This thesis addresses modeling transport phenomena in porous media with special attention being paid to convective characteristics of variable viscosity fluids in a homogeneous and isotropic medium. Two different categories of flows, with totally different driving forces, are considered being forced and free convection (both side and bottom heating, for a square enclosure, are studied). To account for property variation, the density is modeled by an Oberbeck–Boussinesq approximation while the viscosity is modeled by an exponential function. The limitations of the previous work, addressing the issue, are discussed in detail and improvements, in terms of thermo-hydraulic performance of the system are suggested. Dealing with the global aspects of the problem, the two major methods being the reference temperature and the property ratio approach are implemented. For natural convection problems, the former method is used; while for forced convection the latter is undertaken. New correlations, which are proved to be more accurate, are proposed for both forced and free convection problems. Besides, closed form solutions are reported for some cases of constant and variable viscosity. Convection visualization is also studied in detail where the concept of Energy Flux Vectors is put forward along with the application of heatlines and energy streamlines. It was mathematically shown that in two-dimensional space heatlines and energy streamlines, which were invented independently, are the same as each other. Moreover, the newly developed concept, energy flux vectors serve as a new tool for convection visualization with the main advantage that this new technique, unlike heatlines and energy streamlines, does not require further (and sometimes complicated) numerical analysis in addition to solving momentum and thermal energy equations. This, in its turn, reduces the time and computer resources required to see the flow of energy. Finally, in Chapter 7, the summary of the work along with the conclusions are presented. Finally, recommendations for future studies are put forward.

Fluid flow in porous media is important for a number of fields including nuclear waste disposal, oil and gas, fuel cells, water treatment and civil engineering. The aim of this work is to improve the current understanding of how the pore space governs the fluid flow in porous media in the context of nuclear waste disposal. The effects of biofilm formation on flow are also investigated. The thesis begins with a review of the current porous media characterisation techniques and the means for converting the pore space into pore network models and their existing applications. Further, I review the current understanding of biofilm lifecycle in the context of porous media and its interactions with fluid flow. The model porous media used in this project is Hollington sandstone. The pore space of the material is characterised by X-ray CT and the equivalent pore networks from two popular pore network extraction algorithms are compared comprehensively. The results indicate that different pore network extraction algorithms could interpret the same pore space rather differently. Despite these differences, the single-phase flow properties of the extracted networks are in good agreement with the estimates from a direct approach. However, it is recommended that any flow or transport study using pore network modelling should entail a sensitivity study aiming to determine if the model results are extraction method specific. Following these results, a pore merging algorithm is introduced aimed to improve the over segmentation of long throats and hence improve the quality of the extracted statistics. The improved model is used to study quantitatively the pore space evolution of shale rock during pyrolysis. Next, the extracted statistics from one of the algorithms is used to explore the potential of regular pore network models for up-scaling the flow properties of porous materials. Analysis showed that the anisotropic flow properties observed in the irregular models are due to the different number of red (critical) features present along the flow direction. This observation is used to construct large regular models that can mimic that behaviour and to discuss the potential of estimating the flow properties of porous media based on their isotropic and anisotropic properties. Finally, a long-term flow-through column experiment is conducted aiming to understand the effects of bacterial colonisation on flow in Hollington sandstone. The results show that such systems are quite complex and are susceptible to perturbations. The flow properties of the sandstone were reduced significantly during the course of the experiment. The possible mechanisms responsible for the observed reductions in permeability are discussed and the need for developing new imaging techniques that can allow examining biofilm development in-situ is underlined as necessary for drawing more definitive conclusions.

Porous media affect hydrate stability by forcing hydrate-liquid interfaces to form high curvature geometries and by forcing the molecules of the hydrate, liquid, and sedimentary particles that compose the medium to interact where they are in close proximity. To evaluate these effects we first create synthetic spherical packings to approximate pore space geometry. We use the synthetic pore space to calculate the perturbation to the chemical potential caused by the geometrical constraints. Our model predictions agree with published data for ice-water and water-vapor systems. When particles are well-approximated as spheres, our model fits the data with R-squared values that range between about 80% to over 99%. However, our model needs to be improved for porous media that contain a significant fraction of non-equant particles such as clay. Lastly, we demonstrate how our model can be used in predictions for the evolution of hydrate saturation. This thesis includes unpublished co-authored material.

