Simulacó numérica directa de la dispersió turbulenta de plomalls amb flotació en un flux en un canal Alexandre Fabregat Tomás, Tarragona, octubre del 2006 1 IntroduccióL'objectiu d'aquest treball és estudiar la dispersió turbulenta de calor en diferents configuracions basades en el canal desenvolupat mitjançant DNS (Direct Numerical Simulations). Aquesta eina ha demostrat ser de gran utilitat a l'hora d'estudiar fluxos turbulents ja que permet, donada una malla computacional capaç de capturar totes les estructures del flux i un esquema que minimitzi els errors i la dissipació numérica, descriure acuradament l'evolució temporal del flux. Permet a més, donada la descripció tridimensional i temporal del flux, determinar amb precisió qualsevol quantitat que seria impossible d'obtenir experimentalment.En el flux en un canal, el fluid esmou entre dues parets planes, llises i paral·leles separades una distància 2d impulsat per un gradient constant mitjà de pressió. El flux s'anomena desenvolupat quan ja no hi ha efectes de regió d'entrada i la única inhomogeneïtat es troba en la direcció normal a la paret. Sota aquestes condicions, les quantitats promitjades esdevenen estacionàries en el temps.En aquest treball s'ha validat el codi computacional mitjançant la reproducció d'algunes configuracions de flux prèviament estudiades per altres autors. Els nous coneixements en l'estudi de la dispersió turbulenta de calor s'han obtingut a l'incloure, en un flux totalment desenvolupat en un canal, una font lineal centrada verticalment que provoca l'aparició d'un plomall amb una temperatura més alta que la del flux del fons i que per tant, al tenir una menor densitat, experimenta flotació i es deflecteix. L'amitjanament temporal del flux permet estudiar les diferents contribucions dels diferents termes rellevants en les equacions de transport.És d'especial interés la comparativa d'aquests resultats amb els corresponents a la formació d'un plomall a partir d'una font lineal d'un escalar passiu.Per altra banda també s'ha estudiat l'eficiència en paral·lel dels mètodes multigrid en la resolució d'equacions de Poisson. Aquestes equacions són d'especial interés ja que apareixen en el càlcul de la pressió i representen un coll d'ampolla en termes de costos computacionals. Aquest mètode numèric ha estat comparat amb els mètodes de gradient conjugat (anteriorment emprats en el codi 3DINAMICS) en la resolució de diferents problemes comparant els costos en termes de temps de CPU i la seua escalabilitat en la màquina multiprocessador de memòria distribuïda del grup de recerca de Mecànica de Fluids de Tarragona.2 Descripció matemàticaUn cop adimensionalitzades mitjançant les escales adequades, les equacions de transport de quantitat de moviment i energia han estat discretitzades sobre una malla desplaçada mitjançant el mètode de volums finits emprant un esquema centrat de segon ordre. La discretització dels termes advectius en els casos amb fonts lineals ha requerit, però, d'un cura especial ja que la no-linealitat d'aquests termes pot provocar oscil·lacions artificials en el camp dels escalars. La difusió numèrica dels mètodes upwind, com el QUICK, ha estat quantificada i comparada amb resultats obtinguts per a esquemes centrats de segon ordre. Les equacions han estat integrades en el temps mitjançant un esquema implícit de segon ordre tipus Crank-Nicholson. També ha estat necessari implementar condicions de sortida per a la temperatura en els casos A i C del tipus no reflectant per tal de garantir la conservació i evitar l'aparició d'estructures artificials en el flux.3 Descripció físicaLa figura 1 presenta un esquema del domini computacional corresponent al canal desenvolupat. De l'esquema es desprén que x, y i z corresponen a les direccions principal del flux, la perpendicular i la normal a les parets respectivament. Les configuracions del flux estudiades es troben resumides a la taula 1 on s'indica la resolució de la xarxa computacional, el nombre de Reynolds (basat en la velocitat de fricció ut) i en el casos amb flotació, el nombre de Grashof, la temperatura de referència i la direcció de flotació (la direcció del vector gravetat).Les dimensions del canal s´on 8pd×2pd×2d en les direccions x, y i z respectivament.En el cas A la temperatura representa un escalar de manera que el plomall format és passiu, és a dir, no hi ha acoblament entre les equacions de quantitat de moviment i energia. A diferència d'aquest, en els casos B i C totes dues equacions queden acoblades pel terme de flotació. Aquest terme apareix quan les diferències de temperatura en el si del fluid generen diferències de densitat. En el cas B, el canal vertical amb convecció mixta, cada paret del canal es troba a una temperatura constant però diferent. El vector gravetat i la direcció del corrent estan alineades de manera que aquesta direcció continua sent homogènia. En la zona propera a la paret calenta la flotació actua en la direcció del corrent imposada pel gradient mitjà de pressió. En canvi, en la zona propera a la paret