Mathematical modelling of LiFePO4 cathodes

LiFePO4 is a commercially available battery material with good theoretical discharge capacity, excellent cycle life and increased safety compared with competing Li-ion chemistries. It has been the focus of considerable experimental and theoretical scrutiny in the past decade, resulting in LiFePO4 cathodes that perform well at high discharge rates. This scrutiny has raised several questions about the behaviour of LiFePO4 material during charge and discharge. In contrast to many other battery chemistries that intercalate homogeneously, LiFePO4 can phase-separate into highly and lowly lithiated phases, with intercalation proceeding by advancing an interface between these two phases. The main objective of this thesis is to construct mathematical models of LiFePO4 cathodes that can be validated against experimental discharge curves. This is in an attempt to understand some of the multi-scale dynamics of LiFePO4 cathodes that can be difficult to determine experimentally. The first section of this thesis constructs a three-scale mathematical model of LiFePO4 cathodes that uses a simple Stefan problem (which has been used previously in the literature) to describe the assumed phase-change. LiFePO4 crystals have been observed agglomerating in cathodes to form a porous collection of crystals and this morphology motivates the use of three size-scales in the model. The multi-scale model developed validates well against experimental data and this validated model is then used to examine the role of manufacturing parameters (including the agglomerate radius) on battery performance. The remainder of the thesis is concerned with investigating phase-field models as a replacement for the aforementioned Stefan problem. Phase-field models have recently been used in LiFePO4 and are a far more accurate representation of experimentally observed crystal-scale behaviour. They are based around the Cahn-Hilliard-reaction (CHR) IBVP, a fourth-order PDE with electrochemical (flux) boundary conditions that is very stiff and possesses multiple time and space scales. Numerical solutions to the CHR IBVP can be difficult to compute and hence a least-squares based Finite Volume Method (FVM) is developed for discretising both the full CHR IBVP and the more traditional Cahn-Hilliard IBVP. Phase-field models are subject to two main physicality constraints and the numerical scheme presented performs well under these constraints. This least-squares based FVM is then used to simulate the discharge of individual crystals of LiFePO4 in two dimensions. This discharge is subject to isotropic Li+ diffusion, based on experimental evidence that suggests the normally orthotropic transport of Li+ in LiFePO4 may become more isotropic in the presence of lattice defects. Numerical investigation shows that two-dimensional Li+ transport results in crystals that phase-separate, even at very high discharge rates. This is very different from results shown in the literature, where phase-separation in LiFePO4 crystals is suppressed during discharge with orthotropic Li+ transport. Finally, the three-scale cathodic model used at the beginning of the thesis is modified to simulate modern, high-rate LiFePO4 cathodes. High-rate cathodes typically do not contain (large) agglomerates and therefore a two-scale model is developed. The Stefan problem used previously is also replaced with the phase-field models examined in earlier chapters. The results from this model are then compared with experimental data and fit poorly, though a significant parameter regime could not be investigated numerically. Many-particle effects however, are evident in the simulated discharges, which match the conclusions of recent literature. These effects result in crystals that are subject to local currents very different from the discharge rate applied to the cathode, which impacts the phase-separating behaviour of the crystals and raises questions about the validity of using cathodic-scale experimental measurements in order to determine crystal-scale behaviour.

The effect of juice composition on the scaling rate and scale composition in sugar mill evaporators

To date, the formation of deposits on heat exchanger surfaces is the least understood problem in the design of heat exchangers for processing industries. Dr East has related the structure of the deposits to solution composition and has developed predictive models for composite fouling of calcium oxalate and silica in sugar factory evaporators.

Half metallicity in finite-length zigzag single walled carbon nanotube : A first-principle prediction

We predict here from first-principle calculations that finite-length (n,0) single walled carbon nanotubes (SWCNTs) with H-termination at the open ends displaying antiferromagnetic coupling when n is greater than 6. An opposite local gating effect of the spin states, i.e., half metallicity, is found under the influence of an external electric field along the direction of tube axis. Remarkably, boron doping of unpassivated SWCNTs at both zigzag edges is found to favor a ferromagnetic ground state, with the B-doped tubes displaying half-metallic behavior even in the absence of an electric field. Aside of the intrinsic interest of these results, an important avenue for development of CNT-based spintronic is suggested.

