This thesis deals with diffusion and flow of sub-critical hydrocarbons in activated carbon by using a differential permeation method. The hydrocarbons are selected according to the effect on environmental concerns and their unique characteristics such as polarity and affinity towards activated carbon. Although it has been known that transport processes in activated carbon consist of Knudsen diffusion, gaseous viscous flow, adsorbed phase diffusion (so called, surface diffusion) and condensate flow, there have been no rigorous models to describe the transport processes in activated carbon with a full range of pressures. In particular among the four processes, the mechanism of adsorbed phase diffusion in activated carbon is still far from complete understanding. Also due to the dispersion interactions between adsorbing molecules and the solid surface, one would expect that Knudsen diffusion is influenced by the dispersive forces. From intensive experimental observations with a great care over a full range of pressures, conventional methods (for example, direct estimation from inert gas experiments) to determine adsorbed phase diffusion are found to be inadequate for strongly adsorbing vapors in activated carbon. By incorporating the effect of adsorbate-adsorbent interactions into Knudsen diffusivity, the general behavior of adsorbed phase diffusion in terms of pressure (or surface loading) can be obtained, showing a significant role in transport at low pressures. For non-polar hydrocarbons such as benzene, carbon tetrachloride and n-hexane, a mathematical model, which accounts for the effects of adsorbate-adsorbent interactions and pore size distribution, is formulated and validated, resulting in a good agreement with experimental data. Moreover, the adsorption and dynamic behaviors of alcohol molecules (which are polar compounds) are investigated with an aim to compare their behaviors against those of non-polar compounds.

This thesis deals with diffusion and flow of sub-critical hydrocarbons in activated carbon by using a differential permeation method. The hydrocarbons are selected according to the effect on environmental concerns and their unique characteristics such as polarity and affinity towards activated carbon. Although it has been known that transport processes in activated carbon consist of Knudsen diffusion, gaseous viscous flow, adsorbed phase diffusion (so called, surface diffusion) and condensate flow, there have been no rigorous models to describe the transport processes in activated carbon with a full range of pressures. In particular among the four processes, the mechanism of adsorbed phase diffusion in activated carbon is still far from complete understanding. Also due to the dispersion interactions between adsorbing molecules and the solid surface, one would expect that Knudsen diffusion is influenced by the dispersive forces. From intensive experimental observations with a great care over a full range of pressures, conventional methods (for example, direct estimation from inert gas experiments) to determine adsorbed phase diffusion are found to be inadequate for strongly adsorbing vapors in activated carbon. By incorporating the effect of adsorbate-adsorbent interactions into Knudsen diffusivity, the general behavior of adsorbed phase diffusion in terms of pressure (or surface loading) can be obtained, showing a significant role in transport at low pressures. For non-polar hydrocarbons such as benzene, carbon tetrachloride and n-hexane, a mathematical model, which accounts for the effects of adsorbate-adsorbent interactions and pore size distribution, is formulated and validated, resulting in a good agreement with experimental data. Moreover, the adsorption and dynamic behaviors of alcohol molecules (which are polar compounds) are investigated with an aim to compare their behaviors against those of non-polar compounds.

This thesis deals with diffusion and flow of sub-critical hydrocarbons in activated carbon by using a differential permeation method. The hydrocarbons are selected according to the effect on environmental concerns and their unique characteristics such as polarity and affinity towards activated carbon. Although it has been known that transport processes in activated carbon consist of Knudsen diffusion, gaseous viscous flow, adsorbed phase diffusion (so called, surface diffusion) and condensate flow, there have been no rigorous models to describe the transport processes in activated carbon with a full range of pressures. In particular among the four processes, the mechanism of adsorbed phase diffusion in activated carbon is still far from complete understanding. Also due to the dispersion interactions between adsorbing molecules and the solid surface, one would expect that Knudsen diffusion is influenced by the dispersive forces. From intensive experimental observations with a great care over a full range of pressures, conventional methods (for example, direct estimation from inert gas experiments) to determine adsorbed phase diffusion are found to be inadequate for strongly adsorbing vapors in activated carbon. By incorporating the effect of adsorbate-adsorbent interactions into Knudsen diffusivity, the general behavior of adsorbed phase diffusion in terms of pressure (or surface loading) can be obtained, showing a significant role in transport at low pressures. For non-polar hydrocarbons such as benzene, carbon tetrachloride and n-hexane, a mathematical model, which accounts for the effects of adsorbate-adsorbent interactions and pore size distribution, is formulated and validated, resulting in a good agreement with experimental data. Moreover, the adsorption and dynamic behaviors of alcohol molecules (which are polar compounds) are investigated with an aim to compare their behaviors against those of non-polar compounds.