freda, la flotació s'oposa al moviment del flux.El cas C és similar al cas A però en aquesta ocasió la temperatura no es considera un escalar passiu i per tant la flotació acobla el camp dinàmic amb el de temperatures. El vector gravetat actua en aquest cas en la direcció normal. La inhomogeneïtat en la direcció del flux no permet continuar emprant condicions de contorn periòdiques i per tant, al domini presentat en la figura 1, se li ha acoblat una regió auxiliar a l'entrada on es resolen únicament les equacions de quantitat de moviment. Els camps de velocitat i pressió per a un canal totalment desenvolupat obtinguts en aquest domini auxiliar s'empraran com a condició de contorn a l'entrada del domini de computació. No és necessari cap tipus d'interpolació ja que la resolució del a xarxa d'aquest domini auxiliar és la mateixa que l'emprada en el domini de computació.4 ResultatsEls resultats per a les simulacions presentades en la taula 1 contenen, principalment, els perfils de velocitat i temperatura mitjans així com la intensitat de les fluctuacions. A més, es presenten els perfils de les diferents contribucions dels termes relevants de les equacions de transport amitjanades. Per al cas C, els camps dinàmics i de temperatura no estan desenvolupats. Els perfils mitjans a diferents posicions aigües avall permeten estudiar l'evolució del plomall ascendent a més d'analitzar com la flotació afecta al balanç de les diferents contribucions. La figure 2 presenta el camp mitjà de temperatures per al cas C amb les tres posicions en la direcció principal del flux per a les quals s'han inclòs els perfils.Finalment, es presenten els resultats corresponents a la comparativa entre els diferents solvers per a una equació de Poisson. Tots els mètodes numèrics han es-3Figura 2: Camp mitjà de temperatures per al cas C tat paral·lelitzats mitjançant les llibreries Message Passing Interface. En la figura 3 es presenten com a exemple els resultats (en termes de temps de CPU i speedup) per a la resolució de l'equació de Poisson per al desacoblament de pressió i velocitat en el cas del flux desenvolupat en un canal.Els resultats de speed-up per als diferents mètodes mostren la baixa escalabilitat del solver multigrid comparat amb els altres mètodes del tipus gradient conjugat. La raó radica en les grans necessitats de comunicació d'un algoritme construït sobre un esquema de relaxació tipus SOR. Tanmateix, multigrid és el mètode numèric que requereix menys temps de CPU per concloure la tasca. El factor respecte als mètodes de gradient conjugat pot arribar a ser de 30 i per tant és el millor candidat per a la resolució d'aquests tipus de problemes. / The main goal of this work is to study the turbulent heat transfer in a developed channel flow using Direct Numerical Simulations (DNS). These simulations solve explicitly all the scales present in the turbulent flow so, even for moderate Reynolds numbers, the discretization grids need to be fine enough to capture the smallest structures of the flow and, consequently, DNS demands large computational resources. The flow, driven by a mean constant pressure gradient in the streamwise direction, is confined between two smooth, parallel and infinite walls separated a distance 2d.The turbulent heat transport is studied for three different flow configurations.Some of them are used as benchmark results for this work. The three cases reported can be summarized as:· case A: Scalar plume from a line source in a horizontal channel.· case B:Mixed convection with the gravity vector aligned with the streamwise direction (vertical channel).· case C: Buoyant plume from a line source in a horizontal channel.In addition, preliminary results for a turbulent reacting flow in a fully developed channel are also presented.In the case B heat flux results from a temperature difference between the channel walls. The gravity vector is aligned with the streamwise direction and the Grashof, Reynolds and Prandtl numbers are Gr = 9.6 · 106, Ret = 150 and Pr = 0.71 respectively. Close to the hot wall, buoyancy acts aligned to the flow direction imposed by the mean pressure gradient so velocities are generally increased in comparison with a purely forced convection flow. Oppositely, near the cold wall, buoyancy is opposed to the flow and consequently velocities are decreased.Cases A and C are similar because in both cases a hot fluid is released within a cold background flow through a line source vertically centered in the wall-normal direction located at the inlet. The height of the source is 0.054d. The injected hot fluid disperses forming a hot plume that is convected downstream between the two adiabatic walls of the channel.The difference between cases A and C lies in the fact that for case A heat and momentum are decoupled and temperature acts as an scalar. Advection and diffusion are the only phenomena responsible for the evolution of the plume. On the other hand, in case C, buoyancy couples heat and momentum and, consequently, the plume floats drifting upward as it advances in the