Estimation of effective diffusion coefficients is essential to be able to describe the diffusive transport of solutes in porous media. It has been shown in theory that in the case of uncharged porous materials the effective diffusion coefficient of solutes is a function of the pore morphology of the material and can be described by their tortuosity (tensor). To estimate the apparent diffusion coefficients, the values of tortuosity and porosity should be known first. In contrast with calculation of porosity, which can be easily obtained, estimation of tortuosity is intricate, particularly with increasing micro-geometry complexity in porous media. Moreover, many engineering materials (e.g, clays and shales) are characterized by electrical surface charges on particles of the porous material which can strongly affect the diffusive transport properties of ions. For these materials, estimation of effective diffusion coefficients have been mostly based on phenomenological equations with no link to underlying microscale properties of these charged materials although a few recent studies have used alternative methods to obtain the diffusion parameters. / In the first part of this thesis a numerical method based on a recently proposed up-scaled Poisson-Nernst-Planck type of equation (PNP) and its microscale counterpart is employed to estimate the tortuosity and thus the effective and apparent diffusion coefficients in thin charged membranes. Beside this, a new mathematical approach for estimation of tortuosity is applied and validated. This mathematical approach is also derived while upscaling of micro-scale Poisson-Nernst-Planck system of equations using the volume averaging method. A variety of different pore 2D and 3D micro-geometries together with different electrochemical conditions are studied here. To validate the new approaches, the relation between porosity and tortuosity has been obtained using a multi-scale approach and compared with published results. These include comparison with the results from a recently developed numerical method that is based on macro and micro-scale PNP equations. / Results confirm that the tortuosity value is the same for porous media with electrically uncharged and charged particles but only when using a consistent set of PNP equations. The effects of charged particles are captured by the ratio of average concentration to effective intrinsic concentration in the macroscopic PNP equations. Using this ratio allows to consistently take into account electro-chemical interactions of ions and charges on particles and so excludes any ambiguity generally encountered in phenomenological equations. / Steady-state diffusion studies dominate this thesis; however, understanding of transient ion transport in porous media is also important. The last section of this thesis briefly introduces transient diffusion through bentonite. To do so, the micro Nernst-Planck equation with electro-neutrality condition (NPE) is solved for a porous medium which consists of compacted bentonite. This system has been studied before in another research using an experimental approach and the results are available for both transient and steady-state phases. Three different conditions are assumed for NPE governing equations and then the numerical results from these three conditions are compared to the experimental values and analytical phenomenological solution. The tortuosity is treated as a fitting parameter and the effective diffusion coefficient can be calculated based on these tortuosity values. The results show that including a sorption term in the NPE equations can render similar results as the experimental values in transient and steady state phases. Also, as a fitting parameter, the tortuosity values were found varying with background concentration. This highlights the need to monitor multiple diffusing ion fluxes and membrane potential to fully characterize electro-diffusive transport from fundamental principles (which have been investigated in first part of this thesis) rather than phenomenological equations for predictive studies. / This research has lead to two different journal articles submissions, one already accepted in Computers and Geotechnics (October 22, 2009, 5-yrs Impact Factor 0.884) and the other one still under review.

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Basierend auf den physikalischen Eigenschaften der unterschiedlichen ölintrinsischen und injizierten Ladungsträger wird ein neues Leitfähigkeitsmodell für Isolieröl und -papier für die Belastung mit hoher Gleichspannung aufgestellt. Das Modell wird mit der Wahl geeigneter Randbedingungen für das elektrische Feld und der Teilchenströme auf die Poisson-Nernst-Planck-Gleichung übertragen. Es steht damit ein Werkzeug zur Verfügung, das dielektrische Verhalten der Öl-Papier-Isolierung zu modellieren, dessen Parameter auf den physikalischen Ladungsträgereigenschaften wie Mobilität und Diffusion basieren. Mit dessen Hilfe werden sowohl die nichtlineare Leitfähigkeit als auch das Durchschlagverhalten als deren Extrapolation feldstärkeabhängig erklärt.

Basierend auf den physikalischen Eigenschaften der unterschiedlichen ölintrinsischen und injizierten Ladungsträger wird ein neues Leitfähigkeitsmodell für Isolieröl und -papier für die Belastung mit hoher Gleichspannung aufgestellt. Das Modell wird mit der Wahl geeigneter Randbedingungen für das elektrische Feld und der Teilchenströme auf die Poisson-Nernst-Planck-Gleichung übertragen. Es steht damit ein Werkzeug zur Verfügung, das dielektrische Verhalten der Öl-Papier-Isolierung zu modellieren, dessen Parameter auf den physikalischen Ladungsträgereigenschaften wie Mobilität und Diffusion basieren. Mit dessen Hilfe werden sowohl die nichtlineare Leitfähigkeit als auch das Durchschlagverhalten als deren Extrapolation feldstärkeabhängig erklärt.