This thesis deals with diffusion and flow of sub-critical hydrocarbons in activated carbon by using a differential permeation method. The hydrocarbons are selected according to the effect on environmental concerns and their unique characteristics such as polarity and affinity towards activated carbon. Although it has been known that transport processes in activated carbon consist of Knudsen diffusion, gaseous viscous flow, adsorbed phase diffusion (so called, surface diffusion) and condensate flow, there have been no rigorous models to describe the transport processes in activated carbon with a full range of pressures. In particular among the four processes, the mechanism of adsorbed phase diffusion in activated carbon is still far from complete understanding. Also due to the dispersion interactions between adsorbing molecules and the solid surface, one would expect that Knudsen diffusion is influenced by the dispersive forces. From intensive experimental observations with a great care over a full range of pressures, conventional methods (for example, direct estimation from inert gas experiments) to determine adsorbed phase diffusion are found to be inadequate for strongly adsorbing vapors in activated carbon. By incorporating the effect of adsorbate-adsorbent interactions into Knudsen diffusivity, the general behavior of adsorbed phase diffusion in terms of pressure (or surface loading) can be obtained, showing a significant role in transport at low pressures. For non-polar hydrocarbons such as benzene, carbon tetrachloride and n-hexane, a mathematical model, which accounts for the effects of adsorbate-adsorbent interactions and pore size distribution, is formulated and validated, resulting in a good agreement with experimental data. Moreover, the adsorption and dynamic behaviors of alcohol molecules (which are polar compounds) are investigated with an aim to compare their behaviors against those of non-polar compounds.

Consideramos um modelo hamiltoniano do movimento eletrostático de deriva para investigar o trasnporte caótico de partículas na borda de plasmas confinados em Tokamaks. Este modelo leva em conta a turbulência eletrostática de deriva, responsável pelo transporte anômalo. O modelo Hamiltoniano provê as equações de movimento, que são dependentes de uma função para o potencial elétrico. Esta função é caracterizada por um potencial de equilíbrio mais um termo correspondente às ondas de deriva. Assumimos três diferentes perfis radiais para o campo elétrico radial de equilíbrio: um linear e outros dois não-monotônicos com extremos suaves. Para estes perfis, mostramos que o modelo pode ser reduzido a três mapas simpléticos bidimensionais e não integráveis: o mapa padrão, o mapa padrão não twist e um mapa modelo não twist introduzido neste trabalho. O mapa padrão não twist e o mapa modelo violam a condição twist, fundamental para os teoremas KAM e de Birkhoff. Para estes mapas não twist, estudaremos numericamente barreiras de transporte criadas próximas às curvas shearless. Mostramos que, para o mapa modelo, a barreira de transporte é robusta, isto é, persiste em um amplo intervalo de variação de um de seus parâmetros. Dentro da região da barreira, descrevemos o nascimento de cadeias de ilhas com períodos par e ímpar devido à variação do parâmetro de controle. Analisamos estes dois cenários calculando os números de rotação dentro da barreira e identificando as bifurcações que criam as ilhas. Finalmente, conjecturamos que todas as ilhas dentro da região da barreira são criadas por estes dois cenários. Além disso, se o número de rotação da curva shearless atinge um número racional, as cadeias de ilhas são criadas de acordo com os cenários descritos. / We consider a hamiltonian model of the electrostatic drift motion to investigate chaotic particle transport in the Tokamak plasma edge. This model takes into account the electrostatic drift turbulence, which is responsible for the anomalous transport. The Hamiltonian model provides the basic equations of motion, which are dependent on the form of an electric potential function. This function is characterized by the equilibrium potential and the term corresponding to the drift waves. We assume three diferent radial profiles for the equilibrium radial electric field: one linear and the other two non-monotonic with a smooth extremum. For these profiles, we show that the model can be reduced to three symplectic maps: the standard map, the nontwist standard map, and a nontwist model map introduced in this work. The nontwist standard map and the model map violate the twist condition, a property of fundamental importance for the applicability of the KAM and Birkhoff theorems. For these nontwist maps, we study numerically the transport barriers created around their shearless curves. We show for the model map that the transport barrier is robust,i.e., remains for a wide range of one of its parameters. Inside the barrier region, we describe the birth of island chains with even or odd periods due to the control parameter variation. We analyse these two scenarios by calculating the winding numbers inside the barrier region and identifying the bifurcations that create the islands. Finally, we conjecture that all the island chains inside the barrier are created by these two scenarios. Moreover, if the winding number of the shearless curve reachs a rational number, the island chains are created according to the described scenarios.