channel due to its lower density. In case C, the streamwise direction is not homogenous because of the coupling between heat and momentum. To guarantee developed conditions at the inlet of the channel it has been necessary to attach a buffer domain just before the computational domain. In this buffer domain, the momentum transport equations for a fully developed channel are solved with the same resolution used in the main domain.The results of cases A and B have been used to validate the 3DINAMICS CFD code by comparison with data reported in the literature. This code is written in FORTRAN 90 and parallelized using the Message Passing Interface (MPI-CHlibrary). It uses the second order in time Crank-Nicholson scheme to integrate numerically the transport equations which are discretized spatially using the centered second-order finite volume approach.The analysis of averaged turbulent quantities and the contributions of the different terms of the time-averaged transport equations is used to show how buoyancy affects the turbulent transport of momentum and heat along the channel.Finally, following a similar configuration than that of case A, a chemical reactantA released through line source reacts with a background reactant B following a second order chemical reaction with Damkh¨oler number of 1. Preliminary results for turbulent species transport are also included in this work.Special attention have been devoted to the discretization of the advective terms to avoid non-realistic values of the variables because of the non-linearities of the transport equations. The conservative non-reflecting boundary conditions have been implemented at the outlet to simulate the convected outflow when the streamwise direction can not be considered homogeneous, as in case C. For homogeneous directions, periodic boundary conditions have been used.Large grid resolutions (up to 8 million grid nodes for case C including the buffer region) demand important computational resources. A parallel Multigrid solver has substituted the previous conjugate gradient method to solve the Poisson equation in the pressure calculation. This step was the most expensive in terms of CPU costs. The Multigrid method efficiency has been compared with two different versions of the conjugate gradient approach and it has been demonstrated that this method is the most efficient in terms of CPU time although the current algorithmcan be improved to enhance the scalability inmultiprocessor computers.

A comprehensive understanding of the hydrodynamics in vegetated open-channels and flow-vegetation interaction is of high interest to researchers and practitioners alike for instance in the content of river and coastal restoration schemes. The focus of this study was to investigate the effect of the presence of vegetation on flow resistance, turbulence statistics, and the instantaneous flow in open channels by performing three-dimensional computational-fluid-dynamics (CFD) simulations. Firstly, fully developed turbulent flow in fully-vegetated channel was analyzed by employing the method of high-resolution Large-Eddy Simulation (LES). Flow through a staggered array of rigid, emergent cylinders was simulated and the LES was validated through experiments. After validation, numerical simulations were performed at an extended parameter range of two different cylinder Reynolds numbers (ReD = 500 and 1340) and three different vegetation densities (φ = 0.016, 0.063, and 0.251). Flow structures and statistics were analyzed on the instantaneous flow and the effect of the vegetation density and cylinder Reynolds number was assessed. Moreover, drag forces exerted on the cylinders were calculated explicitly, and the effect of both ReD and φ on the drag coefficient was quantified. Secondly, two new alternative simulation strategies, a RANS based strategy with a vegetative closure model and a low-resolution Large-Eddy Simulation, were devised. They were evaluated by simulating several experimental cases with diverse conditions of the cylinder arrangement (i.e., staggered vs. random distribution), vegetation densities (φ = 0.016, 0.022, 0.063, 0.087, 0.091, 0.150, and 0.251), and cylinder Reynolds number (ReD = 170 - 1700). For the RANS based strategy, the importance of a-priori knowledge was assessed, and for the low-resolution LES, the efficiency and accuracy was demonstrated. Finally, a numerical strategy based on a porosity approach was developed and applied to open-channel flow through a natural plant. The simulated velocities were compared with experimentally acquired ones and results showed reasonable agreement. The results obtained in this research contribute to the understanding of fundamental mechanism of flow-vegetation interaction in vegetated open-channels, resolving turbulent flow-vegetation interaction explicitly. In addition, the new numerical strategies developed as part of this research are expected to allow describing the behavior of turbulent flow through artificial and natural vegetation with high efficiency and accuracy.