SILVA, Jorge Roberto Pereira da. Invasões múltiplas em meios porosos desordenados. 2013. 73 f. Dissertação (Mestrado em Física) - Programa de Pós-Graduação em Física, Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2013. / Submitted by Edvander Pires (edvanderpires@gmail.com) on 2015-10-22T19:09:24Z No. of bitstreams: 1 2013_dis_jrpsilva.pdf: 6800786 bytes, checksum: 53e5d20e14900eaa6675cb43b9feeb62 (MD5) / Approved for entry into archive by Edvander Pires(edvanderpires@gmail.com) on 2015-10-22T21:33:14Z (GMT) No. of bitstreams: 1 2013_dis_jrpsilva.pdf: 6800786 bytes, checksum: 53e5d20e14900eaa6675cb43b9feeb62 (MD5) / Made available in DSpace on 2015-10-22T21:33:14Z (GMT). No. of bitstreams: 1 2013_dis_jrpsilva.pdf: 6800786 bytes, checksum: 53e5d20e14900eaa6675cb43b9feeb62 (MD5) Previous issue date: 2013 / In this dissertation, we investigate by means of numerical simulations geometrical and transport properties related with the invasion phenomena through disordered porous media in a very slow invasion regime, using two and three dimensions porous medias. Here, the porous media is modeling by means of a random structure, where each pore is represented by a random number comes from a uniform distribution. We assume that the invasion process occurs in the limit of very low viscous force, which means that the invasion process is controlled by capillary force. In this limit the invasion percolation model without trap is suitable. The new aspect incorporated here, consists basically of a multiple invasion process, where after the first invasion takes place only part of the structure of the porous, that was invaded previous, can be invaded again. We study, how the multiple invasion changes the fractal dimension of the invaded cluster. Estimated values for the fractal dimension of the invaded region reveal that the critical exponents vary as a function of the generation number G, i.e., where the number of times the invasion takes place. On base in numerical datas, we show the averaged mass M of the invaded region decreases with a power law as a function of G, M ∼ G{−β} , where the exponents β ≈ 0.59 (2D) and β ≈ 0.73 (3D). We also investigated, how the fractal dimension changes as a function of G, find that the fractal dimension of the invaded cluster changes from df = 1.89 ± 0.02 to ds = 1.22 ± 0.02 and df = 2.52 ± 0.02 to ds = 1.46 ± 0.02 for (2D) and (3D), respectively. These results confirm that the multiple invasion process follows a continuous transition from one universality class (nontrapping invasion percolation) to another (optimal path), furthermore these change are continuos for both dimensionality. Another aspect investigated, was the avalanche distribution in the invasion process. We analyzed how the distribution of avalanche changes as function of G, more precisely, how the multiple invasion process changes the exponent τ of the power law distribution. Regardless the values, we find that the behaviour of the exponents τ looks like the same for both dimensions studied. The exponents τ , initially change in a very slow way until reach a region, of certain value of G which depend on the dimension, they start to decrease in a deep way until reach the saturation value. The saturation value is close, for (2D), to one-dimension case. / Nesta dissertação, investigamos por meio de simulação computacional propriedades geométricas e de transportes relacionadas ao fenômeno de invasão em meios porosos desordenados no regime de invasão muito lento em sistemas bidimensionais e tridimensionais. O meio poroso considerado aqui é representado por meio de uma estrutura desordenada onde a cada poro que compõe este meio se associa um número aleatório obtido a partir de uma distribuição uniforme. Considerando o regime lento de invasão, onde as forças capilares dominam o escoamento em relação as forças viscosas, utilizando para a dinâmica de invasão o modelo de percolação invasiva sem aprisionamento. Introduzimos um variante no modelo de percolação invasiva, assumindo o aspecto de múltiplas invasões, onde a cada nova invasão apenas parte do substrato utilizado na invasão anterior pode ser invadido novamente. Em uma primeira parte, estudamos como o processo de múltipla invasão altera as características do agregado invadido. Valores estimados para a dimensão fractal da região invadida revelam que os expoentes críticos variam em função do número de geração G, isto é, o número de vezes que o processo de invasão foi repetido. Com base em dados numéricos, mostramos que a massa média do agregado invadido decresce na forma de uma lei de potência como função de G, M ~ G^{-β}, com o expoente β = 0.59 (2D) e 0.73 (3D). Investigamos como a dimensão fractal do agregado invadido varia em função dos repetitivos processo de invasão, mostrando que as mesmas variam de df = 1.89 ± 0.02 até ds = 1.22 ± 0.02 para o caso (2D) e df = 2.52 ± 0.02 até ds = 1.46 ± 0.02 para o caso (3D). Os resultados confirmam que o processo de múltiplas invasões segue uma transição continua entre as classes de universalidade do modelo de percolação invasiva sem aprisionamento e ótimo caminho, sendo este comportamento observado em duas e três dimensões. Um outro aspecto investigado nessa dissertação, foi o fenômeno de avalanche que ocorre durante o processo de invasão. Investigamos como a distribuição de tamanhos de avalanche, que se comporta na forma de uma lei de potência P(S, L) ~ S^{-τ} , altera-se em função das múltiplas invasões. Mais precisamente, calculamos como o expoente que governa o comportamento das avalanches se altera em função do número de geração G. Verificamos que este comportamento do expoente em função de G é semelhante para duas e três dimensões, apresentando uma região de mudança suave seguida por uma mudança mais acentuada até atingir um limite de saturação, onde o sistema se comporta de maneira parecida com o caso unidimensional.