Experimental impact and finite element analysis of a composite, portable road safety barrier

This thesis provides an experimental and computational platform for investigating the performance and behaviour of water filled, plastic portable road safety barriers in an isolated impact scenario. A schedule of experimental impact tests were conducted assessing the impact response of an existing design of road safety barrier utilising a novel horizontal impact testing system. A coupled finite element and smooth particle hydrodynamic model of the barrier system was developed and validated against the results of the experimental tests. The validated model was subsequently used to assess the effect of certain composite materials on the impact performance of the water filled, portable road safety barrier system.

Tensile properties of pumpkin peel and flesh tissue and review of current testing methods

In South and Southeast Asia, postharvest loss causes material waste of up to 66% in fruits and vegetables, 30% in oilseeds and pulses, and 49% in roots and tubers. The efficiency of postharvest equipment directly affects industrial-scale food production. To enhance current processing methods and devices, it is essential to analyze the responses of food materials under loading operations. Food materials undergo different types of mechanical loading during postharvest and processing stages. Therefore, it is important to determine the properties of these materials under different types of loads, such as tensile, compression, and indentation. This study presents a comprehensive analysis of the available literature on the tensile properties of different food samples. The aim of this review was to categorize the available methods of tensile testing for agricultural crops and food materials to investigate an appropriate sample size and tensile test method. The results were then applied to perform tensile tests on pumpkin flesh and peel samples, in particular on arc-sided samples at a constant loading rate of 20 mm min-1. The results showed the maximum tensile stress of pumpkin flesh and peel samples to be 0.535 and 1.45 MPa, respectively. The elastic modulus of the flesh and peel samples was 6.82 and 25.2 MPa, respectively, while the failure modulus values were 14.51 and 30.88 MPa, respectively. The results of the tensile tests were also used to develop a finite element model of mechanical peeling of tough-skinned vegetables. However, to study the effects of deformation rate, moisture content, and texture of the tissue on the tensile responses of food materials, more investigation needs to be done in the future.

Elastic buckling analysis of ideal thin-walled structures under combined loading using a finite strip method

The details of an application of the finite strip method to the elastic buckling analysis of thin-walled structures with various boundary conditions and subjected to single or combined loadings of longitudinal compression, transverse compression, bending and shear are presented. The presence of shear loading is accounted for by modifying the displacement functions which are commonly used in cases when shear is absent. A program based on the finite strip method was used to obtain the elastic buckling stress, buckling plot and buckling mode of thin-walled structures and some of these results are presented.

Size characterization of airborne SiO2 nanoparticles with on-line and off-line measurement techniques : an interlaboratory comparison study

Results of an interlaboratory comparison on size characterization of SiO2 airborne nanoparticles using on-line and off-line measurement techniques are discussed. This study was performed in the framework of Technical Working Area (TWA) 34—“Properties of Nanoparticle Populations” of the Versailles Project on Advanced Materials and Standards (VAMAS) in the project no. 3 “Techniques for characterizing size distribution of airborne nanoparticles”. Two types of nano-aerosols, consisting of (1) one population of nanoparticles with a mean diameter between 30.3 and 39.0 nm and (2) two populations of non-agglomerated nanoparticles with mean diameters between, respectively, 36.2–46.6 nm and 80.2–89.8 nm, were generated for characterization measurements. Scanning mobility particle size spectrometers (SMPS) were used for on-line measurements of size distributions of the produced nano-aerosols. Transmission electron microscopy, scanning electron microscopy, and atomic force microscopy were used as off-line measurement techniques for nanoparticles characterization. Samples were deposited on appropriate supports such as grids, filters, and mica plates by electrostatic precipitation and a filtration technique using SMPS controlled generation upstream. The results of the main size distribution parameters (mean and mode diameters), obtained from several laboratories, were compared based on metrological approaches including metrological traceability, calibration, and evaluation of the measurement uncertainty. Internationally harmonized measurement procedures for airborne SiO2 nanoparticles characterization are proposed.

Validating SMPS-measured size distribution of double-mode spherical Silica nanoparticles by Transmission Electron Microscope (TEM)

A nanoparticles size is one of their key physical characteristics that can affect their fate in a human’s respiratory tract (in case of inhalation) and also in the environment. Hence, measuring the size distribution of nanoparticles is absolutely essential and contributes greatly to their characterization. For years, Scanning Mobility Particle Sizers (SMPS), which rely on measuring the electrical mobility diameter of particles, have been used as one of the most reliable real-time instruments for the size distribution measurement of nanoparticles. Despite its benefits, this instrument has some drawbacks, including equivalency problems for non-spherical particles (i.e. assuming a non-spherical particle is equal to a spherical particle of diameter d due to the same electrical mobility), as well as limitations in terms of its use in workplaces, because of its large size and the complexity of its operation...