O perfil de concentração do soluto próximo à interface cristal/liquido foi estudado durante o processo de crescimento e dissolução de cristais de iodeto de mercúrio (\'ALFA\'-Hg\'I IND.2\') com a técnica óptica medida de fase par difração, denominada de \"diffrasor\". A técnica é simples, sensível a fenômenos hidrodinâmicos e pode ser usada tanto em macro com em micro-observações. Com essa técnica medimos, pela primeira vez, o perfil de concentração do soluto até 10 \'mu\'m da superfície do cristal. Os resultados mostram que o crescimento do \'ALFA\'-Hg\'I IND.2\' é fortemente afetado pela supersaturação da solução, a qualidade da superfície cristalina, a convecção da solução, a história do processo de crescimento e o número de faces vinculadas. A difusão do soluto e o fluxo interfacial são considerados os responsáveis pelo transporte de massa durante o processo de crescimento da face (001) do \'ALFA\'-Hg\'I IND.2\'. Uma anomalia no perfil de concentração próximo da interface foi detectada, pela primeira vez, durante a dissolução de um cristal de iodeto de mercúrio. Nós acreditamos QUe essa anomalia está diretamente associada aos fluxos de soluto. / The solute concentration profile near to the crystal/liquid inter-face was studied during mercuric iodide crystal growth and dissolution with phase measurement by diffraction optical technique - \"diffrasor\". It\'s simple, sensitive to hydrodynamics phenomena and may be used either in macro or in micro-observations. With this technique we measured, for the first time, the solute concentration profile up to 10 um from the a-Hg12 crystal surface- The state of the art results the us first that \'ALFA\'-Hg\'I IND.2\' is strongly affected by supersaturation, convenction in the solution, history of the growth process, surface quality and of the tied facets numbers- The solute diffusion and interfacial flow are considered responsible by mass transport during crystal growth. A anomaly in the concentration profile near interface was detected, for the first time, during the mercuric iodide crystal dissolution- We believe that this anomaly is directly associated with the solute flux during dissolution process.

A demanda do silício de grau solar (SiGS) utilizado na indústria fotovoltaica cresce atualmente em uma média de 35% ao ano e a projeção para a próxima década é de constante crescimento. Entretanto, a disponibilidade de matéria-prima para a produção do SiGS não tem crescido na mesma taxa, resultando em uma elevação de seu custo. Logo, a obtenção de rotas alternativas menos onerosas para a produção do SiGS torna-se crucial, principalmente sendo o Brasil o 3o maior produtor mundial de silício de grau metalúrgico. Tendo como objetivo a purificação do silício, o presente trabalho de pesquisa apresenta um estudo detalhado da solidificação direcional do silício, que é uma das etapas utilizadas em todas as rotas alternativas atualmente pesquisadas com o objetivo de purificação. Este estudo foi realizado em um forno do tipo Bridgman vertical, onde o silício líquido contido em um molde foi extraído da região quente do forno, resultando em uma solidificação direcional controlada e ascendente. Dois tipos de silício foram escolhidos como material de entrada para o processo de refino: o silício de grau metalúrgico e o silício de grau metalúrgico pré-refinado por lixiviação. Quatro velocidades de extração do molde entre 5 a 110 mm/s foram empregadas nos ensaios. A macrossegregação de impurezas nos lingotes obtidos foi medida através de análises químicas e a estrutura metalúrgica observada através de macro e micrografias. Os lingotes solidificados com menor velocidade de extração, onde se observa evidências de uma interface sólido-líquido plana, apresentam um grau de refino superior aos de maior velocidade, que mostram evidências de uma interface celular ou dendrítica. As análises químicas mostram que, após a solidificação direcional, os teores de Fe, Al, Cr e Ti medidos nas regiões da base e central dos lingotes atingem níveis especificados para o SiGS por alguns autores. / The demand for solar grade silicon (SiGS) in the photovoltaic industry has grown 35% per year and a constant growth rate is predicted for the next decade. The availability of feedstock to produce SiGS, however, has not grown at the same rate, resulting in increasing SiGS cost. Consequently, the development of less expensive alternative processing routes is of paramount importance to the photovoltaic industry in general, and