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Recent advancements in microfabrication technology have led to the development of micro-total analytical systems (μ-TAS), more popularly known as lab-on-a-chip (LOC) devices. These devices have a relatively small size and are capable of performing sample and reagent handling steps together with analytical measurements. Rapid mixing is essential in such microfluidic systems for various applications e.g., biochemical analysis, sequencing or synthesis of nucleic acids, and for reproducible biological processes that involve cell activation, enzyme reactions, and protein folding. In this work a numerical model is developed using a lattice Boltzmann method (LBM) to study microscale mixing. The study involves two mixing methods, namely, electroosmotic mixing and magnetic assisted mixing. A single component LBM model is developed to study electroosmotic flow in a square cavity. Mixing is studied by introducing two types of tracer particles in the steady electroosmotic flow and characterized by various mixing parameters. The results show that rapid mixing can be achieved by using a steady electric field and a homogeneous zeta potential. A multicomponent LBM method is also developed to study magnetic assisted mixing in a channel configuration. The ferrofluid flow is influenced by two magnets placed across a microchannel. The interacting field induced by these magnets promotes cross-stream motion of the ferrofluid, which induces its mixing with the other nonmagnetic fluid. Two fluids, one magnetic and another non-magnetic fluid, are introduced in a channel, when two magnets are placed across it at a distance apart. In the presence of the magnetic field, the magnetic fluid tries to follow a zig-zag motion generating two rolls of vortices thereby enhancing mixing. A parametric study characterizes the effects of diffusivity, magnetic field strength, and relative magnet positions on a mixing parameter. Mixing is enhanced when the magnetic field strength and diffusivity are increased. However, contrary to the observed trend, placing the magnets very close to each other axially results in local ferrofluid agglomeration rather than promoting mixing. / Ph. D.

The metallic interconnect of a solid oxide fuel cell (SOFC) contains chromium in order to protect the metal from the corrosive environment in the fuel cell. Unfortunately, the chromium introduces chemical instability in the cathode as it migrates from the interconnect to the pores in the cathode. A model was developed previously in Asinari et al. [1] and Kasula et al [2] to model the flow of particles in a fuel cell electrode. To learn more about the migration of the chromium, the previous code is modified in this thesis work to include the effects of the chromium. The model uses Kinetic Theory to simulate the fuel cell at a mesoscopic scale. The discretized form of the Lattice Boltzmann equation is modified for enhanced performance and for use on a parallel processing system. With the new model, the migration of the chromium in the cathode and the performance degradation of the fuel cell are predicted. / Master of Science

