Intrinsic kinetics of titania photocatalysis : simplified models for their investigation

Even though titanium dioxide photocatalysis has been promoted as a leading green technology for water purification, many issues have hindered its application on a large commercial scale. For the materials scientist the main issues have centred the synthesis of more efficient materials and the investigation of degradation mechanisms; whereas for the engineers the main issues have been the development of appropriate models and the evaluation of intrinsic kinetics parameters that allow the scale up or re-design of efficient large-scale photocatalytic reactors. In order to obtain intrinsic kinetics parameters the reaction must be analysed and modelled considering the influence of the radiation field, pollutant concentrations and fluid dynamics. In this way, the obtained kinetic parameters are independent of the reactor size and configuration and can be subsequently used for scale-up purposes or for the development of entirely new reactor designs. This work investigates the intrinsic kinetics of phenol degradation over titania film due to the practicality of a fixed film configuration over a slurry. A flat plate reactor was designed in order to be able to control reaction parameters that include the UV irradiance, flow rates, pollutant concentration and temperature. Particular attention was paid to the investigation of the radiation field over the reactive surface and to the issue of mass transfer limited reactions. The ability of different emission models to describe the radiation field was investigated and compared to actinometric measurements. The RAD-LSI model was found to give the best predictions over the conditions tested. Mass transfer issues often limit fixed film reactors. The influence of this phenomenon was investigated with specifically planned sets of benzoic acid experiments and with the adoption of the stagnant film model. The phenol mass transfer coefficient in the system was calculated to be km,phenol=8.5815x10-7Re0.65(ms-1). The data obtained from a wide range of experimental conditions, together with an appropriate model of the system, has enabled determination of intrinsic kinetic parameters. The experiments were performed in four different irradiation levels (70.7, 57.9, 37.1 and 20.4 W m-2) and combined with three different initial phenol concentrations (20, 40 and 80 ppm) to give a wide range of final pollutant conversions (from 22% to 85%). The simple model adopted was able to fit the wide range of conditions with only four kinetic parameters; two reaction rate constants (one for phenol and one for the family of intermediates) and their corresponding adsorption constants. The intrinsic kinetic parameters values were defined as kph = 0.5226 mmol m-1 s-1 W-1, kI = 0.120 mmol m-1 s-1 W-1, Kph = 8.5 x 10-4 m3 mmol-1 and KI = 2.2 x 10-3 m3 mmol-1. The flat plate reactor allowed the investigation of the reaction under two different light configurations; liquid and substrate side illumination. The latter of particular interest for real world applications where light absorption due to turbidity and pollutants contained in the water stream to be treated could represent a significant issue. The two light configurations allowed the investigation of the effects of film thickness and the determination of the catalyst optimal thickness. The experimental investigation confirmed the predictions of a porous medium model developed to investigate the influence of diffusion, advection and photocatalytic phenomena inside the porous titania film, with the optimal thickness value individuated at 5 ìm. The model used the intrinsic kinetic parameters obtained from the flat plate reactor to predict the influence of thickness and transport phenomena on the final observed phenol conversion without using any correction factor; the excellent match between predictions and experimental results provided further proof of the quality of the parameters obtained with the proposed method.

Visualisation of complex flows using texture-based techniques

Complex flow datasets are often difficult to represent in detail using traditional vector visualisation techniques such as arrow plots and streamlines. This is particularly true when the flow regime changes in time. Texture-based techniques, which are based on the advection of dense textures, are novel techniques for visualising such flows (i.e., complex dynamics and time-dependent). In this paper, we review two popular texture-based techniques and their application to flow datasets sourced from real research projects. The texture-based techniques investigated were Line Integral Convolution (LIC), and Image-Based Flow Visualisation (IBFV). We evaluated these techniques and in this paper report on their visualisation effectiveness (when compared with traditional techniques), their ease of implementation, and their computational overhead.

Visualisation of complex flows using texture-based techniques

Detailed representations of complex flow datasets are often difficult to generate using traditional vector visualisation techniques such as arrow plots and streamlines. This is particularly true when the flow regime changes in time. Texture-based techniques, which are based on the advection of dense textures, are novel techniques for visualising such flows. We review two popular texture based techniques and their application to flow datasets sourced from active research projects. The techniques investigated were Line integral convolution (LIC) [1], and Image based flow visualisation (IBFV) [18]. We evaluated these and report on their effectiveness from a visualisation perspective. We also report on their ease of implementation and computational overheads.