En récupération assistée du pétrole (EOR), des mousses sont injectées dans des milieu poreux pour améliorer l’efficacité de l’extraction. L’intérêt est d’éviter les digitations visqueuses, la mousse possédant une forte viscosité effective à faible nombre capillaire (Ca). Les mousses sont produites par co-injection de gaz et de solutions aqueuses de tensio-actifs. Cette thèse se propose de comprendre les mécanismes de formation et de transport de mousse en milieu poreux à travers un micromodèle hétérogène fabriqué en NOA. Les études de formation de mousse sont envisagées de deux manières. La première consiste à étudier une co-injection de deux fluides dans un milieu poreux grâce à un jet généré au centre du système. Cette expérience nous permet de constater qu’une dispersion des deux phases est visible pour des nombres capillaire d’injection plus grand que 10-5. Une deuxième expérience d’injection directe d’un train de bulle dans un milieu poreux montre que les bulles se divisent jusqu’à atteindre un diamètre proche de la taille des pores, pour des Ca suffisamment importants. Par ailleurs, nous avons étudié les propriétés de transport d’une mousse dans un milieu poreux. Des mesures directes montrent que la pression générée par l’écoulement peut être jusqu’à 3000 fois plus importante que la pression due à de l’eau à même débit d’injection pour Ca=10-6. Ce rapport diminue fortement avec le nombre capillaire. Une analyse des chemins parcourus par observation directe souligne que pour des faibles débits relatifs de gaz, seuls quelques chemins sont actifs. Il se trouve cependant qu’une augmentation de Ca ou du débit relatif de gaz conduisent à une homogénéisation du balayage de la mousse dans le milieu. A travers différents modèles de simple canaux droits à section constante ou variable, nous notons que la différence de pression créée par une seule bulle suit la loi de Bretherton en Ca^{2/3}. Cependant, la présence de constrictions conduit à l’existence d’un seuil en pression en-dessous de Ca=2.10-4, et donne lieu à des écoulements intermittents. Enfin, nous présentons des observations de formation et transport de mousse en présence d’huile. Nous constatons alors que la présence d’huile n’a pas d’impact notable pour la solution de tensio-actifs, que ce soit sur la formation ou le transport. / In enhanced oil recovery (EOR), foams are injected in porous media to improve oil recovery efficiency. The objective is to limit viscous fingering thanks to the high effective viscosity of the foam at low capillary number Ca. Foam is produced by the co-injection of a gas and a solution of surfactants. This thesis focuses on foam formation and transport mechanisms in model porous media using a heterogeneous micromodel made in NOA. Foam formation is studied using two different approaches. The first one consists in studying a co-injection of two fluids thanks to a jet flowing in the center of the system. This experiment shows that the less wetting fluids is dispersed in the other one when the capillary number is higher than 10-5. A second set of experiments is conducted by injected a pre-formed train of big bubbles in model a porous media. The bubbles divide until they reach a diameter of the order of to the pore size, for high enough capillary numbers Ca. Besides, we studied the transport properties of foam in similar model porous media. Direct measurements show that the pressure drop induces by the flow can be at Ca=10-6 as high as 3000 times the pressure corresponding to water injected at the same injection flow rate. This ratio decreases with capillary number. An analysis of the preferential paths by direct observations shows that, for low relative gas flow rate, only a few paths are active. However, an increase of the capillary number or if relative gas flow rate leads to a homogenization of the flow in the medium. Thanks to different simple models of straight or wavy channels, we measure that the pressure drop induced by a single bubble is in good agreement with Bretherton’s law, and scales as Ca2/3. However, in wavy channels the pressure drop due to a single bubble deviates from this prediction and exhibits a plateau at Ca lower than 10-4. In this regime, the motion of the bubble is usually intermittent. Finally, we focus on foam formation and transport properties in presence of oil. Our observations lead to the conclusion that for our setup and surfactant formulations, oil has a negligible influence.

