Between two neighboring air bubbles in a froth (or foam), a thin liquid film (TLF) is formed. As the bubbles rise upwards, the TLFs thin initially due to the capillary pressure created by curvature changes. As the film thicknesses (H) reach approximately 200 nm, the disjoining pressure created by surface forces in the films also begins to control the film drainage rate and affect the waves motions at the air/water interfaces. If the disjoining pressure is negative, both the film drainage and the capillary wave motion accelerate. When the TLF thins to a critical film thickness (Hcr), the amplitude of the wave motion grows suddenly and the two air/water interfaces touch each other, causing the TLF to rupture and bubbles to coalesce. In the present work, a new model that can predict Hcr has been developed by considering the film drainage due to both viscous film thinning and capillary wave motion. Based on the Hcr model, bubble-coarsening in a dynamic foam has been predicted by deriving the geometric relation between the thickness of the lamella film, which controls bubble-coalescence rate, and the Plateau border area, which controls liquid drainage rate. Furthermore, a model for predicting bubble-coarsening in froth (3-phase foam) has been developed by developing a film drainage model quantifying the effect of particles on pc. The parameter pc is affected by the number of particles and the local capillary pressure around particles, which in turn vary with the hydrophobicity and size of the particles in the film. Assuming that films rupture at free films, the pc corrected for the particles in lamella films has been used to determine the critical rupture time (tcr), at which the film thickness reaches Hcr, using the Reynolds equation. Assuming that the number of bubbles decrease exponentially with froth height, and knowing that bubbles coalesce when film drains to a thickness Hcr, a bubble coarsening model has been developed. The model predictions are in agreement with the experimental data obtained using particle of varying hydrophobicity and size. / Ph. D.

A first principle flotation model has been derived from the basic mechanisms involved in the bubble-particle and bubble-bubble interactions occurring in flotation. It is a kinetic model based on the premise that the energy barrier (E1) for bubble-particle interaction can be reduced by increasing the kinetic energy (Ek) for bubble-particle interaction and by increasing the hydrophobic force in wetting films. The former is controlled by energy dissipation rate (𝜀), while the latter is controlled by collector additions. The model consists of a series of analytical equations to describe bubble generation, bubble-particle collision, attachment and detachment, froth recovery, and bubble coalescence in froth phase. Unlike other flotation models that do not consider role of hydrophobic force in flotation, the first principle model developed at Virginia Tech can predict flotation recoveries and grades from the chemistry parameters such as 𝜁-potentials, surface tension (𝛾), and contact angles (𝜃) that may represent the most critical parameters to control to achieve high degrees of separation efficiencies. The objectives of the present work are to i) validate the flotation model using the experimental data published in the literature, ii) incorporate a froth model that can predict bubble coarsening due to coalescence in the absence of particles, iii) develop a computer simulator for a froth model that can predict bubble coarsening in the presence of particles, and iv) study the effects of incorporating a regrinding mill and using a stronger collector in a large copper flotation circuit. The model validation has been made using the size-by-class flotation rate constants (kij) obtained from laboratory and pilot-scale flotation tests. Model predictions are in good agreement with the experimental data. It has been found that the flotation rate constants obtained for composite particles can be normalized by those for fully liberated particles (kmax), which opens the door for minimizing the number of flotation products that need to be analyzed using a costly and time-consuming liberation analyzer. A bubble coarsening froth model has been incorporated into the flotation model to predict flotation more accurately. The model has a limitation, however, in that it cannot predict bubble-coarsening in the presence of particles. Therefore, a new computer simulator has been developed to predict the effects of particle size and particle hydrophobicity on bubble coarsening in froth phase. In addition, the first principle flotation model has been used to simulate flotation circuits that are similar to the Escondida copper flotation plant to study the effects of incorporating a re-grinding mill and using a more powerful collector to improve copper recovery. The flotation model developed from first principles is useful for predicting and diagnosing the performance of flotation plants under different circuit arrangements and chemical conditions. / Master of Science