particularly to Brazil, which is the 3rd largest producer of metallurgical grade silicon. The objective of the present work is to study the directional solidification of silicon, which is a step adopted in virtually all alternative processing routes under development to refine silicon. The directional solidification of silicon was carried out in a vertical Bridgman furnace, where liquid silicon was poured into a quartz mold, which was extracted at constant velocity from the hot region of the furnace, resulting in ascending directional solidification. Two types of feedstock silicon were used, namely, a metallurgical grade silicon that was refined by leaching prior to directional solidification and metallurgical grade silicon as-received from the manufacturer. The quartz molds with liquid silicon were extracted at four different velocities in the range from 5 to 110 mm/s. In the solidified silicon ingots, the macrosegregation of elements were measured using accurate analytical techniques, whereas the metallurgical structures were observed in macro and micrographs. The ingots solidified at lower extraction velocities, at which evidences of a planar solidliquid interface were observed, showed greater refining effect than those solidified at larger velocities, which showed evidences of a cellular or dendritic solid-liquid interface. The contents of Fe, Al, Cr, and Ti measured at the base and center portions of the solidified ingots comply with the specifications of SiGS proposed by some authors.

Conselho Nacional de Desenvolvimento CientÃfico e TecnolÃgico / Neste trabalho investigamos diversos fenÃmenos de transporte tendo lugar atravÃs de meios irregulares por meio de simulaÃÃo computacional. Inicialmente, tratamos do efeito da desordem crÃtica em redes percolantes de poros sujeitas à difusÃo e reaÃÃo quÃmica. Verificamos a existÃncia de trÃs regimes distintos, determinados pelo parÃmetro adimensional E=D/(Kl^2), onde D à a difusÃo molecular, K o coeficiente de reaÃÃo quÃmica e l um comprimento caracterÃstico. Para valores baixos de E, o fluxo de reagente que penetra a rede obedece à relaÃÃo de escala clÃssica, F~LE^(1/2). Para valores intermediÃrios de E, a influÃncia da morfologia fractal do agregado de percolaÃÃo resulta em um regime anÃmalo, F~L^(A/2)E^B, com um expoente B=0.34. Para valores altos de E, o fluxo de reagente atinge um limite de saturaÃÃo, F_SAT, e escala com o tamanho do sistema na forma F_SAT=L^A, onde A=1.89 corresponde à dimensÃo fractal do agregado incipiente de percolaÃÃo. Em uma segunda etapa do trabalho, analisamos o efeito da geometria irregular na desativaÃÃo seqÃencial de uma interface acessada por difusÃo. Aplicando o conceito de zona ativa, propomos uma conjectura que se constitui numa extensÃo do teorema de Makarov. Na terceira parte deste trabalho, investigamos o transporte estacionÃrio de calor no escoamento de um fluido atravÃs de um tubo bidimensional, cujas paredes sÃo interfaces irregulares. Mais uma vez, utilizando o conceito de zona ativa, investigamos o efeito da geometria da interface na eficiÃncia de troca tÃrmica do sistema em diferentes condiÃÃes difusivo-convectivas. Em condiÃÃes nas quais o mecanismo de transporte dominante à a conduÃÃo, a comparaÃÃo entre os resultados dos tubos liso e rugosos indica que o efeito da rugosidade à quase desprezÃvel sobre a eficiÃncia de dispositivos de transporte de calor. Por outro lado, quando a convecÃÃo torna-se dominante, a rugosidade passa a ter um papel importante e, em geral, o fluxo de calor e o comprimento da zona ativa aumentam com a rugosidade da interface de troca. Finalmente, mostramos que esse Ãltimo comportamento està relacionado com as zonas de recirculaÃÃo, presentes nas reentrÃncias da geometria fractal. / In this work, we investigate different transport phenomena through irregular media by means of numerical simulations. Initially, we study the effect of the critical percolation disorder on pore networks under diffusion-reaction conditions. Our results indicate the existence of three distinct regimes of reactivity, determined by the dimensionless parameter E=D/(Kl^2), where D is the molecular diffusivity of the reagent, K is its chemical reaction coefficient, and l is the length scale of the pore. At low values of E, the flux of the reacting species penetrating the network follows the classical scaling behavior, namely F~LE^(1/2). At intermediate values of E, the influence of the fractal morphology of the percolating cluster