Statistical Analysis of a Semilinear Hyperbolic System Advected by a White in Time Random Velocity Field

We study a system of semilinear hyperbolic equations passively advected by smooth white noise in time random velocity fields. Such a system arises in modeling non-premixed isothermal turbulent flames under single-step kinetics of fuel and oxidizer. We derive closed equations for one-point and multi-point probability distribution functions (PDFs) and closed form analytical formulas for the one point PDF function, as well as the two-point PDF function under homogeneity and isotropy. Exact solution formulas allows us to analyze the ensemble averaged fuel/oxidizer concentrations and the motion of their level curves. We recover the empirical formulas of combustion in the thin reaction zone limit and show that these approximate formulas can either underestimate or overestimate average concentrations when reaction zone is not tending to zero. We show that the averaged reaction rate slows down locally in space due to random advection induced diffusion; and that the level curves of ensemble averaged concentration undergo diffusion about mean locations.Comment: 18 page

Lattice-Boltzmann Modeling of Bacterial Chemotaxis in the Subsurface

The Lattice Boltzmann method (LBM) has been widely used because it is well-suited to model flow and transport in the complex geometries that are typical for subsurface porous media. Bacterial chemotaxis enables motile bacteria to move preferably toward chemoattractants that may be contaminants in the subsurface. This microbial phenomenon provides a valuable mechanism to enhance in situ bioremediation. Therefore, we developed Lattice Boltzmann (LB) models to study bacterial chemotaxis in the subsurface. A multiple-relaxation-time (MRT) LB model was developed to study the formation and migration of traveling bacterial waves caused by chemotaxis (chemotactic waves) in the absence of bacterial growth and decay. This model was validated by comparing simulations with experiments in which the chemotactic bacteria entered a tube filled with substrate due to chemotaxis. Simulations were performed to evaluate the effects of substrate diffusion, initial bacterial concentration, and hydrodynamic dispersion on the formation, shape, and propagation of such chemotactic waves. Wave formation requires a sufficiently high initial number of bacteria and a small substrate diffusion coefficient. Uniform flow does not affect the waves while shear flow does. Bacterial waves move both upstream and downstream when the flow velocity is small. However, the waves disappear once the velocity becomes large due to hydrodynamic dispersion. Generally waves can only be observed if the dimensionless ratio between a particularly defined coefficient, chemotactic sensitivity coefficient, and the effective diffusion coefficient of the bacteria exceeds a critical value, that is, when the biased movement due to chemotaxis overcomes the diffusion-like movement due to the random motility and hydrodynamic dispersion. Another two-relaxation-time (TRT) LB model was also introduced to simulate bacterial chemotaxis and other reactive transport. The TRT LB model can eliminate numerical diffusion by including a velocity correction term. One-dimensional solute transport with initial Gaussian and top hat distributions were investigated to evaluate the accuracy and stability of the TRT models with and without the velocity correction. The TRT model with the correction demonstrated better numerical accuracy and stability than that without the correction. When the velocity is small, the numerical diffusion can be neglected, and the TRT model without the correction attained very similar simulation results as the TRT model with the correction. However, it is necessary for the TRT model to include the velocity correction when the velocity is large. Since bacterial survival is a significant factor for contaminant remediation at contaminated sites, we studied the coupled effects of chemotaxis and growth on bacterial migration and contaminant remediation. The impacts of initial electron acceptor concentration on different bacteria and substrate systems were examined. The simulations showed that bacteria could form a growth/decay/motility wave due to a dynamic equilibrium between bacterial growth, decay and random motility, even though the bacteria perform no chemotaxis. We derived an analytical solution to estimate this growth/decay/motility wave speed. The initial electron acceptor concentration was shown to significantly affect the bacterial movement and substrate removal. The impact of chemotaxis on bacterial migration is determined by comparison of the chemotactic wave speed with the growth/decay/motility wave speed. When chemotaxis is too weak to allow for the formation of a chemotactic wave or its wave speed is less than half of the growth/decay/motility wave speed, it hardly enhances the bacterial propagation. However, chemotaxis significantly improves bacterial propagation once its wave speed exceeds the growth/decay/motility wave speed. The bacterial survival plays a crucial role in determining the efficiency of contaminant removal. If there is no growth, the traveling wave will move with a decreasing speed and finally terminates. Although chemotaxis has been widely observed to be able to improve contaminant degradation in laboratories, it is rarely reported to enhance bioremediation at field sites. We discuss this discrepancy based on our simulation findings and suggest operable measures to take advantage of chemotaxis in in situ bioremediation