Cette thèse porte sur la modélisation des phénomènes de dissolution lors de la phase précoce d'un accident grave de réacteur nucléaire. L'étude s'intéresse à la dissolution de céramiques solides (ZrO2 et UO2) par un métal liquide (Zr). En cas d'hypothétique accident grave dans un Réacteur à Eau Pressurisée, les phénomènes de dissolution jouent un rôle primordial dans l'aggravation de la dégradation et la fusion des oxydes à des températures parfois largement inférieures à leur température de fusion normale. Cela concerne en particulier les principaux constituants des crayons combustibles : les pastilles d'UO2 ainsi que la couche de ZrO2 formée sur la surface externe de la gaine qui vont subir une dissolution par le zircaloy des gaines à partir de 2100 K (la température de fusion de ces oxydes étant supérieure à 2800 K). Dans l'état actuel des connaissances, on peut supposer que les phénomènes de dissolution sont responsables, d'une part, de l'effondrement prématuré des crayons combustibles dans le cœur et, d'autre part, de la formation rapide d'un bain liquide en fond de cuve si des oxydes de fer sont présents. De nombreuses études expérimentales ont été menées sur ce sujet mais la modélisation n'est pas encore satisfaisante à ce jour. Les modèles actuels sont essentiellement des modèles 1D qui ne prennent pas en compte de façon explicite la convection naturelle ni la présence d'une zone de transition diphasique au niveau de l'interface métal / céramique. Un modèle 2D, décrivant les transferts de quantité de mouvement, de chaleur et de masse, établi par prise de moyenne volumique des équations microscopiques de transport a été développé. Ce modèle est basé sur des hypothèses d'équilibre thermique local et de non-équilibre massique local et s'inspire d'un modèle de solidification de mélanges binaires (P. Bousquet-Mélou, 2000). Sur le plan théorique, l'approche est identique. Cependant, la dissolution introduit des contraintes physico-numériques supplémentaires qu'il a fallu prendre en compte. La prise en compte des deux aspects mentionnés (convection et zone diphasique) constitue une nouveauté significative par rapport aux modèles existants. Le modèle a été ensuite étendu au cas ternaire grâce à des développements nouveaux permettant de résoudre certaines difficultés supplémentaires (ajout d'une équation d'espèce, relations d'équilibre non bijectives, plusieurs coefficients de diffusion à déterminer, indétermination sur les flux à l'interface, densité du solide non constante...) afin d'étudier la dissolution UO2 / Zr. Une validation des modèles obtenus est faite à partir de résultats expérimentaux de dissolution de creusets en ZrO2 et UO2 par le zircaloy liquide et montrent la bonne qualité prédictive de notre modèle. / This thesis focuses on the modeling of dissolution phenomena during the early phase of a serious accident of nuclear reactor. The study focuses on the dissolution of solid ceramic (ZrO2 and UO2) by a liquid metal (Zr). In case of hypothetical severe accident in a pressurized water reactor, the phenomena of dissolution play a role in the further decay and melting oxides at temperatures sometimes significantly below the normal melting temperature. This concerns in particular the main constituents of fuel rods : pellets of UO2 and ZrO2 layer formed on the outer surface of the sheath that will suffer by the dissolution of zircaloy sheaths from 2100 K (the melting temperature of these oxides being greater than 2800 K). In the present state of knowledge, we can assume that dissolution phenomena are responsible for, on the one hand, the premature collapse of the fuel rods in the heart and, on the other hand, the rapid formation of a liquid bath in the bottom of the tank where iron oxides are present. Many experimental studies have been conducted on this subject but modeling is not yet satisfactory today. Current models are essentially 1D models that do not explicitly account for natural convection nore the presence of a biphasic transition zone at the interface metal / ceramic. A 2D model describing the transfer of momentum, heat and mass, determined by taking average density of microscopic transport equations has been developed. This model is based on assumptions of local thermal equilibrium and non-local mass balance and it is based on a model of solidification of binary mixtures (P. Bousquet-Mélou, 2000). In theory, the approach is identical. However, the dissolution introduced physico-digital extra constraint that had to be taken into account. Taking into account the two aspects mentioned (convection and two-phase zone) is a novelty in comparison to existing models. The model was then extended to the ternary case with new developments to resolve certain difficulties (addition of an equation of this case, non-bijective equilibrium relations, several diffusion coefficients to be determined, uncertainty on flows in interface, density of the solid non-constant ...) to study the dissolution UO2 / Zr. Validation of models is obtained from experimental results of dissolution of crucibles of UO2 and ZrO2 by liquid zircaloy and show the quality of our predictive model.