Simulation of phosphine flow in vertical grain storage : a preliminary numerical study

To fumigate grain stored in a silo, phosphine gas is distributed by a combination of diffusion and fan-forced advection. This initial study of the problem mainly focuses on the advection, numerically modelled as fluid flow in a porous medium. We find satisfactory agreement between the flow predictions of two Computational Fluid Dynamics packages, Comsol and Fluent. The flow predictions demonstrate that the highest velocity (>0.1 m/s) occurs less than 0.2m from the inlet and reduces drastically over one metre of silo height, with the flow elsewhere less than 0.002 m/s or 1% of the velocity injection. The flow predictions are examined to identify silo regions where phosphine dosage levels are likely to be too low for effective grain fumigation.

Feasibility of agent-based modelling of articular cartilage including a conceptual representation of its structure

Articular cartilage is a complex structure with an architecture in which fluid-swollen proteoglycans constrained within a 3D network of collagen fibrils. Because of the complexity of the cartilage structure, the relationship between its mechanical behaviours at the macroscale level and its components at the micro-scale level are not completely understood. The research objective in this thesis is to create a new model of articular cartilage that can be used to simulate and obtain insight into the micro-macro-interaction and mechanisms underlying its mechanical responses during physiological function. The new model of articular cartilage has two characteristics, namely: i) not use fibre-reinforced composite material idealization ii) Provide a framework for that it does probing the micro mechanism of the fluid-solid interaction underlying the deformation of articular cartilage using simple rules of repartition instead of constitutive / physical laws and intuitive curve-fitting. Even though there are various microstructural and mechanical behaviours that can be studied, the scope of this thesis is limited to osmotic pressure formation and distribution and their influence on cartilage fluid diffusion and percolation, which in turn governs the deformation of the compression-loaded tissue. The study can be divided into two stages. In the first stage, the distributions and concentrations of proteoglycans, collagen and water were investigated using histological protocols. Based on this, the structure of cartilage was conceptualised as microscopic osmotic units that consist of these constituents that were distributed according to histological results. These units were repeated three-dimensionally to form the structural model of articular cartilage. In the second stage, cellular automata were incorporated into the resulting matrix (lattice) to simulate the osmotic pressure of the fluid and the movement of water within and out of the matrix; following the osmotic pressure gradient in accordance with the chosen rule of repartition of the pressure. The outcome of this study is the new model of articular cartilage that can be used to simulate and study the micromechanical behaviours of cartilage under different conditions of health and loading. These behaviours are illuminated at the microscale level using the socalled neighbourhood rules developed in the thesis in accordance with the typical requirements of cellular automata modelling. Using these rules and relevant Boundary Conditions to simulate pressure distribution and related fluid motion produced significant results that provided the following insight into the relationships between osmotic pressure gradient and associated fluid micromovement, and the deformation of the matrix. For example, it could be concluded that: 1. It is possible to model articular cartilage with the agent-based model of cellular automata and the Margolus neighbourhood rule. 2. The concept of 3D inter connected osmotic units is a viable structural model for the extracellular matrix of articular cartilage. 3. Different rules of osmotic pressure advection lead to different patterns of deformation in the cartilage matrix, enabling an insight into how this micromechanism influences macromechanical deformation. 4. When features such as transition coefficient were changed, permeability (representing change) is altered due to the change in concentrations of collagen, proteoglycans (i.e. degenerative conditions), the deformation process is impacted. 5. The boundary conditions also influence the relationship between osmotic pressure gradient and fluid movement at the micro-scale level. The outcomes are important to cartilage research since we can use these to study the microscale damage in the cartilage matrix. From this, we are able to monitor related diseases and their progression leading to potential insight into drug-cartilage interaction for treatment. This innovative model is an incremental progress on attempts at creating further computational modelling approaches to cartilage research and other fluid-saturated tissues and material systems.

Numerical techniques for simulating a fractional mathematical model of epidermal wound healing

A number of mathematical models investigating certain aspects of the complicated process of wound healing are reported in the literature in recent years. However, effective numerical methods and supporting error analysis for the fractional equations which describe the process of wound healing are still limited. In this paper, we consider the numerical simulation of a fractional mathematical model of epidermal wound healing (FMM-EWH), which is based on the coupled advection-diffusion equations for cell and chemical concentration in a polar coordinate system. The space fractional derivatives are defined in the Left and Right Riemann-Liouville sense. Fractional orders in the advection and diffusion terms belong to the intervals (0, 1) or (1, 2], respectively. Some numerical techniques will be used. Firstly, the coupled advection-diffusion equations are decoupled to a single space fractional advection-diffusion equation in a polar coordinate system. Secondly, we propose a new implicit difference method for simulating this equation by using the equivalent of Riemann-Liouville and Grünwald-Letnikov fractional derivative definitions. Thirdly, its stability and convergence are discussed, respectively. Finally, some numerical results are given to demonstrate the theoretical analysis.