NASA thesaurus. Volume 1: Hierarchical Listing

There are over 17,000 postable terms and nearly 4,000 nonpostable terms approved for use in the NASA scientific and technical information system in the Hierarchical Listing of the NASA Thesaurus. The generic structure is presented for many terms. The broader term and narrower term relationships are shown in an indented fashion that illustrates the generic structure better than the more widely used BT and NT listings. Related terms are generously applied, thus enhancing the usefulness of the Hierarchical Listing. Greater access to the Hierarchical Listing may be achieved with the collateral use of Volume 2 - Access Vocabulary and Volume 3 - Definitions

NASA Thesaurus. Volume 1: Hierarchical listing

There are 16,713 postable terms and 3,716 nonpostable terms approved for use in the NASA scientific and technical information system in the Hierarchical Listing of the NASA Thesaurus. The generic structure is presented for many terms. The broader term and narrower term relationships are shown in an indented fashion that illustrates the generic structure better than the more widely used BT and NT listings. Related terms are generously applied, thus enhancing the usefulness of the Hierarchical Listing. Greater access to the Hierarchical Listing may be achieved with the collateral use of Volume 2 - Access Vocabulary

NASA thesaurus. Volume 2: Access vocabulary

The Access Vocabulary, which is essentially a permuted index, provides access to any word or number in authorized postable and nonpostable terms. Additional entries include postable and nonpostable terms, other word entries, and pseudo-multiword terms that are permutations of words that contain words within words. The Access Vocabulary contains 40,738 entries that give increased access to the hierarchies in Volume 1 - Hierarchical Listing

NASA thesaurus. Volume 2: Access vocabulary

The access vocabulary, which is essentially a permuted index, provides access to any word or number in authorized postable and nonpostable terms. Additional entries include postable and nonpostable terms, other word entries and pseudo-multiword terms that are permutations of words that contain words within words. The access vocabulary contains almost 42,000 entries that give increased access to the hierarchies in Volume 1 - Hierarchical Listing

Computational fluid dynamics techniques for fixed-bed biofilm systems modeling : numerical simulations and experimental characterization