Water scarcity is among the most serious, long-term challenges in the world. To an ever increasing degree, sustainable water supply depends on the utilization of water of impaired initial quality. This is particularly true in developing nations and in water-stressed areas such as the American Southwest. Water of impaired quality could be water of high salinity such as brackish groundwater. Traditionally, reverse osmosis (RO) would be chosen to desalinate the brackish groundwater, since RO costs are competitive with those of thermal desalination, even for seawater applications. However, both conventional thermal distillation and RO are energy intensive, complex processes that discourage decentralized or rural implementation. In addition, both technologies require enhanced expertise for operation and maintenance, and are susceptible to scaling and fouling unless extensive feed pretreatment is employed. Membrane distillation (MD), driven by vapor pressure gradients, can potentially overcome many of these drawbacks. MD can operate using low-grade, sub-boiling temperature heat sources. When it is driven by solar energy it does not require highly concentrating collection devices, non-aqueous working fluids, or complex temperature control systems, nor does it require extensive operational expertise. Membrane Distillation (MD) applications, background and modeling efforts are discussed in the first part of this dissertation. Two main studies are presented in this document: Firstly, Sweeping Gas Membrane Distillation (SGMD) through a hollow fiber membrane was studied both experimentally and modeled mathematically to describe performance of SGMD and extend results to predict membrane module efficiency and secondly, SGMD through a flat sheet MD module to study the effect of membrane characteristics in combination with operational variables. A final study was conducted to examine the effect of mesh spacer insertion in flat sheet membrane module on the permeate water production.

In a novel application of the temporal numerical simulation, an investigation ofturbulence modeling techniques is carried for the turbulent wall jet over aconvex surface (Coanda wall jet.) The simultaneous presence of multipleinstability mechanisms and the interaction with the turbulence dynamics at thesolid boundary produces a unique combination of different large turbulentcoherent structures that constitutes both a consistent challenge for numericalsimulations and an ideal test bed for turbulence models.The Temporal Direct Numerical Simulation (TDNS) of the Coanda wall jetrestricts the focus from the global turbulent Coanda wall jet to a smaller, localportion of the flow and offers a wide array of advantages to the present work. Inparticular, the size of the computational domain can be arbitrarily chosen inboth the spanwise and the streamwise directions. This allows to either suppressor enhance individual physical mechanisms and, consequently, to selectivelyreproduce different large coherent structures within the local flow. In the firstpart, temporal numerical simulations are employed to reproduce four differentflow scenarios of the local Coanda wall jet with a level of numerical resolutionthat, because of the reduced size of the computational domain, cannot be matchedby standard DNS of the entire physical flow (spatial DNS, or SDNS.)The TDNS of these four flow scenarios are then used in the second part for ana--posteriori analysis of different turbulence models in order to addresscommon shortcomings shown by Hybrid Turbulence Models (HTM). For each flowscenario, the turbulent flow field is deliberately decomposed in resolved andunresolved flows by the application of different filters in space correspondingto different grid resolution. The behavior of turbulence models can be reproducedfrom the resolved flow and compared to the turbulent stress tensor directlycalculated from the unresolved part of the flow field. Starting from the RANSlimit, turbulence models with different levels of complexity are studied.Successively, the performance of these models is analyzed at intermediatenumerical resolutions between RANS, LES, and DNS. Finally, an improvedformulation of the Flow Simulation Methodology (FSM) is proposed.