The increasing technological need to push service conditions of structural materials to higher temperatures has motivated the development of several alloy systems. Among them, superalloys are an excellent candidate for high temperature applications because of their ability to form coherent ordered precipitates, which enable the retention of high strength close to their melting temperature. The accelerated kinetics of solute diffusion, with or without an added component of mechanical stress, leads to coarsening of the precipitates, and results in microstructural degradation, limiting the durability of the materials. Hence, the coarsening of precipitates has been a classical research problem for these alloys in service. The prolonged hunt for an alternative of nickel base superalloys with superior traits has gained hope after the recent discovery of Co-Al-W based alloys, which readily form high temperature g precipitates, similar to Ni base superalloys. In the present study, coarsening behavior of g precipitates in Co-10Al-10W (at. %) has been carried out at 800°C and 900°C. This study has, for the first time, obtained critical coarsening parameters in cobalt-base alloys. Apart from this, it has incorporated atomic scale compositional information across the g/g interfaces into classical Cahn-Hilliard model for a better model of coarsening kinetics. The coarsening study of g precipitates in Ni-14Al-7 Cr (at. %) has shown the importance of temporal evolution of the compositional width of the g/g interfaces to the coarsening kinetics of g precipitates. This study has introduced a novel, reproducible characterization method of crystallographic study of ordered phase by coupling of orientation microscopy with atom probe tomography (APT). Along with the detailed analysis of field evaporation behaviors of Ni and Co superalloys in APT, the present study determines the site occupancy of various solutes within ordered g precipitates in both Ni and Co superalloys. This study has explained the role of structural and compositional gradients across the precipitates (g)/matrix (g) interfaces on the coarsening behavior of coherent precipitates in both Ni and Co-base superalloys. The observation of two interfacial widths, one corresponding to a structural order-disorder transition, and the other to the compositional transition across the interface, raises fundamental questions regarding the definition of the interfacial width in such systems. The comparative interface analysis in Co and Ni superalloy shows significant differences, which gives insights to the coarsening behaviors of g precipitates in these alloys. Hence, the principal goal of this work is to compare and contrast the Co and Ni superalloys and also, to accommodate atomic scale information related to transitions across interfaces to coarsening models for a better practical applicability of coarsening laws to various alloys.

Os aços com adição de boro temperados e revenidos têm sido utilizados em diversas aplicações que exigem um compromisso entre boas propriedades mecânicas e baixo custo, como por exemplo, indústria automotiva, de petróleo e na fabricação de plataformas marítimas e tubulações. Estudos termodinâmicos indicam que uma pequena adição de boro altera significativamente o diagrama de fases, aumentando a estabilidade dos carbonetos pela substituição de C por B na estrutura cristalina. A avaliação da cinética de precipitação foi realizada indiretamente pela medição da variação de resistividade elétrica de amostras tratadas em temperaturas de 790, 810 e 830°C. Foi possível traçar a curva de precipitação (JMAK) para cada temperatura e propor um diagrama TTP que indicou que as temperaturas testadas estão situadas na parte superior da curva \"C\". A confirmação do fenômeno de precipitação foi obtida por microscopia eletrônica de varredura (MEV-FEG), indicando que a técnica indireta foi eficaz para predição do fenômeno. A cinética de coalescimento foi avaliada em amostras tratadas em 880°C de forma direta, por microscopia óptica e microscopia eletrônica de varredura, e de forma indireta, por avaliação da energia absorvida em ensaio de impacto Charpy. A determinação da distribuição de tamanho de borocarbonetos em cada condição testada forneceu indícios de que o mecanismo de controle do crescimento é reação na interface. Foi possível, satisfatoriamente, correlacionar o tamanho médio de borocarboneto com a resistência ao impacto Charpy, indicando que a susceptibilidade à fragilização pelo coalescimento de borocarbonetos independe da região da barra laminada. / Boron added steels in quenched and tempered condition have been used in many applications with mechanical properties and low-cost requirements, i.e., automotive, petrochemical and O&G industries. Thermodynamic simulations have shown that boron addition promotes significant change in phase diagram due to carbide stability increase by replacement of carbon by boron. Precipitation kinetic was evaluated by electrical resistivity in samples heat-treated at 790°C, 810°C, and 830°C. It was possible to estimate the precipitation curve (JMAK) for each temperature and to propose a TTP diagram which indicates that tested temperatures were in the upper region of the C-shape curve. Precipitation phenomenon was confirmed by FEG-SEM analysis, indicating that electrical resistivity measurement was effective to evaluate precipitation at these conditions. Coarsening kinetic was evaluated in samples heat-treated at 880°C by Microscopy and by absorbed energy in Charpy impact test. The borocarbide size and distribution determination provided evidence of interface reaction-controlled mechanism. A correlation between absorbed energy in impact test and average borocarbide size was proposed, indicating that embrittlement susceptibility by borocarbide coarsening has no dependence of rolled bar region.

