Thesis (M. S.)--Mechanical Engineering, Georgia Institute of Technology, 2009. / Committee Chair: Cyrus K. Aidun; Committee Member: Marc K. Smith; Committee Member: S. Mostafa Ghiaasiaan. Part of the SMARTech Electronic Thesis and Dissertation Collection.

Thesis (PH.D.)--Michigan State University. Mechanical Engineering, 2008. / Title from PDF t.p. (viewed on Aug. 28, 2009) Includes bibliographical references (p. 154-167). Also issued in print.

Tese (doutorado) - Universidade Federal de Santa Catarina, Centro Tecnológico, Programa de Pós-Graduação em Engenharia Mecânica, 2014 / Made available in DSpace on 2015-06-02T04:04:41Z (GMT). No. of bitstreams: 1 333800.pdf: 7783075 bytes, checksum: c6e9b3bfd105f63cfef6d87840c8f43c (MD5) Previous issue date: 2014 / Na ausência de excitação, neurônios permanecem em repouso. O estado de repouso é caracterizado pela existência de diferenças de potencial elétrico e concentrações iônicas através da membrana do axônio. No entanto, os mecanismos responsáveis e a magnitude dos fluxos durante o estabelecimento do estado de repouso, após uma perturbação externa, não estão ainda completamente elucidados. O estado de repouso não é um estado de equilíbrio, mas um estado dinâmico estacionário. Sabe-se da existência de proteínas, classificadas genericamente como bombas e canais, que transportam íons através da membrana modificando o potencial através da mesma. No entanto, há várias hipóteses contraditórias sobre a magnitude e relação entre os fluxos provocados por tais proteínas e sobre a importância de outros fatores, como, por exemplo, a existência de cargas fixas. Um dos motivos para a dificuldade em escolher as hipóteses que tornam a modelagem mais consistente reside nas escalas de espaço e tempo diminutas dos fenômenos envolvidos o que dificulta a obtenção de medições locais e controladas. Nesse sentido, o desenvolvimento de modelos consistentes permite a avaliação das características e dos efeitos das várias hipóteses e contribui para o estabelecimento de modelos mais confiáveis. Nesse trabalho, utiliza-se, o método lattice Boltzmann para tratar o transporte iônio e o campo elétrico nos meios intra e extra celulares nas vizinhanças da membrana celular de um axônio. Uma caracterização físico-química da região vizinha à membrana de um axônio é feita baseada nos dados experimentais existentes. De posse dessa caracterização, utiliza-se o método numérico para a simulação da eletrodifusão iônica de uma porção de axônio quando uma perturbação a partir do estado de repouso é introduzida. Várias hipóteses são usadas, as soluções numéricas são comparadas com soluções existentes na literatura e com medições e, com base nas simulações, conclui-se quais hipóteses são mais adequadas para se explicar a manutenção do repouso. Além disso, também se observa que são necessários mais experimentos para obter maior confiabilidade sobre os modelos constitutivos de fluxos através dos canais e, principalmente, das bombas.<br> / Abstract: In the absence of excitation, neurons remain in a state called the resting state. The resting state is characterized by differences in electrical potential and ionic concentrations across the axon membrane. However, there is still a lacking of a complete understanding of the local mechanisms responsible and the magnitudes of the fluxes involved during the changes towards the resting state after the neuron suffers an external disturbance. The resting state is most likely a dynamic state, notan equilibrium one. Known mechanisms rely on the action of proteins called generically pumps and channels. These biological devices selectively transport ionic charges across the membrane. Contradictory hypothesis on the magnitude and relations among the charge transfers and on the effect of other parameters, such as the existence of fixed charges, have been advanced. The main difficult in sorting out the validity of these hypothesis rests on the inherent difficult in obtaining local and controlled measurements. In this sense, a reliable and consistent theoretical formulation may come as an aid to evaluate the effects and features of each mechanism and underlying hypothesis. In this work, the Lattice Boltzmann method is used to simulate the transport of ions and the electrical field in the intra and extra cellular spaces in the surroundings of an axon membrane. A physical-chemical characterization of the system is made based on the experimental evidence available in the literature. This characterization is then used in the numerical simulation of the electro - diffusion problem in a section of an axon when a perturbation from the resting state is introduced. Many hypotheses are used and the numerical solutions are compared with solutions and measurements found in the literature. From the results, the validity of the different hypothesis is assessed. The need for additional measurements to increase the reliability of the models for the constitutive fluxes through channels and pumps is evidenced.