The excessive presence of liquid water in a gas diffusion layer (GDL) hinders the access of reactant gases to the active sites of the catalyst layer leading to decreased performance of a polymer electrolyte membrane fuel cell (PEMFC). Therefore, GDLs are usually treated with a hydrophobic agent to render their fibres more hydrophobic in order to facilitate gas transport and water removal. Numerous studies have been conducted to investigate water transport in PEMFCs in recent years; however, the behaviour of liquid water in a GDL at a pore-level is poorly understood. Macroscopic models fail to incorporate the influence of the structural morphology of GDLs on liquid water transport behaviour. Experimental methods are not conducive towards a good understanding at a microscopic level because of the diminutive size of the GDLs porous structure. Alternatively, the Lattice Boltzmann (LB) method has gathered interest as it is found to be particularly useful in fluid flow simulations in porous media due to its capability to incorporate the complex boundaries of actual GDL structures. To date, most studies on fluid transport in GDLs integrated artificial structures generated by stochastic simulation techniques to the LB models. The stochastic-based model, however, does not represent closely the microscopic features of the actual GDL as manufactured. In addition, comparison of liquid water transport behaviour in different GDL structures using the LB method is rare since only a single GDL material has been utilised in most of those studies. This thesis aims to develop our understanding of liquid water transport behaviour in GDLs with morphologically different structures under varying wettability conditions based on the LB method and the X-ray computed tomography (XCT) technique. GDLs with paper and felt structures were reconstructed into 3D digital volumetric models via the XCT process. The digital models were then incorporated into a LB solver to model water saturation distribution through the GDL domains. The GDL wettability was also altered so that the effect on liquid water behaviour in the GDL could be examined. This project is divided into three main sections. In the sensitivity analysis, the effect of image resolution on gas permeability through the X-ray reconstructed GDL was carried out using a single-phase LB model. It was found that the resolution variation could significantly affect the resulting gas permeability in both principal and off-principal directions, as well as computational time. An optimum resolution, however, exists at 2.72 μm/pixel, which consumed 400 times less computational time with less than 8% difference in the resulting permeability compared to the base resolution. This study also served as a guideline for selecting a resolution for generating the XCT images of the GDLs which were utilised in the following studies. In the structure analysis, the structures of the paper and felt GDLs were generated using the XCT and the key properties of each GDL, including thickness, porosity, permeability and tortuosity, were characterised. The thickness and the through-plane porosity distributions of each GDL were examined based on the tomography images. The resulting local through-plane porosity distributions were then used to calculate through-plane permeability and tortuosity distributions using an analytical model available in the literature. This study revealed the heterogeneity of the GDLs and how the heterogeneous nature of the GDL structures affects others properties of the GDLs. In this study, the absolute through-plane permeability and tortuosity of the X-ray-reconstructed GDL samples were also characterised using the single-phase LB model. The results from the two models were then compared and validated against data in the literature. In the water transport analysis, the two-phase LB model was employed to examine the effects of GDL structures on the behaviour of liquid water in the GDLs, including invasion patterns, saturation distribution and breakthrough behaviour under varying GDL wettability conditions. It was found that wettability was responsible for invasion patterns and water saturation levels whilst the GDL structure was mostly responsible for breakthrough occurrence and saturation distribution. It was observed that water travelled with stable displacement saturating all pores in hydrophilic GDLs, while it travelled with capillary fingering causing decreased saturation in hydrophobic GDLs, about 50% in the highly hydrophobic cases. The GDL structure was found to play a key role in breakthrough behaviour in the hydrophilic GDL as it was seen that the through-plane fibres in the felt structure and the through-plane binders in the paper structure encouraged water removal from the GDL in the thickness direction. Conversely, the GDL structure was found to have negligible influence on breakthrough in the hydrophobic GDL. Each GDL structure, however, contributed to a distinct difference in water distribution in the GDL with hydrophobic wettability. The work presented in this thesis contributes to the understanding of liquid water transport behaviour in the GDLs under the combined effects of the GDL structures and wettability conditions, which is essential for the development of effective PEMFC water management and the design of future GDL materials.

Understanding how the water produced in an operating polymer electrolyte membrane fuel cell (PEMFC) is transported in cathode catalyst layer (CCL) is crucial to improving performance and efficiency. In this thesis, a multiple-relaxation-time (MRT) lattice Boltzmann method (LBM) is employed to simulate the high density ratio, multiphase water transport in in the CCL. The three-dimensional structure of the catalyst layer is reconstructed based on experimental data acquired with a dual beam scanning electron microscope/focused ion beam system and a stochastic method using lower order statistical functions (e.g. porosity and two point correlation functions). Simulations of the water transport dynamics are performed to examine the effect of a range of physical parameters: wettability, viscosity ratio, pressure gradient, and surface tension. The water penetration patterns in the catalyst layers reveal a complex fingering process and transition of the water transport pattern from a capillary fingering regime to a stable displacement regime is observed when the wettability potential of the catalyst layer changes. The second part of the analysis focuses on quantifying the impact of liquid water distribution and accumulation in the catalyst layer on effective transport properties by coupling two numerical methods: the two-phase LBM is used to determine equilibrium liquid water distribution, and then a finite volume-based pore-scale model (FV-PSM) is used to compute transport of reactant and charged species in the CL accounting for the impact of liquid water saturation .The simulated results elucidate and quantify the significant impact of liquid water on the effective oxygen and water vapor diffusivity, and thermal conductivity in CLs. / Graduate

