Research Doctorate - Doctor of Philosophy (PhD) / Permeability is an important property that arises in many fields of study. The ability to predict the permeability for a particular material is necessary as it affects the design of many materials handling and storage solutions. There are an abundance of equations that predict permeability for specific applications, but the underlying theory for these equations remains constant. Key factors affecting permeability that appear in many equations are the pore space, individual pore size, and pore connectivity. Many existing equations seek to quantify these factors in some form, with void ratio, particle diameter and tortuosity the most commonly used. Each of these factors is investigated throughout this thesis to further investigate their influence on permeability. These factors are investigated with specific reference to two equations; the Ergun equation and the Kozeny-Carman equation, and with specific reference to two types of materials; spherical particle mixtures and fibrous particle mixtures. Numerical simulation methods are used to build assemblies of spherical and fibrous particles. The assemblies of particles are used to extract fundamental information regarding the pore size and connectivity. The average size of the individual voids can be found as well as the average length the flowing fluid takes through the voids of the material. The use of the simulated assemblies to find material properties such as these allows for new insight into the structure of these types of packed beds. This new insight allows for an improvement in the way permeability is characterised for the materials studied in this thesis.

<p>This thesis concerns the modelling of acoustical and vibrational properties of open cell porous foams in multi-layered structures, especially multi-layered panels. The object is to enable optimisation of the microscopic geometry of the foam with respect to macroscopic quantities such as sound pressure level, surface velocity, total mass or cost. The developed method is based on numerical solutions to Biot's equations were scaling laws has been used to connect the microscopic geometry of the foam to macroscopic properties such as density, flow resistivity and characteristic length. Efforts have also been made to establish a scaling law for tortuosity that allows for adaptation to different strut shapes.</p>

Tortuosity of eye fundus blood vessels is one of parameters that describe state of the blood vessels. It can be detected from fundus images. The increase in vessel tortuosity was observed in eyes of patients with advanced background diabetic retinopathy, papilloedema, arterial hypertension, even in some completely healthy eyes (in this case tortuosity does not change in time). Thus the feature of the line – tortousity – could be used as the diagnostic feature in medical applications. Unfortunately, completely reliable definition and numerical estimation of tortuosity of line (blood vessel) does not exist, although there were some more or less successful attempts to define it. This work presents a new way to estimate the tortuosity using the integral of square derivative of curvature. It is compared with the existing methods both theoretically and experimentally. Three types of lines have been used for experimental comparison: theoretical models of retinal vessels (straight line, parabola, sinusoid and their combinations), lines extracted from real fundus images and lines extracted from optometric scale for retinal vessel evaluation. To ease the extraction of the lines from these images a new version of one of the methods for vessel tracking has been created and implemented.

Petrophysical interpretation of 1H NMR relaxation responses from saturated rocks is complicated by paramagnetic species present in fluids. Oxygen dissolved in liquids is one common example. Dipolar interactions of oxygen’s unpaired electron spins with the magnetic moment of fluid nuclei provide a strong relaxation mechanism known as paramagnetic relaxation enhancement (PRE). As a result even low concentrations of dioxygen in its common triplet ground state significantly shorten longitudinal and transverse relaxation times of host fluids. This effect may be employed similarly to any standard tracer technique to study pore connectivity in porous media by detecting a change of oxygen concentration due to diffusion resolved in time and space. Since relaxation enhancement effect is likely stronger in non-wetting phase than in wetting one (where surface relaxation process dominates) this difference can be utilized to study wettability in immiscible multiphase systems. We use a relaxation time contrast between air-saturated and oxygen-free fluids to evaluate oxygen concentration change within two fluid phases saturating rock, to estimate time required to establish equilibrium concentration and to calculate a mutual diffusion coefficient of oxygen. A spatially- and time-resolved T2(z,t) experiment provides the time-dependent oxygen concentration change along the fully- and partially-saturated carbonate core plug exposed to air saturated oil at its inlet. We derive an effective mutual diffusion coefficient of oxygen and accordingly a tortuosity estimate as a function of position along the core and rock saturation. The spatially resolved oxygen diffusion-based tortuosity is compared to simulated conductivitybased tortuosity. The latter is calculated on a high-resolution micro-tomographic image of Mount Gambier limestone by solving the Laplace equation for conductivity.

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Electrode microstructure influences ionic transport and electronic transport and is a key factor that affects lithium-ion battery performance. Non-uniform microstructure or heterogeneity in battery electrodes has long been observed and leads to non-uniform transport properties. This work provides a better understanding of in-plane heterogeneity at millimeter length scale and through-plane heterogeneity at micrometer length scale, through a combination of experiment and modeling. The first part of this work develops the aperture probe technique, which is an experimental method and associated model to locally estimate ionic transport, represented by MacMullin number, in the electrode. By generating contour maps of MacMullin number, the in-plane variation of ionic transport is visualized in the electrodes. The local ionic transport measurement technique is validated by comparing with another measurement technique and showing an agreement between the results obtained from the two techniques. The second part of this work focuses on characterizing dual-layer anodes that consist of two layers of coating with distinctly different microstructures. The aperture probe technique was adapted to determine the MacMullin numbers in the two layers separately. The method was validated by a series of virtual experiments and by comparing in one case to an electrode film that was delaminated from the current collector and experimentally sampled from both sides. Because both the electronic transport and the ionic transport are found to be related with the electrode microstructure, it is of interest to understand how these two transport properties relate to each other. The local electronic conductivity and MacMullin number of several commercial-grade electrodes were mapped. The correlation between the two transport properties is distinct for each electrode and significant at length scales larger than about 6 mm. The last part of this work investigates how heterogeneity of ionic transport affects the cycling performance of a lithium-ion cell. A localized MacMullin number measurement is made to characterize the ionic transport heterogeneity of electrodes prior to cycling. Then synchrotron-based X-ray diffraction is applied to analyze the heterogeneity in state of lithiation after high-rate cycling. When comparing the ionic transport map and the state-of-charge map, no strong correlation is observed. While this experiment was inconclusive, it suggests that other factors are more responsible for spatial variations in state of lithiation.

