Environmental separation processes such as removal of heavy metals from aqueous solutions, electrosorption in groundwater remediation, and capacitive desalination, as well as energy storage in supercapacitors, are based on the electrical double layer (EDL) formation within nanoporous carbon materials. This research is focused on the nano-scale phenomena of EDL formation inside the confined space of nanopores. The electrosorption behavior of nanoporous carbon materials was characterized by measuring the double-layer capacitance using cyclic voltammetry. The presence of micropores results in the occurrence of EDL overlapping, corresponding to a considerable loss of the double-layer capacitance. Hence, pore size distribution plays an important role in determining the double-layer capacitance. EDL formation has significant influence on ion transport and sorption inside nanopores. The data obtained by simple diffusion and electrochemically-aided diffusion experiments demonstrated the size-exclusion effects on pore accessibility by ions. A larger ion-exclusion volume prevents larger ions from penetrating inside the pores. Batch equilibrium electrosorption experiments using nanoporous carbon materials showed that selective electrosorption, imposed by the difference in the size of hydrated ions, occurs in a competitive environment. Molecular modeling based on Monte Carlo methods was developed to simulate the EDL formation in a slit-type nanopore. Simulation results indicated that the competition in asymmetries of ion charge and size not only determines the screening of surface charge but also affects the electrolyte distribution within charged pores. In a mixture of electrolytes, the charge/size competitive effects can dominate pore accessibility. Multivalent counterions with large size have the energetic advantage of screening surface charge. On the other hand, small monovalent counterions present a ¡§size affinity¡¨ to access the pores. Therefore, electrosorption selectivity of counterions with different properties is a result of a counterbalance between minimization of potential energy and size-exclusion effects. Manipulation of electrosorption selectivity to separate ions could in principle be achieved via tuning the EDL formation inside the pores. The findings of the thesis have several significant implications for the development of advanced techniques for selective separation of ions in environmental systems and energy storage.

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Thesis (Ph. D.). UM #74-17,941. / Title from document title page. Includes bibliographical references. Available in PDF format via the World Wide Web.

Thesis (Ph. D.)--Ohio State University, 2006. / Title from first page of PDF file. Includes bibliographical references (p. 169-180).

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Ce travail est dédié au calcul des propriétés de transfert thermique et de transport dans les milieux hétérogènes périodiques. Les résultats sont établis dans le cadre d'homogénéisation périodique pour lequel les propriétés macroscopiques sont obtenues par la résolution de problèmes élémentaires pour la cellule irréductible. Plusieurs contributions sont ainsi apportées, visant à établir de nouvelles estimations par des approches analytiques ou en développant des méthodes numériques adaptées. Ainsi dans une première partie, on s'intéresse à la modélisation des propriétés non linéaires de filtration dans les milieux poreux. A l'échelle microscopique l'écoulement est régi par l'équation de Navier-Stokes. En développant la solution en série, on obtient par homogénéisation, une loi de filtration polynomiale. Tous les coefficients constitutifs de cette loi sont alors obtenus en résolvant en cascade des problèmes élémentaires sur la cellule à l'aide de schémas itératifs utilisant sur la transformée de Fourier rapide. On propose ensuite de nouvelles expressions analytiques pour les propriétés de conductivité thermique de composites périodiques renforcés par des inclusions sphériques. On résout l'équation intégrale de Lippmann-Schwinger par des développements en série de Neumann et en choisissant une polarisation constante dans les inclusions. Des expressions analytiques sont alors obtenues pour diverses configurations spatiales : réseaux cubiques et répartitions aléatoires isotropes. Dans la dernière partie de ce travail, on détermine les propriétés de transfert thermique par conduction et convection dans les milieux poreux saturés par un fluide. A nouveau, on propose des schémas de résolution basés sur la transformée de Fourier rapide pour le calcul du tenseur de diffusivité de milieux poreux / In this work, we determine the macroscopic properties of thermal transfer and mass transport in periodic heterogeneous materials. All the results are established in the framework of periodic homogenization, for which, the macroscopic properties are deduced by solving elementary problems for the irreducible cell. Various contributions are provided, leading to the derivation of new closed-form expressions for the effective properties or by developing numerical tools. In the first part, we determine the nonlinear filtration properties of porous media. At the microscopic scale, the fluid flow obeys to the Navier-Stokes equation. By expanding the solution into power series, we obtain, after homogenization, a polynomial type macroscopic filtration law. All the constitutive coefficients of are determined by solving a hierarchy of cell problems by means of a numerical approach based on the Fast Fourier Transform algorithm. The problem of conductivity of periodic composites reinforced by spherical inclusions is thereafter considered by an analytic approach. We solve the Lippmann-Schwinger integral equation using Neumann series and a constant polarization in the inclusion. Closed-form estimate of the macroscopic conductivity are then obtain for different spatial configurations: cubic lattice and isotropic distribution of inclusions. In the last part, we determine the thermal transfer properties by conduction and convection of porous media fulfilled by a viscous fluid. Again, numerical tools based on FFT are considered to solve the unit cell problems and to compute the diffusivity tensor