Established techniques for the detection of pathogens, such as bacteria and viruses, require long timeframes for culturing. State of the art biosensors rely on the diffusion of the target analyte to the sensor surface. AC electric fields can be exploited to enhance the sampling of pathogens and concentrate them at specific locations on the sensor surface, thus overcoming these bottlenecks. AC electrokinetic effects like the dielectrophoretic force and electrothermal flows apply forces on the particle and the bulk fluid, respectively. While dielectrophoresis forces pathogens towards a target location, electrothermal flows circulates the fluid, thus replenishing the local concentration. Numerical simulations and experimental proof of principle demonstrate how AC electrokinetics can be used to collect model bioparticles on an antibody functionalized selective surface from a heterogeneous solution having physiologically relevant conductivity. The presence of parallel channels in a quadrupolar microelectrode design is identified as detrimental during the negative dielectrophoretic collection of bioparticles at the centre of the design while simultaneously providing secondary concentration points. These microelectrodes were incorporated onto the surface of a novel cantilever design for the rapid positive dielectrophoretic collection of Escherichia coli bacteria and enabled the subsequent detection of the bacteria by measuring the shift in the resonance frequency of the cantilever. Finally, a proof of principle setup for a Raman coupled, AC electrokinetically enhanced sampling and detection of viruses is shown where the presence of M13 phages are identified on a selective antibody functionalized surface using Raman spectroscopy. / Thesis (Ph.D, Chemical Engineering) -- Queen's University, 2012-01-30 19:23:48.958

Lors du fonctionnement d'une installation hydraulique, l'apparition de zone de cavitation dans l'écoulement peut entraîner un endommagement important sur la surface des matériaux. La quantification de l'intensité de cavitation sur les composants hydrauliques serait utile à la fois pour mieux concevoir les nouveaux équipements en projet, mais aussi pour améliorer la conduite et optimiser la maintenance des matériels existants. Au vu du grand nombre de paramètres régissant les écoulements cavitants, l'élaboration de lois de similitudes universelles à partir d'expériences est délicate. Avec l'augmentation des moyens de calculs, la simulation numérique est un outil pour étudier ce phénomène sur des géométries variées. La principale difficulté de cette démarche réside dans la différence d'échelles existant entre les simulations numériques U-RANS servant à simuler l'écoulement cavitant et les mécanismes d'implosion de bulles jugés responsables de l'endommagement sur le solide. La méthode proposée dans ce manuscrit s'appuie sur un post-traitement des simulations U-RANS afin de caractériser une distribution de bulles et de simuler leurs comportements à de plus petites échelles spatiales et temporelles. Dans un premier temps, notre travail consiste à expliciter les équations locales de conservation de masse, de quantité de mouvement et d'énergie pour un écoulement liquide/gaz comprenant deux espèces eau/air. Ce travail mène à l'élaboration de grandeurs de mélange prenant notamment en compte la présence de gaz incondensables au sein du fluide. Des hypothèses permettent de rendre ce système équivalent à ceux, utilisant une approche homogène, implémentés dans les codes de simulations d'écoulements cavitants instationnaires développés précédemment au laboratoire. La caractérisation des populations de bulles effectuée par le post-traitement prend ainsi en considération à la fois la tension superficielle et la présence de gaz incondensables. Dans un deuxième temps, l'élaboration d'un code de calcul permettant la simulation de la dynamique d'un nuage de bulles est débutée. Ce dernier a pour ambition de tenir compte à la fois des interactions entre les bulles et des déformations non sphériques que celles-ci peuvent subir à l'aide d'une méthode potentielle. Des premiers résultats de simulations sont présentés dans ce manuscrit et permettent de tenir compte de faibles déformations des bulles. La dernière étape de ce travail consiste à proposer une méthode de chaînage entre ces deux échelles en initialisant le calcul de dynamique de bulles à l'aide des résultats du calcul U-RANS. L'énergie émise lors de l'implosion des bulles et impactant la surface solide est ainsi calculée, caractérisant de ce fait le chargement imposé par l'écoulement sur le matériau. Cette méthode est par la suite appliquée sur différentes géométries en comparant à chaque fois les résultats obtenus à des expériences. Nous comparons également nos résultats à des méthodes précédemment établies au sein du laboratoire afin d'évaluer la pertinence de cette approche. / During the life's cycle of a hydraulic installation, the occurrence of cavitation can cause significant damages