and experimental data to find good agreement. / Graduation date: 1997

Saturn's magnetosphere is unique in the solar system. The rotation-driven convection consists of alternating channels of cool plasma from an interior source moving outward and hot plasma from outside moving inward, making Saturn’s inner magnetosphere a dynamical region. This thesis describes work on developing numerical models to simulate the plasma convection pattern in Saturn's inner magnetosphere. Chapter 2 introduces the numerical Rice Convection Model (RCM), a multi-fluid model that was originally developed for Earth’s magnetosphere. We adapt it for Saturn’s conditions in this thesis. In Chapter 3, we show results of initial RCM simulation runs, in which only cool plasma from the interior source is considered. We also include the Coriolis force and the pickup effect. Because the cool plasma is much denser than the hot plasma and always dominant in determining the convection pattern, it is important and necessary to investigate it first. Chapter 4 compares several cool plasma source models and determines the one that produces the best simulation results when compared to Cassini spacecraft observations. In Chapter 5, we add the finite temperature and associated plasma pressure of the cool plasma. The effect of ionospheric Pedersen conductance is also investigated. Finally in Chapter 6, we add hot plasma at the outer boundary, and simulate the V-shape signatures of the injection-dispersion events, which are considered the most definitive evidence of rotation-driven convection in Saturn's inner magnetosphere. Our simulations conform to the observed fact that wider, slower outflow channels of cooler, denser plasma alternate with narrower, faster inflow channels of hotter, more tenuous plasma. Comparisons between simulated and observed results show great consistency.