The fluid-structure interactions of wall-mounted slender structures, such as cilia, filaments, flaps, and flags, play an important role in a broad range of physical processes: from the coherent waving motion of vegetation, to the passive flow control capability of hair-like surface coatings. While these systems are ubiquitous, their coupled nonlinear response exhibits a wide variety of behaviours that is yet to be fully understood, especially when multiple structures are considered. The purpose of this work is to investigate, via numerical simulation, the fluid-structure interactions of arrays of slender structures over a range of input conditions. A direct modelling approach, whereby the individual structures and their dynamics are fully resolved, is realised via a lattice Boltzmann-immersed boundary model, which is coupled to two different structural solvers: an Euler-Bernoulli beam model, and a finite element model. Results are presented for three selected test cases - which build in scale from a single flap in a periodic array, to a small finite array of flaps, and finally to a large finite array - and the key behaviour modes are characterised and quantified. Results show a broad range of behaviours, which depend on the flow conditions and structural properties. In particular, the emergence of coherent waving motions are shown to be closely related to the natural frequency of the array. Furthermore, this behaviour is associated with a lock-in between the natural frequency of the array and the predicted frequency of the fluid instabilities. The original contributions of this work are: the development and application of a numerical tool for direct modelling of large arrays of slender structures; the characterisation of the behaviour of slender structures over a range of input conditions; and the exposition of key behaviour modes of slender structures and their relation to input conditions.

Les méthodes de Boltzmann sur réseaux (LBM) ont été appliquées avec beaucoup de succès aux écoulements hydrodynamiques en milieux poreux. Cependant, la limitation de ces méthodes aux écoulements hydrodynamiques et isothermes, les rendent insuffisantes pour simuler des écoulements de gaz dans des milieux micro-poreux. Dans ce cas, il est en effet fréquent que le libre parcours moyen des molécules du gaz, soit du même ordre de grandeur que la taille des pores dans lesquels il s’écoule. De tels écoulements ne seront alors plus en régime hydrodynamique, mais dans des régimes qualifiés de glissement et de transitionnel ; régimes pour lesquels les LBM standards ne sont plus valides. D’autre part, le caractère isotherme des LBM les rendent inutilisables, par exemple dans le cas où le gaz subit une détente à travers le milieu. Il est nécessaire, pour décrire de tels écoulements et phénomènes, de se placer au niveau cinétique. La démarche proposée repose sur la décomposition de la fonction de distribution sur la base des polynômes d’Hermite et l’emploi de la quadrature de Gauss-Hermite associée à cette projection. L’aspect systématique de ce développement amène naturellement à considérer divers ordres d’approximation de l’équation de Boltzmann-BGK sous diverses quadratures. Il résulte alors de ces différentes approximations toute une famille de discrétisations de l’équation de Boltzmann-BGK, dont les LBM classiques ne sont qu’un membre. La détermination de l’approximation la plus adaptée est réalisée par analyse systématique des résultats obtenus aux différents ordres d’approximation. Ces méthodes sont testées avec succès dans des cas modèles. / The lattice Boltzmann method (LBM) have been applied very successfully to hydrodynamic flows in porous media. However, the limitation of these methods to isothermal and hydrodynamic flows, make them inadequate to simulate gas flows in micro-porous media. Indeed, in these conditions, the mean free path of the molecules could be of the same magnitude order as the pore size in which gas flows. Such flows will not be in hydrodynamic regime, but in regimes qualified of, slip or transitional ; for which the LBM are no longer valid. On the other hand, the isothermal character of LBM make them unusable, for example, in the case where the gas undergoes expansion through the media. It is then necessary, to take the kinetic point of view to describe such flows and phenomena. The proposed approach is based on the decomposition of the distribution function on the Hermite polynomials basis and the use of Gauss-Hermite quadrature associated with this projection. The systematic nature of this development naturally leads to consider different order of approximation of the Boltzmann-BGK equation in various quadratures. It then follows from these various approximations, a family of discretizations of the Boltzmann-BGK equation, whose classical LBM are a member. Determining the most suitable approximation is achieved by systematic analysis of the results obtained with different approximation orders. These methods are successfully tested in model cases.