Cabonate-hosted hydrocarbon reservoirs will play an increasingly important role in the energy supply, as 60% of the world's remaining hydrocarbon resources are trapped within carbonate rocks. The properties of carbonates are controlled by deposition and diagenesis, which includes calcite cementation that begins immediately after deposition and may have a strong impact on subsequent diagenetic pathways. This thesis aims to understand the impact of early calcite cementation on reservoir properties through object-based modelling and Lattice Boltzmann ow simulation to obtain permeability. A Bayesian inference framework is also developed to quantify the ability of Lattice Boltzmann method to predict the permeability of porous media. Modelling focuses on the impact of carbonate grain type on properties of early cemented grainstones and on the examination of the theoretical changes to the morphology of the pore space. For that purpose process-based models of early cementation are developed in both 2D (Calcite2D) and 3D (Calcite3D, which also includes modelling of deposition). Both models assume the existence of two grain types: polycrystalline and monocrystalline, and two early calcite cement types specific to these grain types: isopachous and syntaxial, respectively. Of the many possible crystal forms that syntaxial cement can take, this thesis focuses on two common rhombohedral forms: a blocky form 01¯12 and an elongated form 40¯41. The results of the 2D and 3D modelling demonstrate the effect of competition of growing grains for the available pore space: the more monocrystalline grains present in the sample, the stronger this competition becomes and the lesser the impact of each individual grain on the resulting early calcite cement volume and porosity. The synthetic samples with syntaxial cements grown of the more elongated crystal form 40¯41 have lower porosity for the same monocrystalline grains content than synthetic samples grown following more blocky crystal form 01¯12. Moreover, permeability at a constant porosity is reduced for synthetic samples with the form 40¯41. Additionally, synthetic samples with form 40¯41 exhibit greater variability in the results as this rhombohedral form is more elongated and has the potential for producing a greater volume of cement. The results of the 2D study suggest that for samples at constant porosity the higher the proportion of monocrystalline grains are in the sample, the higher the permeability. The 3D study suggests that for samples with crystal form 01¯12 at constant porosity the permeability becomes lower as the proportion of monocrystalline grains increase, but this impact is relatively minor. In the case of samples with crystal form 40¯41 the results are inconclusive. This dependence of permeability on monocrystalline grains is weaker than in the 2D study, which is most probably a result of the bias of flow simulation in the 2D as well as of the treatment of the porous medium before the cement growth model is applied. The range of the permeability results in the 2D modelling may be artificially overly wide, which could lead to the dependence of permeability on sediment type being exaggerated. Poroperm results of the 2D modelling (10-8000mD) are in reasonable agreement with the data reported for grainstones in literature (0.1-5000mD) as well as for the plug data of the samples used in modelling (porosity 22 - 27%, permeability 200 - 3000mD), however permeability results at any given porosity have a wide range due to the bias inherent to the 2D flow modelling. Poroperm results in the 3D modelling (10 - 30, 000mD) exhibit permeabilities above the range of that reported in the literature or the plug data, but the reason for that is that the initial synthetic sediment deposit has very high permeability (58, 900mD). However, the trend in poroperm closely resembles those reported in carbonate rocks. As the modelling depends heavily on the use of Lattice Boltzmann method (flow simulation to obtain permeability results), a Bayesian inference framework is presented to quantify the predictive power of Lattice Boltzmann models. This calibration methodology is presented on the example of Fontainebleau sandstone. The framework enables a systematic parameter estimation of Lattice Boltzmann model parameters (in the scope of this work, the relaxation parameter τ ), for the currently used calibrations of Lattice Boltzmann based on Hagen-Poiseuille law. Our prediction of permeability using the Hagen-Poiseuille calibration suggests that this method for calibration is not optimal and in fact leads to substantial discrepancies with experimental measurements, especially for highly porous complex media such as carbonates. We proceed to recalibrate the Lattice Boltzmann model using permeability data from porous media, which results in a substantially different value of the optimal τ parameter than those used previously (0.654 here compared to 0.9). We augment our model introducing porosity-dependence, where we find that the optimal value for τ decreases for samples of higher porosity. In this new semi-empirical model one first identifies the porosity of the given medium, and on that basis chooses an appropriate Lattice Boltzmann relaxation parameter. These two approaches result in permeability predictions much closer to the experimental permeability data, with the porosity-dependent case being the better of the two. Validation of this calibration method with independent samples of the same rock type yields permeability predictions that fall close to the experimental data, and again the porosity-dependent model provides better results. We thus conclude that our calibration model is a powerful tool for accurate prediction of complex porous media permeability.

