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The development of nanoporous materials has received considerable attention in nanofluidic studies in recent years. Furthering earlier research, the present thesis offers a systematic study of two nanoporous materials-nanoporous alumina membranes and carbon nanotube membranes-with a view to establishing their electroosmotic and fluid-flow behaviour at the nanoscale. The nanoporous alumina membranes were studied for their own electroosmotic and fluid-flow properties, and utilised as templates for the production of the carbon nanotube membranes also investigated in this study. The advanced control provided by the fabrication processes of both materials allowed for systematic investigations into the effects of pore diameter and surface chemistry on both electroosmotic and pressure-driven flows. Nanoporous alumina membranes were developed with pore diameters of< 10 nm. The effect of nanostructure and surface chemistry on macro wetting properties was analysed in detail. Flow enhancements were observed in hydrophilic alumina nanochannels with inner diameters of 40 to 25 nrm. Atomic force microscopy force measurements provided further insight into fluid-solid interactions at the nanoscale. A systematic investigation of nanoporous alumina DC electroosmotic pumps with pore diameters down to 8 run was also undertaken with sodium tetraborate buffer operated at Δ V = 10 V. Concentration polarization was identified as the principal challenge to sustained electroosmotic flow. By optimising the electroosmotic process, particularly the rig design and buffer concentration, an EO pump was developed with a lifetime of up to 4 hours. Carbon nanotube membranes with a range of pore diameters were also investigated for their electroosmotic and pressure-driven flow properties. The synthesis of carbon nanotubes was optimised to obtain unblocked and functioning membranes. Flow enhancements were observed in engineered carbon nanotube membranes with pore diameters down to 16 run. Electroosmotic flow rates in carbon nanotube membranes were similar to those of nanoporous alumina. Two electrolytes-sodium tetraborate and sodium chloride-were investigated in electroosmotic flow experiments with carbon nanotube membranes. This allowed for further investigation of electroosmosis and electric double layer overlap.

The thesis concerns the development of a virtual permeameter that will enable the structure-flow relationships for bulk porous media to be assessed using numerical methods. Ultimately, the intention is to link a digital packing algorithm with lattice Boltzmann modelling (LBM) to predict the permeability of porous media and filtration performance using simulated microstructures, with potential applications to filter design and the oil industry applications. In order to prove the approach being pursued, the micro-structural details of porous media samples are gathered using X-ray tomography (XMT), rather than from packing algorithms, using small samples of such media to permit the subsequent prediction of their bulk permeability and related properties. The thesis presents a systematic sensitivity analysis of using LBM for predicting the permeability of packed beds. Individual packed beds have been created using spherical glass beads with a mean diameter of 116.4 urn, sand particles with a mean diameter of 223 urn, and polymorphous particles with a diameter between 115 to 375 IJm with XMT used to image samples of the beds and to permit the reconstruction of a three-dimensional image of the sample for use as the basis of the LBM simulations. LBM predictions are also compared to permeability measurements obtained from a packed bed formed by passing a low concentration saline solution through the various ) particles in a filtration rig. The saline solution allows the packed bed, once dried or encased in wax, to form a more solid structure from which samples can be more easily removed for analysis. In order to assess the possible effects of uncertainty in the accuracy of representation of the packing on the simulation results, sensitivity studies and XMT were employed to investigate the degree of representation of the sample required to reduce digitisation errors of the packed bed to a minimum. It concluded that any section of the sample scanned using XMT, as long as the sample is homogenous throughout, will give reproducible simulation results, irrespective of the section from which it is cut, with an average accuracy of 18% between simulation and experimental data for glass beads and 22% for sand particles. Polymorphous particles required averaging of several layers of the sample giving an acceptable error between simulation and experimental of 42%. Also, it is demonstrated that, regardless of wall effects, a digitised sphere must be greater than 16 voxels in diameter for relatively accurate results; furthermore, it is found that there is less than a 10% error between predictions and measurements if a 32 voxel diameter is used. The work also provides recommendations for the minimum dimensions necessary in sampling packed beds to allow the accurate simulation of filter performance using LBM. Lastly, the work 3 indicates a deviation from experimental results inherent in using the Carman-Kozeny formula frequently used for predicting the permeability of a packed bed, with the present LBM approach giving superior predictions. Overall, the work demonstrates that, with sufficient care, it is possible to use small representative samples of porous media for use as input to LBM to permit the accurate prediction of its permeability and filtration performance under laminar conditions regardless of particle geometry. The highest pressure used was 1.5 bar through the porous media giving a Reynold's number (Re) of under Re=2. Higher pressures where laminar flow tends towards transitional or turbulent flow have not been covered. The thesis also explores the accuracy of representing the micro-structure of such media using a digital packing algorithm, rather than obtaining such information from XMT and concludes that there is a noticeable reduction in error when using a packing algorithm compared to XMT scanned beds. 4.