Pour des mousses 2D(et 3D sphériques) sèches à l'équilibre nous montrons une équivalence étoile-triangle. Cette équivalence affirme que chaque bulle ayant trois bulles voisines peut être considérée comme une décoration des prolongements des côtés externes qui la rejoignent. Cette propriété, déjà connue dans une des ses applications, nous la démontrons en utilisant des méthodes de dualisation, de géométrie projective et l'invariance des mousses 2D par homographies. Plus en général, nous prouvons l'invariance par transformations conformes des mousses 2D. En considérant des mousses en incidence normale sur une paroi, nous avons montré comment les lois d'équilibre en 3D impliquent celles en 2D sur la surface de contact. Ces lois nous permettent d'étudier théoriquement les récentes expériences où une mousse monodisperse est mise entre deux plaques de verre courbes non parallèles. Dans la limite de petit interstice, nous relions le profil à l'application conforme observée expérimentalement. La contribution de la courbure des films dans la direction orthogonale aux plaques est décisive pour corriger des prédictions erronées de la géométrie 2D.

This thesis highlights a comprehensive research for the cell nucleation, growth and coarsening mechanisms during plastic foaming processes. Enforced environmental regulations have forced the plastic foam industry to adopt alternative blowing agents (e.g., carbon dioxide, nitrogen, argon and helium). Nevertheless, the low solubilities and high diffusivities of these viable alternatives have made the production of foamed plastics to be non-trivial. Since the controls of the cell nucleation, growth and coarsening phenomena, and ultimately the cellular morphology, involve delicate thermodynamic, kinetic, and rheological mechanisms, the production of plastics foams with customized cell morphology have been challenging. In light of this, the aforementioned phenomena were investigated through a series of theoretical studies, computer simulations, and experimental investigations. Firstly, the effects of processing conditions on the cell nucleation phenomena were studied through the in-situ visualization of various batch foaming experiments. Most importantly, these investigations have led to the identification of a new heterogeneous nucleation mechanism to explain the inorganic fillers-enhanced nucleation dynamics. Secondly, a simulation scheme to precisely simulate the bubble growth behaviors, a modified heterogeneous nucleation theory to estimate the cell nucleation rate, and an integrated model to simultaneously simulate cell nucleation and growth processes were developed. Consequently, through the simulations of the cell nucleation, growth, and coarsening dynamics, this research has advanced the understanding of the underlying sciences that govern these different physical phenomena during plastic foaming. Furthermore, the impacts of various commonly adopted approximations or assumptions were studied. The end results have provided useful guidelines to conduct computer simulation on plastic foaming processes. Finally, an experimental research on foaming with blowing agent blends served as a case example to demonstrate how the elucidation of the mechanisms of various foaming phenomena would aid in the development of novel processing strategies to enhance the control of cellular structures in plastic foams.

This thesis highlights a comprehensive research for the cell nucleation, growth and coarsening mechanisms during plastic foaming processes. Enforced environmental regulations have forced the plastic foam industry to adopt alternative blowing agents (e.g., carbon dioxide, nitrogen, argon and helium). Nevertheless, the low solubilities and high diffusivities of these viable alternatives have made the production of foamed plastics to be non-trivial. Since the controls of the cell nucleation, growth and coarsening phenomena, and ultimately the cellular morphology, involve delicate thermodynamic, kinetic, and rheological mechanisms, the production of plastics foams with customized cell morphology have been challenging. In light of this, the aforementioned phenomena were investigated through a series of theoretical studies, computer simulations, and experimental investigations. Firstly, the effects of processing conditions on the cell nucleation phenomena were studied through the in-situ visualization of various batch foaming experiments. Most importantly, these investigations have led to the identification of a new heterogeneous nucleation mechanism to explain the inorganic fillers-enhanced nucleation dynamics. Secondly, a simulation scheme to precisely simulate the bubble growth behaviors, a modified heterogeneous nucleation theory to estimate the cell nucleation rate, and an integrated model to simultaneously simulate cell nucleation and growth processes were developed. Consequently, through the simulations of the cell nucleation, growth, and coarsening dynamics, this research has advanced the understanding of the underlying sciences that govern these different physical phenomena during plastic foaming. Furthermore, the impacts of various commonly adopted approximations or assumptions were studied. The end results have provided useful guidelines to conduct computer simulation on plastic foaming processes. Finally, an experimental research on foaming with blowing agent blends served as a case example to demonstrate how the elucidation of the mechanisms of various foaming phenomena would aid in the development of novel processing strategies to enhance the control of cellular structures in plastic foams.