on the material's surface. The quantification of the cavitation intensity in different geometry can be useful to get better designs for new installations, but also to improve the operating and to optimize maintenance of existing equipments. The development of universal laws of similarity from experiments is difficult due to the large number of parameters governing cavitating flows. With the increase of computational performance, numerical simulations offer the opportunity to study this phenomenon in various geometries. The main difficulty of this approach is the scale's difference existing between the numerical simulations U-RANS used to calculate the cavitating flow and mechanisms of bubble's collapse held responsible for damages on the solid. The proposed method in this thesis is based on a textbf{post-treatment} of the textbf{U-RANS} simulations to characterize a distribution of bubbles and to simulate their behavior at lower spatial and temporal scales. Our first objective is to make explicit a system of equations corresponding to phenomena occurring locally in the two-phase flow. This work leads to the development of mixture variables taking into account the presence of non-condensable gases in the fluid. Assumptions are taken to make the system, after using the Reynolds averaging procedure, equivalent to those, using a homogeneous approach, implemented in the unsteady cavitating flows solvers previously developed in the laboratory. The characterization of bubbles made by this post-treatment takes into account both the surface tension and the presence of non-condensable gases. The development of a solver for the simulation of the dynamic of a bubble cloud is started. It aims to take into account both the interactions between bubbles and non-spherical deformations with a potential method. First results of these simulations are presented and small non-spherical deformations occurring during the collapse can be observed. Finally, we propose a chained method between these two systems initializing the bubble dynamic solver with results of U-RANS simulations. The energy emitted during the implosion of bubbles impacting the solid surface is calculated. So the aggressiveness of the flow on the material can be characterized. We apply this method on different flows to compare numerical and experimental results.

Numerical simulations are a useful tool to understand galaxies. In addition to gravitation, other processes can be included for chemodynamical simulations: star formation, feedback of newly formed and evolving stars, metal enrichment, cooling of the interstellar medium, etc. These simulations describe in a self-consistent way the hydrodynamical and chemical evolution of galaxies. I use chemodynamical simulations to build up a model of evolution of the dust mass, solid component of the interstellar medium, in our Galaxy and in dwarf galaxies. I have performed simulations of a massive galaxy to understand localeffects on dust evolution while simulations of dwarf galaxies have been carried out to follow the dust mass in low metallicity environments. Chemodynamical simulations have shown that they are useful. Indeed, local effects and transport mechanisms are naturally included and turn out to be important for a model of dust mass production and destruction.

Natural Attenuation can be an effective cleanup option for remediation of Groundwater contamination by BTEX. One of the important aspects of the methodology that has been recognized recently is that mass removal rates, the most important parameters used to determine effectiveness of the methodology, is controlled by groundwater flow regime, which to a large extent controlled by aquifer heterogeneity. Considering this recognition, the primary objective of this research is to quantitatively describe the relationship between natural attenuation rates of BTEX and aquifer heterogeneity using numerical solution techniques. To represent different levels of aquifer heterogeneity, hydraulic conductivity distributions are simulated using Turning Bands Algorithm, changing statistical parameters Coefficient of Variation (CV) and correlation length (h). Visual MODFLOW is used to model the transport of BTEX contamination, at different hydraulic conductivity fields. Degradation rates are calculated by Buscheck&amp / Alcantar and Conservative Tracer Methods. The results show that, for a given h, as CV increases, the plume slows down and stays longer at the domain, so areal extent of plume decreases. For anisotropic field, plumes are more dispersed along x and y-direction, and areal extents of the plumes are greater. During MNA feasibility studies, for the aquifer heterogeneity level of CV and h smaller than 100 % and 10 m, respectively, a minimum recommended biodegradation rate constant of 0.02 d-1 can be used, whereas for the aquifer heterogeneity level of CV and h greater than 100 % and 10 m, respectively, using a minimum biodegradation rate constant of 0.06 d-1 can be recommended.