Deformation of a porous medium due to the pressure applied by an interacting fluid passing through it is a phenomenon which occurs in a number of applications such as filtration and membrane separation processes. Mathematical modelling of these systems using porous medium theory has proved to be beneficial in the design of experiments and equipments as well as gaining better insight about multi-physics phenomenon such as combined fluid flow and solid deformation regimes. In the present work the interaction of fluid and porous solid medium has been studied.

Commercially available inorganic solids and organically functionalised silicas and silica-polysaccharide composite materials synthesised in the laboratory were characterised by various techniques. These included direct infrared spectroscopic measurements, infrared and UV-visible probing techniques using probe molecules such as water, ammonia, d3-actonitrile, aniline, Reichardt’s dye and iodine and also by the application of the Knoevenagel condensation as a model reaction. As well as the information obtained about the surface activity of the solids, this review of techniques revealed the advantages and limitations of well-known and less frequently used methods. In particular, the use of iodine as a UV-visible probe molecule allowed the observation of differences between materials that are extremely difficult to analyse such as sodium carbonate and sodium acetate. However with current levels of knowledge about the electronic transitions of iodine adsorbed on surfaces, the results are not straight forward to interpret. The silica-polysaccharide composites also showed interesting properties, both in terms of their morphology and their chemistry and merit further study.

Coarse graining of equations for flow in porous media is an important aspect in modelling permeable subsurface geological systems. In the study of hydrocarbon reservoirs as well as in hydrology, there is a need for reducing the size of the numerical models to make them computationally efficient, while preserving all the relevant information which is given at different scales. In the first part, a new renormalization method for upscaling permeability in Darcy’s equation based on Haar wavelets is presented, which differs from other wavelet based methods. The pressure field is expressed as a set of averages and differences, using a one level Haar wavelet transform matrix. Applying this transform to the finite difference discretized form of Darcy’s law, one can deduce which permeability values on the coarse scale would give rise to the average pressure field. Numerical simulations were performed to test this technique on homogeneous and heterogeneous systems. A generalization of the above method was developed designing a hierarchical transform matrix inspired by a full Haar wavelet transform, which allows us to describe pressure as an average and a set of progressively smaller scale differences. Using this transform the pressure solution can be performed at the required level of detail, allowing for different resolutions to be kept in different parts of the system. A natural extension of the methods is the application to two-phase flow. Upscaling mobility allows the saturation profile to be calculated on the fine or coarse scale while based on coarse pressure values. To conclude, an alternative approach to upscaling in multi-phase flow is to upscale the saturation equation itself. Taking its Laplace transform, this equation can be reduced to a simple eigenvalue problem. The wavelet upscaling method can now be applied to calculate the upscaled saturation profile, starting with fine scale velocity data.

Cette thèse est consacrée à la détermination des états limites de l'adaptation des matériaux ductiles poreux sur la base du théorème de Melan et en considérant le modèle de la sphère creuse. Dans un premier temps, nous proposons le critère analytique macroscopique d'adaptation avec la matrice de von Mises sous deux charges particuliers, alterné et pulsé. Le critère analytique dépend des première et seconde invariants des contraintes macroscopiques, du signe du troisième et du coefficient de Poisson. Ensuite, ce critère est étendu aux charges cycliques répétées générales par la construction d'un champ de contraintes résiduelles d'essai plus approprié permettant simultanément des calculs analytiques et l'amélioration du modèle précédent. De plus, il est également utilisé pour les matériaux ductiles poreux avec une matrice de Drucker-Prager.L'idée repose d'abord sur la solution exacte pour le charge purement hydrostatique. Il s'avère que la ruine se produit par fatigue. Ensuite, des champs de contrainte d'essai appropriés sont construits avec des termes supplémentaires pour capter les effets de cisaillement. Le domaine de sécurité, défini par l'intersection du domaine d'adaptationet celui d'analyse limite (la ruine survenant brusquement par formation d'un mécanisme au premier cycle), est entièrement comparé avec des simulations élasto-plastique incrémentales et des calculs directs simplifiés.Enfin, nous fournissons une méthode numérique directe pour prédire le domaine de sécurité de l'adaptation des matériaux poreux soumis à des charges variant de manière indépendante en considérant le chemin critique du domaine de chargement au lieu de l'histoire entière. Le problème de l'adaptation est transformé en un problème d'optimisation de grande taille, qui peut être résolu efficacement par l'optimiseur non-linéaire IPOPT pour donner non seulement le facteur de charge limite, mais aussi le champ de contrainte résiduelle correspondant à l'état d'adaptation. / This thesis is devoted to the determination of shakedown limit states of porous ductile materials based on Melan's static theorem by considering the hollow sphere model, analytically and numerically. First of all, we determine the analytical macroscopic shakedown criterion of the considered unit cell with von Mises matrix under alternating and pulsating special loading cases. The proposed macroscopic analytical criterion depends on the first and second macroscopic stresses invariants, the sign of the third one and Poisson's ratio. Then, the procedure is extended to the general cyclically repeated loads by the construction of a more appropriate trial residual stress field allowing analytical computations and the improvement of the previous model simultaneously. Moreover, this approach is applied to porous materials with dilatant Drucker-Prager matrix.The idea relies firstly on the exact solution for the pure hydrostatic loading condition. It turns out that the collapse occurs by fatigue. Next, suitable trial stress fields are built with additional terms to capture the shear effects. The safety domain, defined by the intersection of the shakedown limit domain and the limit analysis domain corresponding to the sudden collapse by development of a mechanism at the first cycle, is fully compared with step-by-step incremental elastic-plastic simulations and simplified direct computations. At last, we provide a direct numerical method to predict the shakedown safety domain of porous materials subjected to multi-varying independent loadings by considering the critical loading path of the load domain instead of the whole history. The shakedown problem is transformed into a large-size optimization problem, which can be solved efficiently by the non-linear optimizer IPOPT to give out not only the limit load factor, but also the corresponding residual stress field for the shakedown state.