This thesis is focused on the development of one-phase and multiphase models using computational fluid dynamics (CFD) techniques to analyze biosystems behavior at mesoscale. In the first part, the operation of a fixed-bed biofilm reactor was simulated using Eulerian one-phase models, coupling fluid flow dynamics with biokinetics. The results reproduced accurately bioreactor performance, being experimentally verified hydrodynamics and species transport. However, the models had to be adapted to reproduce real scenarios where the biofilm motion can play a key role. On further consideration, this thesis suggested the development of Eulerian two-phase models using volume of fluid (VOF) method, defining the biofilm as an independent fluid phase by means of a comprehensive analysis of its rheological properties. This characterization became essential for accurately reproducing the fluid-biofilm interaction, describing the biofilm as a non-Newtonian fluid, which parameters were strongly dependent on its density. Thus, in the second part of this thesis, this novel continuum approach for biosystems modeling was tested, considering the required implementations to reproduce the species transfer at the interface (liquid-biofilm), and the possible growth of the biofilm phase. This new approach coupled fluid dynamics under laminar conditions with biochemical phenomena and/or biofilm mechanical behavior, so being able to reproduce the fluid stress over the biofilm, and its motion. The simulated results were experimentally verified evaluating transport mechanisms under different hydrodynamic conditions, and the model capability to reproduce shear-induced deformation and detachment, and recoil in biofilms was stated. In the third part of this thesis, the capacities of the new approach of continuum model were further tested, in order to reproduce wide range of hydrodynamic conditions to which biosystems can be exposed. Particularly, Eulerian multiphase models were developed and solved to characterize turbulent gas flows behavior over biofilms attached to walls. A coupled method of VOF and level-set, and shear stress transport (SST) k-omega model were used, reproducing accurately gas-biofilm interactions, turbulence and near-wall treatment. The simulated results were experimentally verified to confer identity to developed CFD approach, correctly describing the interfacial instabilities on the fixed-bed biofilm, such as ripples formation, and biofilm displacement and removal from its original position. The results also revealed that biofilm fluidization was the mechanisms behind the impact of turbulent air flows. Finally, in the last part of this thesis, the work was focused on the accurate analysis of fluid-biofilm interface, and on the necessity of acquiring local experimental data to verify models. The applicability of needle-probes as an innovative technique for in-situ biofilm layer and fluid interfaces detection was examined. The sensor probe performance was calibrated and verified in multiphase systems, revealing its practicability for interface detection, depth measuring, and surface reconstruction. So, a feasible tool for the experimental characterization of biosystems and models verification at mesoscale was provided. Therefore, the Eulerian multiphase approach proposed in this thesis, together with the experimental analyses, revealed the potential of CFD techniques as an alternative tool for fixed-bed biofilm systems modeling, allowing to reproduce simultaneous spatial and temporal, physical and biochemical phenomena under different operating conditions and biosystems configurations. The proposed approach helped to address key aspects of biofilm modeling such as its deformation and detachment under laminar and turbulent conditions.El estudio y modelización de los sistemas biológicos o biosistemas sigue siendo un reto que requiere explorar los fenómenos físicos y bioquímicos desde diferentes niveles de resolución espacial y temporal. Incluso para el régimen de flujo laminar más simple, las interacciones fluido- biopelícula deben ser investigadas en detalle. La dinámica de fluidos computacional (CFD, del inglés computational fluid dynamics) es una herramienta prometedora y extendida para modelar rigurosamente la hidrodinámica en reactores, la cual recientemente ha surgido como un enfoque alternativo para el modelo de biorreactores. Sin embargo, las complicadas interacciones entre la biopelícula y las fases fluidas (gas y líquido), aún no han sido descritas utilizando este tipo de técnicas. En esta tesis, se diseñaron y desarrollaron modelos monofásicos y multifásicos utilizando códigos comerciales CFD para analizar el comportamiento de los biosistemas a nivel de mesoescala. En la primera parte, se simuló la operación de un reactor de biopelícula de lecho fijo utilizando modelos monofásicos Eulerianos, acoplando la dinámica del flujo de fluido con la biocinética, e implementando un modelo de pérdidas de presión hidráulica para considerar las características físicas de la biopelícula. Esta técnica permitió obtener resultados precisos