results in an anomalous behavior, F~L^(A/2)E^B, with an exponent B=0.34. At high values of E, the flux of the reagent reaches a saturation limit, F_SAT, that scales with the system size as F_SAT=L^A, with an exponent A=1.89, corresponding to the fractal dimension of the sample-spanning cluster. In the second part of this work, we study how the irregularity of the geometry influences the sequential deactivation of an interface accessed by diffusion. By using the notion of active zone, we propose a conjecture which constitutes an extension of Makarov theorem. In the third part, we investigate the steady-state heat transport in a fluid flowing through a two-dimensional channel whose walls are irregular interfaces. Once more, we apply the notion of active zone to investigate the effect of the interface geometry on the heat exchange efficiency of the system for different conductive-convective conditions. Compared with the behavior of a channel with smooth interfaces and under conditions in which the mechanism of heat conduction dominates, the results indicate that the effect of roughness is almost negligible on the efficiency of the heat transport system. On the other hand, when the convection becomes dominant, the role of the interface roughness is to generally increase both the heat flux across the wall as well as the active length of heat exchange, when compared with the smooth channel. Finally, we show that this last behavior is closely related with the presence of recirculation zones in the reentrant regions of the fractal geometry.

O tema desta tese é a propriedade não-twist em sistemas Hamiltonianos. Sistemas com essa propriedade violam a condição twist ao longo de uma curva sem shear e, consequentemente, sua topologia não é descrita pelos cenários típicos previstos pelos teoremas KAM (Kolmogorov - Arnold - Moser) e Poincar´e - Birkhoff. A curva sem shear é identificada pelo valor de máximo ou mínimo no perfil espacial do número de rotação do sistema. Além disso, próximo `a curva sem shear podemos observar algumas bifurcações atípicas como: colisões de ´orbitas periódicas e reconexão de separatrizes. As características dos sistemas não-twist são bem particulares, mas n´os demonstramos que seus cenários podem ser encontrados, localmente, em sistemas Hamiltonianos genéricos, devido ao nascimento de uma curva sem shear no interior de ilhas regulares. Inicialmente, nossas investigações numéricas constataram que esse fenômeno pode surgir não somente para a concomitante bifurcação de período 3 do ponto elíptico, mas também para outras bifurcações, tais como período 4 e período 5. Posteriormente, consideramos um modelo que descreve o comportamento das linhas de campos magnéticos em tokamaks com limitadores ergódigos. Nesse caso, o modelo utilizado é um mapa simplético parametrizado a partir das características físicas de um tokamak de grande razão de aspecto. Para esse sistema, estudamos os efeitos no transporte causados pelas bifurcações oriundas da presença da curva sem shear secundária e, também, pelas modificações do perfil rotacional das linhas de campo. / The topic of this Thesis is the nontwist property in Hamiltonian systems. Systems with such property violate the twist condition along the shearless curve and, therefore, its topology is not described for typical scenarios provided by KAM (Kolmogorov - Arnold - Moser ) and Poincar´e Birkhoff theorems. The shearless curve is identified by the maximum or minimum values of the spatial rotation number profile of the system. Moreover, close to the shearless curve we observe some atypical bifurcations as periodic orbits collisions and separatrix reconnection. The features of nontwist systems are very particular, but we have shown that its scenarios can be found locally in generic Hamiltonian systems, due to the onset of a secondary shearless curve within regular islands. Initially, our numerical investigations have found that this phenomenon may arise not only for the concomitant period 3 bifurcation of the elliptic point, but also for others bifurcations such as period 4 and period 5. Subsequently, we considered a model that describes magnetic field lines in tokamaks with ergodic limiters. In this case, the model is a symplectic map parameterized from the physical characteristics of a large aspect ratio tokamaks. For this system, we studied the effects on the transport caused by the presence of secondary shearless torus and also by changing the field lines rotational profile.