Thesis (MScEng (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2006. / An analytical modelling procedure for predicting the streamwise pressure gradient for steady laminar incompressible flow of a Newtonian fluid through homogeneous isotropic granular porous media is introduced. The modelling strategy involves the spatial volume averaging of a statistical representative portion of the porous domain to obtain measurable macroscopic quantities from which macroscopic transport equations can be derived. A simple pore-scale model is introduced to approximate the actual complex granular porous microstructure through rectangular cubic geometry. The sound physical principles on which the modelling procedure is based avoid the need for redundant empirical coefficients. The model is generalized to predict the rheological flow behaviour of non-Newtonian purely viscous power law fluids by introducing the dependence of the apparent viscosity on the shear rate through the wall shear stress. The field of application of the Newtonian model is extended to predict the flow behaviour in fluidized beds by adjusting the Darcy velocity to incorporate the relative velocity of the solid phase. The Newtonian model is furthermore adjusted to predict fluid flow through Fontainebleau sandstone by taking into account the effect of blocked throats at very low porosities. The analytical model as well as the model generalizations for extended applicability is verified through comparison with other analytical and semi-empirical models and a wide range of experimental data from the literature. The accuracy of the predictive analytical model reveals to be highly acceptable for most engineering designs.

Thesis (MSc (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2007. / The understanding and quantitative description of fluid flowthrough porousmedia, is a science which has been going on for many years and investigated in a variety of disciplines. Studies in this field have primarily been based on models, which can either be described as empirical or theoretical. Part of the current study is to understand fluid flow in porous media through studying three recent theoretical pore-scale models based on the concept of a Representative Unit Cell (RUC), to represent a porous medium. Amongst other assumptions, these models assumed plane Poiseuille flow throughout each pore section of a rectangular RUC. The main objective of this study is to numerically verify this assumption using Computational Fluid Dynamics (CFD) software, FLUENT version 6.2.16. Attention is also paid to comparison between these models with the experimental data, obtained during the model tests of airflow through a timber stack end, undertaken in a wind tunnel. The laminar and intermediate airflow through a timber stack end is simulated using the commercial software FLUENT, and the results are validated against the theoretical pore-scale models and experimental data. Two turbulence models which are, the Standard k − e and Reynolds-Stress models are used in these computations, the aimbeing to determine howwell they are able to reproduce the experimental data. The numerical results are in good agreement with one of the theoretical models presented and the experimental data.

Thesis (MScEng (Mathematical Sciences. Applied Mathematics))--University of Stellenbosch, 2006. / This work entails the improvement of an existing three dimensional pore-scale model. Stagnant zones are included, the closure of the volume averaged pressure gradient is improved and an improved calculation of pore-scale averages, using the RUC, is done for the model to be a more realistic representative of the REV and thus of the foamlike material. Both the Darcy and the Forchheimer regimes are modelled and a general momentum transport equation is derived by means of an asymptotic matching technique. The RUC model is also extended to cover non-Newtonian flow. Since metallic foams are generally of porosities greater than 90%, emphasis is put on the accurate prediction of permeability for these porosities. In order to improve permeability predictions for these high porosity cases an adaptation to the RUC model was considered, whereby rectangular prisms were replaced by cylinders. Although this adaptation appears to give more accurate permeabilities at very high porosities, its implementation in a generalised model seems impractical. The prediction of the characteristic RUC side length is discussed and results of both the cylindrical strand model and the square strand model are compared to experimental work.