relacionados con el rendimiento del bioreactor, verificando experimentalmente la hidrodinámica y el transporte de las especies. Sin embargo, estos modelos necesitaron ser mejorados para poder reproducir escenarios reales donde el movimiento de la biopelícula puede jugar un papel importante. Por ello, se sugirió el desarrollo de modelos Eulerianos de dos fases utilizando el método de volumen de fluido (VOF, del inglés volume of fluid), donde la biopelícula se definió como una fase líquida independiente. Para desarrollar estos modelos, la caracterización experimental de las propiedades de la biopelícula fue imprescindible para adquirir un conocimiento profundo de los fenómenos implicados, especialmente para reproducir con precisión la interacción fluida sobre la biopelícula, ya que tiene un efecto directo sobre la estructura de la biopelícula. Como resultado, se desarrolló un análisis reológico integral bajo flujos de cizallamiento estables, oscilatorios y transitorios, para obtener las propiedades mecánicas macroscópicas y analizar los mecanismos de unión entre los componentes estructurales a microescala. Los resultados experimentales señalaron que las biopelículas mostraban un carácter gelatinoso, y teniendo un comportamiento de adelgazamiento del cizallamiento con una tensión de fluencia. Así, la biopelícula se caracterizó como un fluido no Newtoniano, cuyos parámetros dependían en gran medida de la densidad de la biopelícula estudiada. En la segunda parte de esta tesis, se propuso, implementó y probó un nuevo enfoque continuo para el modelado de biosistemas. Esto incluyó la definición de biopelícula como una fase fluida no Newtoniana, y otras implementaciones para reproducir la transferencia de especies en la interfaz (líquido-biopelícula), y para vincular el posible crecimiento de la fase de biopelícula con las especies transportadas y transferidas, entre otras consideraciones. Este nuevo enfoque combinó la dinámica de fluidos en condiciones laminares con fenómenos bioquímicos y/o comportamiento mecánico de la biopelícula, calculando con precisión la fracción volumétrica de las fases a lo largo del dominio, pudiendo así reproducir la interacción fluido-biopelícula en caso de movimiento de la biopelícula. Los resultados simulados fueron verificados experimentalmente evaluando los mecanismos de transporte bajo diferentes condiciones hidrodinámicas. Adicionalmente, se mostró la capacidad del modelo desarrollado para reproducir deformaciones y desprendimientos inducidos por cizallamiento y el retroceso (o recuperación) en las biopelículas, estando los resultados simulados en concordancia cualitativa con las observaciones experimentales. Con el fin de reproducir una amplia gama de condiciones hidrodinámicas a las que pueden estar expuestos los biosistemas, las capacidades del nuevo enfoque del modelo continuo se probaron más a fondo. En particular, se desarrollaron y resolvieron modelos Eulerianos multifásicos para caracterizar el comportamiento de los flujos de gas turbulento sobre biopelículas adheridas a la pared, utilizando un método acoplado de VOF y de conjunto de nivel (en inglés level-set) y el modelo SST k-ω, con el fin de reproducir con precisión las interacciones gas-biopelícula, la turbulencia y el tratamiento cercano a la pared. Los resultados simulados fueron verificados experimentalmente para conferir identidad al enfoque de CFD desarrollado, describiendo correctamente las inestabilidades interfaciales en la biopelícula de lecho fijo, tales como la formación de ondulaciones, y el desplazamiento y desprendimiento de la biopelícula de su posición original. Los resultados también revelaron que la fluidización del biopelícula era el mecanismo que se encontraba detrás del impacto de flujos de aire turbulentos. Finalmente, en la última parte de esta tesis, el trabajo se centró en el análisis preciso de la interfase fluido-biopelícula, y en la necesidad de adquirir datos experimentales locales para verificar modelos, como se había comentado en los capítulos anteriores. Se examinó la aplicabilidad de las sondas de aguja como técnica innovadora para la detección in-situ de la capa de biopelícula y de las interfases de los fluidos. El comportamiento de las sondas fue calibrado y verificado en sistemas multifásicos, mostrando su practicidad para la detección de interfases, medición de profundidad y reconstrucción de superficies. Así pues, se proporcionó una herramienta viable para la caracterización experimental de biosistemas y la verificación de modelos a mesoescala. Por lo tanto, el enfoque multifase Euleriano propuesto en esta tesis, junto con los análisis experimentales, reveló el potencial de las técnicas CFD como una herramienta alternativa al modelo de sistemas de biopelícula de lecho fijo, permitiendo reproducir simultáneamente fenómenos físicos y bioquímicos en espacio y tiempo, y bajo diferentes condiciones de operación y configuraciones de los biosistemas. El enfoque propuesto ayudó a abordar aspectos clave del modelado de biopelículas como su deformación y desprendimiento bajo condiciones laminares y turbulenta