As variáveis de processo determinam as propriedades dos produtos resultantes dos processos de fundição ou de soldagem, que são função da sua macro e microestrutura bruta de solidificação. Um dos parâmetros importantes para se determinar as propriedades de um produto é a posição da transição colunarequiaxial (CET) e, por este motivo, o entendimento dos fenômenos físicos que causam esta transição é essencial. Com o intuito de se prever a formação da CET, surgiram os métodos empíricos e os modelos matemáticos, que são divididos em dois grandes grupos: modelos determinísticos e modelos estocásticos. Estes dois grupos foram bem estudados, porém nunca foram comparados entre si, particularmente em relação à previsão da posição da CET. O presente trabalho tem como um primeiro objetivo preencher esta lacuna através da comparação entre estes modelos. No entanto, o objetivo principal é apresentar, implementar e validar um novo modelo matemático, denominado de híbrido estocástico-determinístico (CADE -\"Cellular Automaton Deterministic\"), que combine características importantes e vantajosas de cada um dos dois grupos de modelos. Inicialmente, um modelo representante do grupo dos modelos estocásticos foi implementado e validado frente a resultados disponíveis na literatura. Durante esta validação, foi necessária a elaboração de um critério baseado na razão de aspecto dos grãos para a identificação da CET nas macroestruturas calculadas pelo modelo. Estes resultados foram então comparados com os resultados de modelos determinísticos para, após cuidadosa discussão, possibilitar a proposta e implementação do modelo híbrido. Os modelos determinísticos que utilizam o critério mecânico para prever o bloqueio de grãos colunares e a ocorrência da CET mostram regiões colunares em geral maiores que as previstas pelo modelo estocástico. Por outro lado, os modelos determinísticos que utilizam um critério de bloqueio a partir da interação do campo de concentração de soluto ao redor dos grãos prevêem uma CET em posições semelhantes às calculadas pelos modelos estocásticos. O modelo implementado no presente trabalho é capaz de prever a macroestrutura bruta de solidificação e ainda utilizar as equações tradicionalmente empregadas nos modelos determinísticos, sem a necessidade de qualquer método extra para prever a posição da frente de crescimento colunar ou o seu bloqueio por grãos equiaxiais. / The processing variables determine many properties of the products obtained by casting and welding processes and these properties, on the other hand, are strongly affected by the as-cast micro and macrostructure. Particularly the position of the columnar-to-equiaxed transition (CET), which determines the amount of columnar and equiaxed grains in the macrostructure, has an important effect on the properties of as-cast parts. Therefore, understanding the important physical phenomena that cause and affect the formation of the CET plays a crucial role in predicting the ascast macrostructure. To predict the CET formation, empirical methods and mathematical models have been developed. These models are frequently divided into two main groups: deterministic and stochastic. Both groups have been thoroughly studied, but a comparison between them was never attempted, especially regarding the prediction of the CET position. One of the main objectives of the present work is to fulfill this gap by carefully comparing these models. Nevertheless, the most important objective is to propose, implement, and validate a hybrid stochastic-deterministic model, referred to as CADE (Cellular Automaton Deterministic), that combines some important and well-known features of each model. Initially, a model from the stochastic group was implemented and validated using results available in the literature and then used to analyze the effects of some processing variables on the CET prediction. To carry out this analyzes, a criteria based on the aspect ratio of the grains was proposed and developed to identify the CET region from macrostructure images calculated by the model. The results were compared with those obtained by deterministic models and finally led to the development of the new proposed model. This new model has some characteristics from each group of mathematical models and, for this reason, was denoted as hybrid. A deterministic model based on a mechanical blocking criterion to block columnar grains and define the CET position showed, for the most part, larger columnar regions than those predicted by the stochastic model. A deterministic model with a solutal blocking criterion to predict the CET showed results similar to those calculated with the stochastic model. The model proposed in the present work (CADE) was able to predict the as-cast macrostructure using the well-established deterministic equations, without the need for a new method to track columnar grains or predict their blocking by equiaxed grains.