La méthode Lattice Boltzmann (LBM) est une alternative viable à la simulation directe (DNS) des équations de Navier et Stokes, particulièrement en Mécanique des Fluides. La clé de son succès se situe dans l’exactitude, la simplicité et la propriété conforme de parallélisation de l’algorithme stream-collision. L’inconvénient majeur de cette méthode provient de la limitation aux mailles cubiques spatialement uniformes. Pour y remédier, plusieurs extensions de la LBM aux mailles non-homogènes ont été proposées. Ces techniques ont été revisitées dans la thèse. La revue de maillage montre que la meilleure technique de raffinement remplit certains critères: elle doit satisfaire aux lois de conservation et doit être stable. Elle suggère l’adoption des approches de type Volumes Finis (FV LBM). Une revue de ces techniques a permis de conclure que bien qu’intéressantes, elles présentent de nombreux inconvénients. Cette étude présente une méthode de discrétisation de type FV pour Lattice Boltzmann de haute précision et avec un faible coût de calcul. Afin d’évaluer la performance de la méthode FV nous effectuons une comparaison systématique axée sur la précision et les performances de calcul avec la méthode de Lattice Boltzmann standard (ST). En particulier, nous cherchons à clarifier si et dans quelles conditions l’algorithme proposé et plus généralement tout algorithme FV peut être considéré comme la méthode de choix pour les simulations en Mécanique des Fluides. Nous présentons la première simulation des écoulements convectifs à haut nombre de Rayleigh réalisée avec une méthode Lattice Boltzmann de type FV avec des mailles réduites près de la paroi. / Lattice Boltzmann Method (LBM) has become a viable alternative to Navier-Stokes Direct Numerical Simulations (DNS) in fluid dynamics research. The key of this success is the accuracy/simplicity and parallelization compliant property of the stream-collision algorithm. One shortcoming however, comes from the limitation to spatially uniform cubic grids. To overcome this, several LBM extension to non-homogeneous grids have been proposed. These techniques have been reviewed in this thesis. Such review suggests that a better refinement technique should fulfill some properties: obey conservation laws and be stable. This suggests a pathway to adopt Finite Volume approaches (FV LBM). A review on such volumetric approach to LBM concludes that although interesting, at present such methods suffer from several drawbacks. In this study, a new FV discretization method for the Lattice Boltzmann equation that combines high accuracy with limited computational cost is presented. In order to assess the performance of the FV method we carry out a systematic comparison, focused on accuracy and computational performances, with the standard streaming (ST) Lattice Boltzmann equation algorithm. In particular we aim at clarifying whether and in which conditions the proposed algorithm, and more generally any FV algorithm, can be taken as the method of choice in fluid-dynamics LB simulations. We report the first successful simulation of high-Rayleigh number convective flow performed by a Lattice Boltzmann FV based algorithm with wall grid refinement.

My dissertation is an investigation into the basic Physics of phase separation fronts. Such phase-separation fronts occur in many practical applications, like the formation of immersion precipitation membranes, Temperature induced phase-separation of polymeric blends, or the formation of steel. Despite the fact that these phenomena are ubiquitous no generally acceptable theory of phase-separation front exists. I believe the reason lies in the complexity of many of these material systems where a large number of physical effects (like phase-separation, crystallization, hydrodynamics, etc) cooperate to generate these structures. As a Physicist, I was driven to develop an understanding of these systems, and we choose to start our investigation with the simplest system that would incorporate a phase-separation front. So we initially limited our study to systems with a purely diffusive dynamics. The phase-separation front is induced by a control-parameter front that is a simple step function advancing with a prescribed velocity. We investigated these systems numerically using a lattice Boltzmann method and also investigated them analytically as much as possible. Starting from a one-dimensional front moving with a constant velocity we then extended the complexity of the systems by increasing the number of dimensions, examining a variable front velocity, and finally by including hydrodynamics.

Dendrite growth is the primary form of crystal growth observed in laser deposition process of most commercial metallic alloys. The properties of metallic alloys strongly depend on their microstructure; that is the shape, size, orientation and composition of the dendrite matrix formed during solidification. Understanding and controlling the dendrite growth is vital in order to predict and achieve the desired microstructure and hence properties of the laser deposition metals. A two dimensional (2D) model combining the finite element method (FE) and the cellular automaton technique (CA) was developed to simulate the dendrite growth both for cubic and for hexagonal close-packed (HCP) crystal structure material. The application of this model to dendrite growth occurring in the molten pool during the Laser Engineered Net Shaping (LENS®) process was discussed. Based on the simulation results and the previously published experimental data, the expressions describing the relationship between the cooling rate and the dendrite arm spacing (DAS), were proposed. In addition, the influence of LENS process parameters, such as the moving speed of the laser beam and the layer thickness, on the DAS was also discussed. Different dendrite morphologies calculated at different locations were explained based on local solidification conditions. And the influence of convection on dendrite growth was discussed. The simulation results showed a good agreement with previously published experiments. This work contributes to the understanding of microstructure formation and resulting mechanical properties of LENS-built parts as well as provides a fundamental basis for optimization of the LENS process.

Yes / For the first time, a set of Lattice-Boltzmann two-way coupling pointwise Euler-Lagrange models is applied to gas mixing of sludge for anaerobic digestion. The set comprises a local model, a “first-neighbour” (viz., back-coupling occurs to the voxel where a particle sits, plus its first neighbours) and a “smoothing-kernel” (forward- and back-coupling occur through a smoothed-kernel averaging procedure). Laboratory-scale tests display grid-independence problems due to bubble diameter being larger than voxel size, thereby breaking the pointwise Euler-Lagrange assumption of negligible particle size. To tackle this problem and thereby have grid-independent results, a novel data-scaling approach to pointwise Euler-Lagrange grid independence evaluation, based on an application of the Buckingham π theorem, is proposed. Evaluation of laboratory-scale flow patterns and comparison to experimental data show only marginal differences in between the models, and between numerical modelling and experimental data. Pilot-scale simulations show that all the models produce grid-independent, coherent data if the Euler-Lagrange assumption of negligible (or at least, small) particle size is recovered. In both cases, a second-order convergence was achieved. A discussion follows on the opportunity of applying the proposed data-scaling approach rather than the smoothing-kernel model.

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