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.

Modeling of airflow resistance in grain bulk requires knowledge of the tortuosity and velocity of the air flow through the grain bulk. In this study, experiments were carried out to determine these characteristics of airflow paths by analyzing digital images of smoke-visualized airflow paths inside a grain bulk obtained with a high speed camera. Colored smoke with approximately the same density as air was introduced into the test box for the visualization of the airflow through the grain bulk. Soybeans with a moisture content of 8.82% on wet basis were used in this study. The high quality videos obtained by recoding the fast movement of the smoke through the grain bulk was first separated into frames using a commercial software, VirtualDub (CRIM, Montreal, Québec, Canada), and the 512× 384 pixel RGB image files (frames) extracted from the recorded videos and read into ImageJ an image processing Java-based software developed by the United State National institute of Health, to track the movement of the smoke in the images, frame by frame to determine lengths, tortuosities of the different flow paths, as well as their velocities.

Modeling of airflow resistance in grain bulk requires knowledge of the tortuosity and velocity of the air flow through the grain bulk. In this study, experiments were carried out to determine these characteristics of airflow paths by analyzing digital images of smoke-visualized airflow paths inside a grain bulk obtained with a high speed camera. Colored smoke with approximately the same density as air was introduced into the test box for the visualization of the airflow through the grain bulk. Soybeans with a moisture content of 8.82% on wet basis were used in this study. The high quality videos obtained by recoding the fast movement of the smoke through the grain bulk was first separated into frames using a commercial software, VirtualDub (CRIM, Montreal, Québec, Canada), and the 512× 384 pixel RGB image files (frames) extracted from the recorded videos and read into ImageJ an image processing Java-based software developed by the United State National institute of Health, to track the movement of the smoke in the images, frame by frame to determine lengths, tortuosities of the different flow paths, as well as their velocities.

Recent advances in retinal imaging have made it possible to take measurements of retinal oxygen saturation noninvasively in humans. This allows studying the supply of oxygen in healthy and diseased retinae, thereby advancing our understanding of both the normal functioning of the retina and of retinal pathologies. However, retinal oximetry is still a research tool only and requires further improvement before being used in a clinical setting. Here, a single-wavelength flickering light was used to increase retinal blood flow in healthy subjects. This increase is revealed by both vasodilation and an increase in retinal oxygen saturation. A flickering light stimulus provides the means to assess the sensitivity of any retinal oximetry system, as such systems should be able to pick up this increase in retinal blood flow. In addition, the flickering light allows for com- parison to be made within rather than between subjects and can be used to examine the activation of the eye. This reduces the influence of potential confounding factors between subjects including differences in fundus pigmentation and illumination. The most commonly used method to measure retinal oxygenation is the optical density ra- tio (ODR) approach. The standard approach is to compute the average ODR for each vessel segment by combining the hundreds of individual ODR readings and then to use the mean of these segment averages as a measure of oxygen saturation. Alternatively, it has been suggested that the peak location of Gaussian functions fitted to histograms of individual ODR readings can be used as an measure of retinal oxygenation. In response to a 10Hz flickering light, the venular diameter increased by 3.44% (SEM: ±0.53%) (n=16, p<0.05) and the arteriolar diameter by 1.87% (±0.72 %) (p<0.05). The optical density ratio, measured with the Gaussian fit, decreased in the venules from 0.713 (±0.015) to 0.694 (±0.015) (p<0.05). No changes in arteriolar optical density ratios were measured. The post-flicker measurement was computed as the average of up to four post-flicker datasets obtained at 10s, 20s, 30s and 40s after onset of flickering. These results suggest that the flickering light increased retinal blood flow. The mean absolute percentage error was lower in venules for the Gaussian fit method than for the gold standard method for datasets taken at 30s and 40s after onset of flickering. Thus, the Gaussian fit method was more robust. All measurements were taken with a custom-made retinal oximeter. The pixel intensity of the blood vessel and the intensity on either side of the vessel had to be extracted to compute the individual optical density ratios. This required the automatic extraction of the retinal vasculature. Two such algorithms were developed and applied to two databases of retinal fundus images: the DRIVE and the novel DR HAGIS database. One algorithm was purely based on the pixel intensities, while the other made use of oriented Gabor filters. These two algorithms segmented the images to a similar accuracy (DRIVE: 94.56% and 94.54%, DR HAGIS: 95.83% and 95.71% for the intensity and Gabor filter based algorithm, respectively) and performed as well as a human expert (DRIVE: 94.73%). These algorithms were of sufficient quality to extract individual segments for the oximetry study and to align fundus images.