The air-water interface in variably saturated porous media is recognized to influence interfacial retention of organic and inorganic contaminants, and mediate various mass-transfer processes. The formation and presence of water films commonly solvating the surfaces of soil/sediment grains in unsaturated systems, as well as their impact on flow and retention processes have been of sustained interest. X-ray microtomography was used to measure air-water interfacial area at multiple wetting-phase saturations for natural porous media. First, a study was conducted to evaluate image-processing procedures suitable for characterizing fluids and associated interfaces in natural porous media. A simple method was developed for the analysis of all phases in the system, using global threshold for phase identification and combination of binary files (M1). This method was then compared to a simultaneous multiphase segmentation approach using locally adaptive threshold selection (M2). Both methods were used to process data sets comprised of multiple drainage steps for water-saturated packed columns imaged via synchrotron x-ray microtomography. The results of both methods were evaluated based on comparison of values determined for porosity and specific solid surface area to independently measured porosity and specific solid surface areas. The results show both methods are suitable for determination of total air-water interfacial area, which requires characterization of only the non-wetting phase. Conversely, determination of capillary interfacial area requires characterization of all phases present and thus, is more sensitive to the challenges associated with image processing. The simultaneous multiple-phase segmentation (M2) method provides an integrated and consistent analysis of the phases, and anticipated to improve water-phase detection. Using the advanced segmentation approach, the air-water interfacial area is presented as a result of direct measurement of contact areas between the two fluids. This is in contrast to previously reported data, which were derived indirectly from calculations based on individually measured phase surface areas and conceptualizations of fluid distributions. The effects of these assumptions on the capillary interfacial behavior are evaluated. Results from this study confirmed the initial hypothesis that the behavior of fluid surface areas will affect the theoretical shape of the capillary curve. The results support the understanding of the capillary interfacial area behavior in response to changes in the configuration of fluid surface areas during a drainage cycle. Furthermore, results for the measured air-water interface allows for further identification of fluid domains, such as the relationship between film interfacial area, capillary domains (menisci), and the total-measurable interfacial area. Experiments were also conducted using aqueous-phase interfacial partitioning tracer tests for comparison. Results support the hypothesis that different methods provide characterization of different interfacial domains. Overall, this study provides an imaging-based approach for evaluation of water configuration, and presents a measurement-based framework for further understanding of the role of fluid-fluid interfaces in natural porous media.

In this dissertation, we present multiscale analytical solutions, in the weak sense, to the generalized Laplace's equation in Ω ⊂ Rⁿ, subject to periodic and nonperiodic boundary conditions. They are called multiscale solutions since they depend on a coefficient which takes a wide possible range of scales. We define forms of nonseparable coefficient functions in Lᵖ(Ω) such that the solutions are valid for the periodic and nonperiodic cases. In the periodic case, one such solution corresponds to the auxiliary cell problem in homogenization theory. Based on the proposed analytical solution, we were able to write explicitly the analytical form for the upscaled equation with an effective coefficient, for linear and nonlinear cases including the one with body forces. This was done by performing the two-scale asymptotic expansion for linear and nonlinear equations in divergence form with periodic coefficient. We proved that the proposed homogenized coefficient satisfies the Voigt-Reiss inequality. By performing numerical experiments and error analyses, we were able to compare the heterogeneous equation and its homogenized approximation in order to define criteria in terms of allowable heterogeneity in the domain to obtain a good approximation. The results presented, in this dissertation, have laid mathematical groundwork to better understand and apply multiscale processes under a deterministic point of view.

This work is devoted to the numerical analysis of saturated porous media, taking into accountthe damage phenomenon on the solid skeleton. The porous media is taken into poroelasticframework, in full-saturated condition, based on the Biot's Theory. A scalar damage model isassumed for this analysis. An implicit Boundary element Method (BEM) formulation, basedon time-independent fundamental solutions, is developed and implemented to couple thefluid flow and the elasto-damage problems. The integration over boundary elements isevaluated by using a numerical Gauss procedure. A semi-analytical scheme for the case oftriangular domain cells is followed to carry out the relevant domain integrals. The non-linearsystem is solved by a Newton-Raphson procedure. Numerical examples are presented, inorder to validate the implemented formulation and to illustrate its efficiency.