Monitored natural attenuation has been particularly used at sites where petroleum hydrocarbons and chlorinated solvents have contaminated soil and groundwater. One of the important aspects of the methodology that has been recognized recently is that the mass removal rates, the most important parameter to determine effectiveness of the methodology, is controlled by the groundwater flow regime and the aquifer heterogeneity. Considering this recognition, the primary objective of this study is to quantitatively describe the relationship between the natural attenuation rates and aquifer heterogeneity using numerical simulation techniques. To represent different levels of aquifer heterogeneity, the hydraulic conductivity distribution (ln K) is statistically simulated with the numerical algorithm, Turning Bands Random Field Generator, by changing the statistical parameters, Coefficient of Variation (CV) and correlation length (h) and Visual MODFLOW and RT3D software programs are used for the simulation of groundwater flow and chlorinated solvent transport. Simulation results showed that degradation rates and the shape of the contaminant plumes show variations for different heterogeneity levels. Increasing CV resulted in the decrease in the transport of the plume and shrinkage in the areal extend. On the other hand, &ldquo / h&rdquo / determined the shape and the size of the plume through its affect on mechanical dispersion. For a given &ldquo / h&rdquo / , degradation rates increased with increasing CV, but change in &ldquo / h&rdquo / did not show a regular trend. Such findings are expected to be beneficial when assessing the effectiveness of natural attenuation process for a selected site during the feasibility studies without need for detailed site characterization.

This thesis develops diffusion models for modern electrochemical experiments involving the transport of particles to electrodes and adsorbing surfaces. In particular, the models are related to the 'impact' method where particles stochastically arrive at an electrode and detected electrochemically. The studies are carried out using numerical simulations and also analytical methods. Chapter 1 is introductory and outlines some fundamental concepts in mass transport and kinetics, and their relation to electrochemical measurements which are of importance for the reader. Chapter 2 describes the numerical methods which are used for electrochemical simulations. Chapter 3 focuses on a specific two dimensional simulation system and the development of a high performance voltammetry simulation. Chapters 4 and 5 study the stochastic impacts of particles at an electrode surface. In Chapter 4, a 'diffusion only' model is developed using a probabilistic study and random walk simulations in order to provide expressions that can be used in so-called `impact' experiments. In Chapter 5, the practical cases of microdisc and microwire electrodes are investigated. Expressions for the number of impacts are developed and the concept of the lower limit of detection in ultra-dilute solutions is introduced. Then, a comparison study between the microwire electrode and the microdisc electrode explores a geometrical effect and its implications for experimental setups. In Chapter 6, a numerical and analytical study is developed to examine the effect of hindered diffusion as a particle moves close to an adsorbing surface. The study identifies the conditions under which this hindered diffusion is signiffcant even in a non-confined space. The study shows that the domination of hindered diffusion is strongly dependant on the sizes of both the particle and the target. The study focuses on a variety of target shapes and allows the number of hits/impacts to be estimated in practical 'impact' experiments. Moreover, a drastic effect on the calculation of the mean first passage time is observed for a sub-micron sized target, showing the importance of this effect not only for electrochemistry but also in biological systems. Chapters 7 and 8 investigate the properties of an adsorbing insulating surface adjacent to an electrode. In Chapter 7, a numerical study of the effect of 'shielding' by the insulating sheath is carried out. The study examines the in uence of this effect on the magnitude of the current in chronoamperometry experiments. Chapter 8 explores the case of reversible adsorption on the insulating surface for voltammetric enhancement by pre-concentration on the sheath surface. The results identify the conditions under which enhancement of the voltammetric signal can be observed. Finally, Chapter 9 looks at geometrical effects on the current response of insulating particles modified with an electroactive surface layer. Numerical models are developed to model the diffusion of charge transfer between electro-active sites on a modified surface of insulating particles. The current-time responses are simulated for particles with the shape of a sphere, a cube/cuboid, and a cylinder on an electrode. The characteristic currenttime responses are calculated for the various shapes. The observations show that the model can be utilised in experiments to determine the coverage or the diffusion coeficient of charge dissipation on modified insulating particles and, in some situations to identify the particle shape.