Neste trabalho é investigada a relaxação longitudinal da magnetização nuclear de água impregnada em pastilhas de pó de alumina (Al IND. 2 O IND. 3) com grau de pureza de 99,8%, objetivando a determinação do diâmentro de poro de uma espuma cerâmica do mesmo material a partir de medidas do tempo de relaxação longitudinal T IND. 1. O trabalho fundamenta-se no fato dos tempos de relaxação da magnetização nuclear T IND. 1 e T IND. 2, spin-rede e spin-spin respectivamente, de um fluido confinado em um meio poroso serem menores que tempos T IND. 1B e T IND. 2B para o mesmo fluido não confinado. Mediram-se os tempos T IND. 1 para graus de impregnação de água nas amostras entre 10 e 100% usando um espectrômetro montado a partir de módulos comerciais e de um gerador de pulsos desenvolvido no IFSC-USP. A partir dos tempos T IND. 1 e dos diâmetros de poro das pastilhas de pó, determinou-se o valor da relaxatividade longitudinal ou intensidade de relaxação superficial (mu IND. 1), um parâmetro que caracteriza a interface água-alumina nestas amostras. Usando o valor de (mu IND. 1) obtido para o pó e o tempo de relaxação T IND. 1 medido nas amostras de espuma cerâmica foi determinado o diâmetro de poro desta. Última, o qual é comparado com os valores obtidos com a microscopia eletrônica e com a injeção de mercúrio. O caráter não invasivo desta técnica em contraste com as outras, faz dela a única possível em algumas aplicações. / Nuclear magnetization relaxation of water imbibed on 99,8% purê alumina (Al IND. 2 O IND. 3) grain packs is investigated aiming to determine the mean pore diameter of ceramic foam pieces of the same material. The work rely on the shortening of the relaxation times T IND. 1 spin-lattice and T IND. 2 spin-spin of the nuclear magnetization of fluids confined on porous media as compared with their T IND. 1B e T IND. 2B bulk values. Relaxation times T IND. 1 were measured, using a spectrometer built from commercial modules and a pulse generator developed at the IFSC-USP, varying the content of water imbibed from 10 to 100%. The longitudinal relaxation (mu IND. 1), or surface sink strength, was determined from the measured T IND. 1 values and the mean pore diameter of the powder packs. This parameter characterizes the water-alumina interface of these samples. Using the (mu IND. 1) value from the powder and the relaxation times T IND. 1 measured on the ceramic foam pieces, the mean pore diameter of these samples were determined and are compared with the values obtained from mercury intrusion and electron microscopie. The non-invasive character of this technique distinguishes it from the other, making it the only possible in some applications.