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I present in this thesis a fluid flow and heat transfer model for porous media using the lattice Boltzmann method (LBM). A computer simulation of this process has been developed and it is written using MATLAB software. The simulation code is based on a two dimensional model, D2Q9. Three physical experiments were designed to prove the simulation model through comparision with numerical results. In the experiments, physical properties of the air flow and the porous media were used as input for the computer model. The study results are not conclusive but show that the LBM model may become a reliable tool for the simulation of natural convection heat transfer in porous media. Simulations leading to improved understanding of the processes of air flow and heat transfer in porous media may be important into improving the efficiency of methods of air heating or cooling by passing air through fragmented rock.

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Transient multi-phase flow problems in porous media are ubiquitous in engineering and environmental systems and processes; examples include heat exchangers, reservoir simulation, environmental remediation, magma flow in the earth crust and water management in porous electrodes of PEM fuel cells. This thesis focuses on the development of accurate and computationally efficient numerical models to simulate such flows. The research challenges addressed in this work fall in two areas. For a numerical standpoint, conventional numerical methods including Newton-Raphson linearization and a simple upwind scheme do not always provide the required computational efficiency or sufficiently accurate resolution of the flow field. From a modelling perspective, closure schemes required in volume-averaged formulations, such as the generalized Leverett J function for capillary pressure, are specific to certain media (e.g. lithologic media) and are not valid for fibrous porous media, which are of central interest in fuel cells. This thesis presents a set of algorithms that are integrated efficiently to achieve computations that are more than two orders of magnitude faster compared to traditional techniques. The method uses an adaptive operator splitting method based on an a posteriori criterion to separate the flow from the transport equations which eliminates unnecessary and costly solution of the implicit pressure-velocity term at every time step; adaptive meshing to reduce the size of the discretized problem; efficient block preconditioned solver techniques for fast solution of the discrete equations; and a recently developed artificial diffusion strategy to stabilize the numerical solution of the transport equation. The significant improvements in accuracy and efficiency of the approach is demosntrated using numerical experiments in 2D and 3D. The method is also extended to advection-dominated problems to specifically investigate two-phase flow in heterogeneous porous media involving capillary transport. Both hydrophilic and hydrophobic media are considered, and insights relevant to fuel cell electrodes are discussed.

In this work, a microfluidics approach is applied to two fuel cell related projects; the study of deformation and contact angle hysteresis on water invasion in porous media and the introduction of bubble fuel cells. This work was carried out as collaboration between the microfluidics and CFCE groups in the Department of Mechanical Engineering at the University of Victoria. Understanding water transport in the porous media of Polymer Electrolyte Membrane fuel cells is crucial to improve performance. One popular technique for both numeric simulations and experimental micromodels is pore network modeling, which predicts flow behavior as a function of capillary number and relative viscosity. An open question is the validity of pore network modeling for the small highly non-wetting pores in fuel cell porous media. In particular, current pore network models do not account for deformable media or contact angle hysteresis. We developed and tested a deformable microfluidic network with an average hydraulic diameter of 5 μm, the smallest sizes to date. At a capillary number and relative viscosity for which conventional theory would predict strong capillary fingering behavior, we report almost complete saturation. This work represents the first experimental pore network model to demonstrate the combined effects of material deformation and contact angle hysteresis. Microfluidic fuel cells are small scale energy conversion devices that take advantage of microscale transport phenomena to reduce size, complexity and cost. They are particularly attractive for portable electronic devices, due to their potentially high energy density. The current state of the art microfluidic fuel cell uses the laminar flow of liquid fuel and oxidant as a membrane. Their performance is plagued by a number of factors including mixing, concentration polarization, ohmic polarization and low fuel utilization. In this work, a new type of microfluidic fuel cell is conceptualized and developed that uses bubbles to transport fuel and oxidant within an electrolyte. Bubbles offer a phase boundary to prevent mixing, higher rates of diffusion, and independent electrolyte selection. One particular bubble fuel cell design produces alternating current. This work presents, to our knowledge, the first microfluidic chip to produce bubbles of alternating composition in a single channel, class of fuel cells that use bubbles to transport fuel and oxidant and fuel cell capable of generating alternating current. / Graduate