In the present study / the effects of the powder metallurgical parameters such as the mixing method, compaction pressure, initial tungsten (W) particle size, composition, sintering temperature and sintering time on the sintering behavior of selected high density W-Ni-Cu alloys were investigated. The alloys were produced through conventional powder metallurgy route of mixing, cold compaction and sintering. The total solute (Ni-Cu) content in the produced alloys was kept constant at 10 wt%, while the copper concentration of the solutes was varied from 2.5 wt% to 10 wt%. Mainly liquid phase sintering method was applied in the production of the alloys. The results of the study were based on the density measurements, microstructural characterizations including optical and scanning electron microscopy and mechanical characterizations including hardness measurements. The results showed that the nature of the mixing method applied in the preparation of the powder mixtures has a considerable effect on the final sintered state of W-Ni-Cu alloys. Within the experimental limits of the study, the compaction v pressure and initial W particle size did not seem to affect the densification behavior. It was found that the sintering behavior of W-Ni-Cu alloys investigated in this study was essentially dominated by the Ni content in the alloy and the sintering temperature. A high degree of densification was observed in these alloys with an increase in the Ni content and sintering temperature which was suggested to be due to an increase in the solubility and diffusivity of W in the binder matrix phase with an increase in these parameters, leading to an increase in the overall sintering kinetics. Based on the results obtained in the present study, a model explaining the kinetics of the diffusional processes governing the densification and coarsening behavior of W-Ni-Cu alloys was proposed.

The multigrid technique is one of the most effective techniques to achieve the reduction of the CPU cost for flow solvers. The multigrid strategy uses the multilevel grids which are the coarsening subsets of fine grid. An explicit solver rapidly reduces the high frequency errors on the computational grids. Since high frequency errors on coarse grids correspond to low frequency errors on fine grids, cycling through the coarse grid levels rapidly reduces the errors ranging from high-to-low frequency. The aim of this study is, therefore, to accelerate SENSE3D solver developed by TUBITAK-SAGE by implementating multigrid concept. In this work, a novel grid coarsening method suitable for cell-centered hybrid/unstructured grids is developed to provide the cells with high aspect ratio. This new grid coarsening technique relies on the agglomeration of cells based on their distribution on octree data structure. Then, the multigrid strategy is implemented to the baseline flow solver. During this implementation, the flux calculation along the face loops is modified without changing cell-centered scheme. The performance of the coarsening algorithm is investigated for all grid types in two and three dimension. The grid coarsening algorithm produces well defined, nested, body fitted coarser grids with aspect ratios of one and the coarse grids have similar characteristics of Cartesian grids. Then, the multigrid flow solutions are obtained at inviscid, laminar and turbulent flows. It is shown that, the convergence accelerations are up to 14 times for inviscid flows and in a range of 4 to 110 fold for turbulent flow solutions.

This dissertation investigates microstructure/property relations in ultrahigh carbon steel (UHCS) with the aim of improving toughness while retaining high hardness. Due to high C contents (ranging from 1 to 2 wt%), UHCS exhibit high strength, hardness, and wear resistance. Despite this, applications for UHCS are currently limited because they typically contain a continuous network of proeutectoid cementite that greatly reduces ductility and toughness. In previous research, thermomechanic processing had seen considerable success in breaking up the network. However, the processing is difficult and has thus far seen very limited industrial application. Chemical modification of the steel composition has also seen some success in network break-up, but is still not well understood. There have been relatively few fundamental studies of microstructure evolution in UHCS; studies in the literature typically focused on lower C steels (up to 1 wt% C) or on cast irons (>2.1 wt% C). Thus, this work was undertaken to gain a better understanding of microstructural changes that occur during heat treatment and/or chemical modification of UHCS with a focus on the distribution of proeutectoid cementite within the microstructure. This dissertation is composed of eight chapters. The first chapter presents an introduction to phases found in UHCS, descriptions of research materials used in each chapter, and the hypotheses and objectives guiding the work. The second chapter describes a study of the microstructure found in a 2C-4Cr UHCS before and after an industrial-scale austenitizating heat treatment that increased hardness and toughness and also produced discrete carbide particles in the matrix. The third chapter establishes and demonstrates a metric for measuring connectivity in carbide networks. The fourth chapter describes a series of heat treatments designed to investigate kinetics of spheroidization and coarsening of carbide particles and denuded zones near cementite network branches in 2C-4Cr UHCS. The fifth chapter describes an additional series of heat treatments comparing coarsening kinetics in 2C-1Cr and 2C-4Cr UHCS. Lowering the Cr content caused clustering of cementite particles near grain boundaries, in contrast to the denuded zones observed in the higher Cr UHCS. The fifth chapter details four in situ confocal laser scanning microscopy heat treatments of 2C-4Cr UHCS. The seventh chapter investigates the effects of a 2wt% Nb addition on 2C-4Cr UHCS. The eighth and final chapter summarizes the findings of all the experiments of the previous chapters and revisits the objectives and conclusions.