Afin d'établir un lien entre les solutions servant de modèles dans la préparation de matériaux mésoporeux, on étudie les propriétés physiques à l'équilibre et hors équilibre de solutions micellaires aqueuses à base de deux tensioactifs fluorés : C8F17C2H4(OC2H4)9OH, [RF8(EO)9] and C7F15C2H4(OC2H4)8OH, [RF7(EO)8]. Cette étude devrait nous aider à comprendre pourquoi on obtient des matériaux mésoporeux bien ordonnés à partir de solutions micellaires du tensioactif RF8(EO)9 et des structures désordonnées lorsque l'on utilise RF7(EO)8. Les expériences sont menées sur quatre systèmes de deux surfactants: RF7(EO)8/H2O, RF7(EO)8/NaI/H2O, RF8(EO)9/H2O et RF8(EO)9/NaCl/H2O. Plusieurs techniques expérimentales sont utilisées: rhéologie, biréfringence d'écoulement et diffusion de neutrons aux petits angles dans le but de décrire ces quatre systèmes. Les diagrammes de phase des deux tensioactifs montrent qu'une phase micellaire L1 existe dans une large gamme de température et concentration. Mais dans tous les cas, la distance à la courbe de miscibilité a une influence sur les caractéristiques rhéologiques bien que toutes les solutions soient une phase L1. La biréfringence d'écoulement des deux systèmes apporte des informations complémentaires quant à la taille et la forme des micelles. Pour les deux systèmes, avec et sans sel, les résultats suggèrent l'existence de petites micelles allongées liées en chaines par des forces faibles excepté pour le système RF8(EO)9 qui ne présente pas de biréfringence notable; les micelles sont probablement petites avec une forme voisine de la sphère. Pour les quatre systèmes, on observe une perte du caractère Maxwellien lorsque les conditions de concentration et de température se rapprochent de la courbe de miscibilité. Ces résultats confortent l'idée selon laquelle : les conditions thermodynamiques choisies pour l'addition de la silice ne doivent pas être trop proches de la courbe de miscibilité, afin d'obtenir des matériaux mésoporeux ordonnés. Dans ces conditions, les solutions sont Maxwelliennes et les matériaux mésoporeux synthétisés sont ordonnés / To provide a link between the micellar templates and the mesoporous material characteristics in the final product, the physical properties of aqueous systems prepared with two kinds of fluorinated surfactants are described and analyzed under equilibrium and out-of-equilibrium conditions: the surfactants are C8F17C2H4(OC2H4)9OH, [RF8(EO)9] and C7F15C2H4(OC2H4)8OH, [RF7(EO)8]. This study may help us to understand why the ordered mesoporous materials are recovered only when RF8(EO)9 micellar solutions are used as building blocks while RF7(EO)8 solutions give rise to wormhole like structure. The distance to the lower consolute boundary (LCB) and a shift in position by salt additions are also taken into account. The experiments concern four systems of two surfactants; 1) pure RF7(EO)8 in water, 2) RF7(EO)8 in the presence of the NaI salt, 3) pure RF8(EO)9 in water, and 4) RF8(EO)9 in the presence of the NaCl salt. Several experimental techniques have been used (rheology, flow birefringence, neutron scattering) to shed light on the physical difference between the four systems. The phase diagrams of both surfactants show that a direct micellar phase (L1) exists in a wide range of concentrations and temperatures. In any cases, the distance to the LCB is a parameter which influences rheological behaviour although the micellar phase still is a L1 phase. The flow birefringence experiments performed on both systems bring complementary information of the size and shape of the micelles. For both systems, with and without salt, the results suggest the existence of small elongated micelles linked by weak forces except for the RF8(EO)9 system which shows no birefringence; the micelles in solution are probably small with a shape close to a sphere. From all four systems, the loss of the Maxwellian character is generally observed when the conditions approach the miscibility curve. These results consolidate the assumption that in order to prepare ordered mesoporous materials, the thermodynamical conditions at which the silica precursor is added to the micellar solution should not be too close to the miscibility curve. Therefore, this study suggests that the Maxwellian character seems to be a pre-requisite condition of the micellar solution for obtaining ordered mesoporous materials