L'objectif de cette thèse est de développer et d'analyser des techniques numériques basées sur la méthode e Boltzmann sur réseau (LBM) pour résoudre des systèmes non linéaires de type advection-réaction-diffusion provenant de la physique et de la biologie. Avec la LBM, des problèmes portant sur des quantités moyennées densité, potentiel, vitesse, etc) sont exprimés à l'échelle particulaire. Nous approchons la solution de l'équation e Boltzmann relative au comportement d'un champs de particules puis nous recomposons les quantités moyennées solutions des équations traitées. Dans un premier temps, nous développons un cadre général approprié permettant de traiter plusieurs types de systèmes non linéaires (paraboliques, elliptiques, ou couplées ' variables réelles ou complexes), avec des applications à des modèles tels que Burger-Fisher, écoulement de fluides en milieu poreux, Helmoltz, Patlar-Keller-Segel, ou encore Schrodinger. Pour chaque problème, nous analysons le comportement asymptotique de la méthode, quand le nombre de Knudsen tend vers zéro (par le développement de Chapman-Enskog) et nous effectuons l'analyse numérique de la convergence et de la stabilité de la méthode. Dans un deuxième temps, nous nous intéressons à un problème réaliste d'électrophysiologie cardio-vasculaire. Nous adaptons la méthode LBM développée pour approcher les solutions d'un système de type bidomaine permettant de simuler le comportement de potentiels électriques et les interactions ioniques ans la région du myocarde. L'étude et la modélisation d'un tel type de problème est un enjeu sanitaire majeur ans le traitement des pathologies liées par exemple à l'arythmie cardiaque. Notre but étant d'obtenir des comportements réalistes, nous introduisons au sein de ce système bidomaine des opérateurs de retard afin de tenir compte des temps de retard dans les transmissions de signaux. Une fois l'existence et l'unicité de la solution démontrées, nous proposons une série de simulations avec des paramètres physiques et biologiques réalistes afin de valider la méthode proposée. / In this thesis, we develop and analyze numerical techniques based on the lattice Boltzmann method LBM) for solving systems of nonlinear advection-diffusion-reaction equations from physics and biology. Wi BM, problems relating to averaged quantities (density, potential, velocities, etc.) are expressed at the particle scale. We approach the solution of Boltzmann equation relating to the behavior of a particle field and then we recompose the averaged quantities solutions of treated systems. In the first part, we develop an appropriate general framework to deal with several types of non-linear systems (parabolic, elliptic, or coupled, with real or complex variables), with applications to models such as Burger-Fisher, fluid flow in a porous medium, Helmoltz, Patlar-Keller-Segel, or Schrodinger. For each problem, we analyze the asymptotic behavior of the method, when the number of Knudsen tends to zero (by the development of Chapman-Enskog) and we perform the numerical analysis of convergence and stability of the method. In the second part, we have taken an interest in a realistic problem of cardio-vascular electrophysiology. We adapt the developed LBM method to approach e solutions of a bidomain type system for simulating the behavior of electrical potentials and ionic interactions in myocardial region. The study and modeling of this type of problem is a major health issue in the treatment of pathologies related, for example, to cardiac arrhythmia. Since our goal is to obtain realistic behaviors, we introduce time-delay operators into this coupled system in order to take into account delay in signal transmissions. Once the existence and uniqueness of solution have been demonstrated, we propose a series of simulations with realistic physical and biological parameters to validate the proposed method.

In this thesis work fluid flow and heat transfer in two-dimensional microchannels are studied numerically. A computer code based on Lattice Boltzmann Method (LBM) is developed for this purpose. The code is written using MATLAB and Jacket software and has the important feature of being able to run parallel on Graphics Processing Units (GPUs). The code is used to simulate flow and heat transfer inside micro and macro channels. Obtained velocity profiles and Nusselt numbers are compared with the Navier-Stokes based analytical and numerical results available in the literature and good matches are observed. Slip velocity and temperature jump boundary conditions are used for the micro channel simulations with Knudsen number values covering the slip flow regime. Speed of the parallel version of the developed code running on GPUs is compared with that of the serial one running on CPU and for large enough meshes more than 14 times speedup is observed.