A medida de tempo de relaxação longitudinal (T1) e transversal (T2) de ressonância magnética nuclear (RMN) é muito utilizada para análise de meios porosos na área do petróleo. Esses tempos de relaxação estão relacionados com tamanho dos poros. As cerâmicas, dependendo da sua temperatura de sinterização, apresentam uma porosidade intrínseca, mas cerâmicas especiais para processo de filtragem e escafoldes de implantes ósseos necessitam de poros maiores e de permeabilidade para suas aplicações. Esse objetivo é alcançado introduzindo um agente porogênico, um material degradável com a temperatura, obtendo assim poros induzidos além dos intrínsecos. O agente porogênico escolhido para este trabalho foi cristais de sacarose, os tamanhos dos poros são controláveis pelo tamanho dos cristais e pela quantidade, tornado esse um meio factível nos estudos de RMN através dos tempos de relaxação. Foram selecionadas, através de peneiras, duas faixas de tamanhos de cristais de sacarose: G (grande) com limite superior de 600μm e inferior de 300μm e P (pequeno) com tamanhos na faixa de 38μm a 150μm. A cerâmica preparada com P apresentou distribuição de tamanho de poros (de 15 à 105μm) com mediana em 40μm, menor que a fabricada com G (de 20 à 125μm), media em 100μm. Distribuições de tamanho de poros com mediana intermediária foram obtidas pelas misturas de P e G na fabricação. Foram preparadas seis cerâmicas para os estudos: pura (sem adição de agente porogênico), 100% com G, 100% com P, mistura de 50% P e 50% G, mistura de 75% P e 25% G e mistura de 25% P e 75% G. As cerâmicas foram saturadas com água por um sistema de vácuo e através da sequência CPMG obtiveram-se os decaimentos multiexponenciais da relaxação transversal para os núcleos de ¹H de moléculas de água confinadas nos poros das cerâmicas. E assim, determinaram-se as distribuições de tempo de relaxação T2. A cerâmica pura apresentou apenas um pico para T2 em 0,053s, assim como obtido por Borgia e colaboradores em outros estudos, e comparando com resultados de porosimetria por intrusão de mercúrio (PIM), determinou-se o coeficiente de relaxatividade superficial de 3,7μm.s-1, valor próximo ao tabelado para a alumina (3μm.s-1) dando confiabilidade aos equipamentos utilizados. As cerâmicas preparadas com agente porogênico apresentaram dois picos na distribuição de T2 com o primeiro localizado na mesma região de tempo que corresponde à porosidade intrínseca (0,053s) e o segundo pico, referente à porosidade induzida, deslocando-se começando com a 100P com o menor tempo T2 (0,38s) e aumentando conforme o aumento da porcentagem de grânulo G (1,02s para 100G) de acordo com era esperado. A parti das imagens de microscopia eletrônica de varredura (MEV), obteve-se as distribuições de tamanho de poros induzidos e, novamente, determinou-se o coeficiente de relaxatividade, 12μm.s-1, valor maior comparado com o anterior devida as impurezas e resíduos da queima dos cristais de sacarose deixado na superfície do poro. Por fim, concluiu-se então que a RMN foi capaz de fazer a análise das cerâmicas de alumina observando poros intrínsecos da ordem de 0,1μm e poros induzidos com tamanho de dezenas a centenas de micrometros. Foram reunidos os resultados necessários para compreender como são formados os poros a partir do agente porogênico podendo fabricar cerâmicas com distribuições de tamanhos de poros conforme desejado. / The measurement of longitudinal (T1) and transversal (T2) nuclear relaxation times is an important method for the analysis of porous media, much used in the petroleum industry. It is possible through this technique the determination of the porosity and pore size distribution of the media. Ceramic materials already have an intrinsic porosity dependent on its sinterization temperature, but some applications such as filtering or scaffolding in bone regeneration demand for a larger porosity and permeability. To achieve this goal, a porogenic agent is introduced in the ceramics production process which is degradable in high temperatures, producing a ceramic with both induced and intrinsic porosity. The porogenic agent chosen for this project were saccharose crystals and the pores size is controlled by the crystals size and by the quantity added in the production process. Two ranges of the saccharose crystals diameters were selected using different sieves: G size, raging from 300μm to 600μm and P size ranging from 38μm to 150μm. The P size ceramic presented pore size distribution ranging from 15 to 105μm, with median in 40μm, smaller than the median found for the ceramic produced with G size saccharose crystals (100μm), for which the porosity ranged from 20 to 125μm. Pore size distribution with median between the results found in P and G ceramics were acquired by using a mixture of P and G saccharose crystals sizes in the ceramic fabrication. Six samples were prepared for this study: pure (with no addition of porogenic agent), 100% G size, 100% P size; mixtures of 50% P and 50% G sizes, 75% P and 25% G sizes, and finally 25% P and 75% G sizes. All samples were saturated with water in a vacuum bomb, and, using the CPMG pulse sequence, the multiexponencial decay of the transverse relaxation time was obtained for the ¹H nuclei of the water molecules confined in the ceramic pores. Through this measurement, the distribution of T2 of the sample was determined. The curve for the pure ceramic presented only one peak at 0,053s, the same result obtained by Borgia at al. in other studies. Comparing this result with the porosity determined by mercury intrusion porosimetry, it was possible to determine the surface relaxation coefficient (3,7μm.s-1), with a good proximity to the value found in literature for alumina (3μm.s-1), showing that the equipment used for the measurements is reliable. The ceramic fabricated with the porogenic agent presented two peaks in the T2 time distribution, with the first peak coincident with the T2 value found for the intrinsic porosity (0,053s) and the second peak, which represents the induced porosity, varying to each ceramic sample, with the 100 % P ceramic presenting the peak with the smallest T2 (0,38s) and moving to higher T2 values as the percentage of G size saccharose crystals in the ceramic increases, (1,02s for the sample with 100% G), as it was expected. Through images from scanning electron microscopy, an assessment of the pore size distribution was made and the surface relaxation coefficient recalculated, arriving at a higher value than the one found for the pure ceramic (12μm.s-1), which shows that residues of the saccharose crystals are left in the pores surface in the burning process. In conclusion, the NMR technique proved capable to characterize the ceramic materials, allowing the observation of both the intrinsic (of magnetude 0,1μm) and the artificial induced porosity (varying from tens to hundreds of micrometers) of the alumina ceramics. The union of all the results of this project encloses the knowledge necessary to comprehend how the pores are formed by the action of the porogenic agent, making it possible to develop a manufacture process of ceramics with controlled pores sizes.

Generalizamos o modelo de percolação por invasão de maneira que vários sítios possam ser simultaneamente invadidos. Propomos dois tipos de generalização: na primeira, o fluxo de fluido invasor e controlado através do perímetro do aglomerado, enquanto que na segunda modificação, o crescimento e governado pela relação de escala entre a massa e o raio de giração dos aglomerados. Estudamos cuidadosamente tanto o perfil de aceitação quanto as dimensões fractais (\'D IND.F\') dos aglomerados assim crescidos. No modelo baseado nas relações de escala, \'D IND.F\' pode ser tratado como um mero parâmetro real que pode assumir qualquer valor no intervalo (0, ?). Nos intervalos (0, \'91 SOB.48\') e (2, ?), o sistema e frustrado. Para \'D IND.F\' > 2, o modelo exibe um fenômeno interessante: em algumas etapas ocorrem explosões no crescimento da massa dos aglomerados (bursts). Na região [\'91 SOB.48\',2], os aglomerados obedecem exatamente e em qualquer escala a relação M ~ RgDF entre a massa m e o raio de giração \'RG\'. Acreditamos que estes fractais cuja estrutura completamente e estabilizada possam ser muito úteis no tratamento de problemas de diluição da mecânica estatística. / We generalize the standard site invasion percolation model to permit simultaneous invasion of several sites. We propose two kinds of generalizations: one in which the invasion flux is controlled by the perimeter size and another where the scaling properties command the growth process. The acceptance profile as well as the fractal dimension \'D IND.F\' are carefully studied. In the model based on scaling relation, \'D IND.F\' can be treated as a mere real parameter in the range (0, ?). In the intervals (0, \'91 SOB.48\') and (2, ?) the system is frustrated. For \'D IND.F\' > 2 the model exhibits also an interesting burst phenomenon that is explained in the text. In the region [\'91 SOB.48\',2], the clusters obey exactly and in any scale the relation M ~ RgDF between the mass M and gyration radius Rg. These stable random fractals may be very useful in the study of dilute systems.