Existence of travelling wave solutions for a model of tumour invasion

The existence of travelling wave solutions to a haptotaxis dominated model is analysed. A version of this model has been derived in Perumpanani et al. (1999) to describe tumour invasion, where diffusion is neglected as it is assumed to play only a small role in the cell migration. By instead allowing diffusion to be small, we reformulate the model as a singular perturbation problem, which can then be analysed using geometric singular perturbation theory. We prove the existence of three types of physically realistic travelling wave solutions in the case of small diffusion. These solutions reduce to the no diffusion solutions in the singular limit as diffusion as is taken to zero. A fourth travelling wave solution is also shown to exist, but that is physically unrealistic as it has a component with negative cell population. The numerical stability, in particular the wavespeed of the travelling wave solutions is also discussed.

Collective motion of dimers

We consider a discrete agent-based model on a one-dimensional lattice and a two-dimensional square lattice, where each agent is a dimer occupying two sites. Agents move by vacating one occupied site in favor of a nearest-neighbor site and obey either a strict simple exclusion rule or a weaker constraint that permits partial overlaps between dimers. Using indicator variables and careful probability arguments, a discrete-time master equation for these processes is derived systematically within a mean-field approximation. In the continuum limit, nonlinear diffusion equations that describe the average agent occupancy of the dimer population are obtained. In addition, we show that multiple species of interacting subpopulations give rise to advection-diffusion equations. Averaged discrete simulation data compares very well with the solution to the continuum partial differential equation models. Since many cell types are elongated rather than circular, this work offers insight into population-level behavior of collective cellular motion.

Building macroscale models from microscale probabilistic models : a general probabilistic approach for nonlinear diffusion and multispecies phenomena

A discrete agent-based model on a periodic lattice of arbitrary dimension is considered. Agents move to nearest-neighbor sites by a motility mechanism accounting for general interactions, which may include volume exclusion. The partial differential equation describing the average occupancy of the agent population is derived systematically. A diffusion equation arises for all types of interactions and is nonlinear except for the simplest interactions. In addition, multiple species of interacting subpopulations give rise to an advection-diffusion equation for each subpopulation. This work extends and generalizes previous specific results, providing a construction method for determining the transport coefficients in terms of a single conditional transition probability, which depends on the occupancy of sites in an influence region. These coefficients characterize the diffusion of agents in a crowded environment in biological and physical processes.

Natural convection heat transfer in a baffled triangular enclosure

To reduce the natural convection heat loss from enclosures many researchers used convection suppression devices in the past. In this study a single baffle is used under the top tip to investigate numerically the natural convection heat loss in an attic shaped enclosure which is a cost effective approach. The case considered here is one inclined wall of the enclosure is uniformly heated while the other inclined wall is uniformly cooled with adiabatic bottom wall. The finite volume method has been used to discretize the governing equations, with the QUICK scheme approximating the advection term. The diffusion terms are discretized using central-differencing with second order accuracy. A wide range of governing parameters are studied (Rayleigh number, aspect ratio, baffle length etc.). It is observed that the heat transfer due to natural convection in the enclosure reduces when the baffle length is increased. Effects of other parameters on heat transfer and flow field are described in this study.

Turbulence measurements in a shallow tidal estuary : analysis based on triple decomposition

In an estuary, mixing and dispersion are the result of the combination of large scale advection and small scale turbulence which are both complex to estimate. A field study was conducted in a small sub-tropical estuary in which high frequency (50 Hz) turbulent data were recorded continuously for about 48 hours. A triple decomposition technique was introduced to isolate the contributions of tides, resonance and turbulence in the flow field. A striking feature of the data set was the slow fluctuations which exhibited large amplitudes up to 50% the tidal amplitude under neap tide conditions. The triple decomposition technique allowed a characterisation of broader temporal scales of high frequency fluctuation data sampled during a number of full tidal cycles.