A teoria da percolação tem se revelado muito útil no tratamento de inúmeros fenômenos da natureza. Devido a sua grande versatilidade, esta teoria é objeto de intensa pesquisa. Aqui, propomos novas formas de percolação e as estudamos através de simulações numéricas. Na primeira parte de nosso trabalho, investigamos a estrutura dos aglomerados gerados pelo modelo de percolação por invasão múltipla. Estimamos os valores das dimensões fractais do esqueleto, do esqueleto elástico, dos pontos de estrangulamento e dos menores caminhos, como função dos parâmetros do modelo. Por ter uma estrutura geométrica bastante estabilizada, o modelo otimizado pode vir a ser muito útil no tratamento de problemas com diluição da mecânica estatística. O modelo de percolação atenuada foi concebido para permitir que, durante o processo de invasão, os poros grandes possam também ser ocupados. Esta ocupação ocorre com uma probabilidade que diminui quando o tamanho do poro aumenta.Estimamos cuidadosamente os limiares de percolação e construímos os diagramas de fase correspondentes. Verificamos que os limiares de percolação de nosso modelo não satisfazem a conjectura de Galam e Mauger. Estudamos o efeito da inércia em fluidos escoando através de meios porosos incorporando uma caminhada de N passos ao modelo de percolação por invasão. A magnitude da inércia é proporcional ao parâmetro N, que representa o número de poros seqüencialmente invadidos após a ruptura do perímetro, em cada etapa do processo. Investigamos este modelo em duas e três dimensões. Verificamos que no caso bidimensional, as caminhadas de N passos são facilmente bloqueadas o que leva ao surgimento de um limite superior para o número de passos efetivamente realizados. Nossas estimativas das dimensões fractais dos aglomerados (como função do parâmetro N), indicam que este modelo pertence a uma classe de universalidade diferente daquela da percolação por invasão ordinária. Propomos um modelo de percolação para tratar um processo de solidificação de dois fluidos imiscíveis na presença de impurezas móveis. O movimento das impurezas ocorre devido a uma interação repulsiva de curto alcance observada experimentalmente por Ulhmann, Chalmers e Jackson (UCJ). Dependendo das concentrações de fluidos e impurezas, pode haver a formação de uma fase sólida que percola todo o sistema. Construímos o diagrama de fases deste modelo no espaço das concentrações e calculamos seus expoentes críticos. Nossos resultados indicam que o modelo pertence à mesma classe de universalidade que a percolação ordinária. Finalmente, estudamos um processo de percolação por invasão na presença de impurezas que se movem segundo o mecanismo UCJ. Encontramos um valor crítico para a concentração de impurezas, acima do qual não mais existe percolação. O perfil de aceitação aproxima-se de uma função de Heavyside, com o ponto de descontinuidade dependendo da concentração de impurezas. / Percolation theory provides a quantitative and conceptual model for the understanding of many natural phenomena. Here, we present new kinds of percolation and study them using Monte Carlo simulation techniques. We start studying the cluster, the backbone and the elastic backbone structures of the multiple invasion percolation for both the perimeter and the optimized versions. The behavior of the mass, the number of cutting sites and loops are investigated and their corresponding scaling exponents are estimated. By construction, the mass of the optimized model scales exactly with the gyration radius of the cluster - we verify that this also happens with the backbone. Our simulation shows that the red sites almost disappear, indicating that the cluster has achieved a high degree of connectivity. We propose a new kind of invasion percolation, which permits that, besides small pores, large pores being also occupied. In our model, the occupation probability of a pore diminishes with the pore\'s size. We estimate their corresponding percolation thresholds and show that they do not satisfy the Galam and Mauger conjecture. In order to take into account the inertia of the invader fluid, a new kind of invasion percolation is introduced. In this model, which we named N-steps invasion percolation, the inertia forces are controlled by the number N of pores (or steps) invaded after the perimeter rupture. The new model belongs to a different class of universality and has its fractal dimension depending on N. A blocking phenomenon takes place in two dimensions. It imposes an upper bound value on N. For pores sizes larger than the critical threshold, the acceptance profile exhibits a permanent tail. We also introduce a model for the solidification process of two immiscible fluids interacting repulsively with mobile impurities on a two dimensional square lattice. In the space of the fluids and impurities concentrations the phase diagram exhibits a critical curve separating a percolating from a non-percolating phase. Estimated values for the fractal dimension and the exponent ? of the order parameter, reveal that the critical exponents do not vary along this curve, i.e., they are independent of the impurities concentration. The universality class we find is that of the ordinary percolation. Finally, based on the main ideas of the dynamic epidemic and invasion percolation models, we propose a model to describe the cleaning process of a dirty porous medium by fluid injection. An analysis of the acceptance profiles strongly indicates that this model is a kind of self-organized system.