Hydrostratigraphic analysis of the MADE site with full-resolution GPR and direct-push hydraulic profiling

Full-resolution 3D Ground-Penetrating Radar (GPR) data were combined with high-resolution hydraulic conductivity (K) data from vertical Direct-Push (DP) profiles to characterize a portion of the highly heterogeneous MAcro Dispersion Experiment (MADE) site. This is an important first step to better understand the influence of aquifer heterogeneities on observed anomalous transport. Statistical evaluation of DP data indicates non-normal distributions that have much higher similarity within each GPR facies than between facies. The analysis of GPR and DP data provides high-resolution estimates of the 3D geometry of hydrostratigraphic zones, which can then be populated with stochastic K fields. The lack of such estimates has been a significant limitation for testing and parameterizing a range of novel transport theories at sites where the traditional advection-dispersion model has proven inadequate.

High-resolution GNSS-tracked drifter for studying surface dispersion in shallow water

The use of GNSS tracked Lagrangian drifters allows more realistic quantification of fluid motion and dispersion coefficients than Eulerian techniques because such drifters are analogues of particles that are relevant to flow field characterisation and pollutant dispersion. Using the fast growing Real Time Kinematic (RTK) positioning technique derived from Global Satellite Navigation Systems (GNSS), drifters are developed for high frequency (10 Hz) sampling with position estimates to centimetre accuracy. The drifters are designed with small size and less direct wind drag to follow the sub-surface flow which characterizes dispersion in shallow waters. An analysis of position error from stationary observation indicates that the drifter can efficiently resolve motion up to 1 Hz. The result of the field deployments of the drifter in conjunction with acoustic Eulerian devices shows higher estimate of the drifter streamwise velocities. Single particle statistical analysis of field deployments in a shallow estuarine zone yielded dispersion coefficients estimate comparable to those of dye tracer studies. The drifters capture the tidal elevation during field studies in a tidal estuary.

Finite volume methods for simulating anomalous transport

In this thesis a new approach for solving a certain class of anomalous diffusion equations was developed. The theory and algorithms arising from this work will pave the way for more efficient and more accurate solutions of these equations, with applications to science, health and industry. The method of finite volumes was applied to discretise the spatial derivatives, and this was shown to outperform existing methods in several key respects. The stability and convergence of the new method were rigorously established.

Turbulence and Mixing in the Environment: Multi-Device Study in a Sub-tropical Estuary

In an estuary, mixing and dispersion result from a combination of large-scale advection and smallscale turbulence, which are complex to estimate. The predictions of scalar transport and mixing are often inferred and rarely accurate, due to inadequate understanding of the contributions of these difference scales to estuarine recirculation. A multi-device field study was conducted in a small sub-tropical estuary under neap tide conditions with near-zero fresh water discharge for about 48 hours. During the study, acoustic Doppler velocimeters (ADV) were sampled at high frequency (50 Hz), while an acoustic Doppler current profiler (ADCP) and global positioning system (GPS) tracked drifters were used to obtain some lower frequency spatial distribution of the flow parameters within the estuary. The velocity measurements were complemented with some continuous measurement of water depth, conductivity, temperature and some other physiochemical parameters. Thorough quality control was carried out by implementation of relevant error removal filters on the individual data set to intercept spurious data. A triple decomposition (TD) technique was introduced to access the contributions of tides, resonance and ‘true’ turbulence in the flow field. The time series of mean flow measurements for both the ADCP and drifter were consistent with those of the mean ADV data when sampled within a similar spatial domain. The tidal scale fluctuation of velocity and water level were used to examine the response of the estuary to tidal inertial current. The channel exhibited a mixed type wave with a typical phase-lag between 0.035π– 0.116π. A striking feature of the ADV velocity data was the slow fluctuations, which exhibited large amplitudes of up to 50% of the tidal amplitude, particularly in slack waters. Such slow fluctuations were simultaneously observed in a number of physiochemical properties of the channel. The ensuing turbulence field showed some degree of anisotropy. For all ADV units, the horizontal turbulence ratio ranged between 0.4 and 0.9, and decreased towards the bed, while the vertical turbulence ratio was on average unity at z = 0.32 m and approximately 0.5 for the upper ADV (z = 0.55 m). The result of the statistical analysis suggested that the ebb phase turbulence field was dominated by eddies that evolved from ejection type process, while that of the flood phase contained mixed eddies with significant amount related to sweep type process. Over 65% of the skewness values fell within the range expected of a finite Gaussian distribution and the bulk of the excess kurtosis values (over 70%) fell within the range of -0.5 and +2. The TD technique described herein allowed the characterisation of a broader temporal scale of fluctuations of the high frequency data sampled within the durations of a few tidal cycles. The study provides characterisation of the ranges of fluctuation required for an accurate modelling of shallow water dispersion and mixing in a sub-tropical estuary.