Remote measurement of diesel locomotive emission factors and particle size distributions

A technique for analysing exhaust emission plumes from unmodified locomotives under real world conditions is described and applied to the task of characterizing plumes from railway trains servicing an Australian shipping port. The method utilizes the simultaneous measurement, downwind of the railway line, of the following pollutants; particle number, PM2.5 mass fraction, SO2, NOx and CO2, with the last of these being used as an indicator of fuel combustion. Emission factors are then derived, in terms of number of particles and mass of pollutant emitted per unit mass of fuel consumed. Particle number size distributions are also presented. The practical advantages of the method are discussed including the capacity to routinely collect emission factor data for passing trains and to thereby build up a comprehensive real world database for a wide range of pollutants. Samples from 56 train movements were collected, analyzed and presented. The quantitative results for emission factors are: EF(N)=(1.7±1)×1016 kg-1, EF(PM2.5)= (1.1±0.5) g·kg-1, EF(NOx)= (28±14) g·kg-1, and EF(SO2 )= (1.4±0.4) g·kg-1. The findings are compared with comparable previously published work. Statistically significant (p<α, α=0.05) correlations within the group of locomotives sampled were found between the emission factors for particle number and both SO2 and NOx.

An introduction to the application of (case 1) best–worst scaling in marketing research

We review and discuss recent developments in best–worst scaling (BWS) that allow researchers to measure items or objects on measurement scales with known properties. We note that BWS has some distinct advantages compared with other measurement approaches, such as category rating scales or paired comparisons. We demonstrate how to use BWS to measure subjective quantities in two different empirical examples. One of these measures preferences for weekend getaways and requires comparing relatively few objects; a second measures academics' perceptions of the quality of academic marketing journals and requires comparing a significantly large set of objects. We conclude by discussing some limitations and future research opportunities related to BWS.

The effect of poser race on the happy categorization advantage depends on stimulus type, set size, and presentation duration

The question as to whether poser race affects the happy categorization advantage, the faster categorization of happy than of negative emotional expressions, has been answered inconsistently. Hugenberg (2005) found the happy categorization advantage only for own race faces whereas faster categorization of angry expressions was evident for other race faces. Kubota and Ito (2007) found a happy categorization advantage for both own race and other race faces. These results have vastly different implications for understanding the influence of race cues on the processing of emotional expressions. The current study replicates the results of both prior studies and indicates that face type (computer-generated vs. photographic), presentation duration, and especially stimulus set size influence the happy categorization advantage as well as the moderating effect of poser race.

Role of particle size and composition in metal adsorption by solids deposited on urban road surfaces

Despite common knowledge that the metal content adsorbed by fine particles is relatively higher compared to coarser particles, the reasons for this phenomenon has gained little research attention. The research study discussed in the paper investigated the variations in metal content for different particle sizes of solids associated with pollutant build-up on urban road surfaces. Data analysis confirmed that parameters favourable for metal adsorption to solids such as specific surface area, organic carbon content, effective cation exchange capacity and clay forming minerals content decrease with the increase in particle size. Furthermore, the mineralogical composition of solids was found to be the governing factor influencing the specific surface area and effective cation exchange capacity. There is high quartz content in particles >150µm compared to particles <150µm. As particle size reduces below 150µm, the clay forming minerals content increases, providing favourable physical and chemical properties that influence adsorption.

Increasing electrospun scaffold pore size with tailored collectors for improved cell penetration

This study investigates the use of patterned collectors to increase the pore size of electrospun scaffolds for enhanced cell infiltration. The morphology of the patterned scaffolds was investigated by scanning electron microscopy, which showed that the collector pattern was accurately mimicked by the electrospun fibres. We observed an enlargement in the pore size and in the pore size distribution compared with conventional electrospinning. Mechanical testing revealed that the mechanical properties could be tailored, to some extent, according to the patterning and that the patterned scaffolds were softer than standard electrospun scaffolds. When NIH 3T3 fibroblasts were seeded onto patterned collectors improved cell infiltration was observed. Cells were able to penetrate up to 250 μm into the scaffolds, compared with 30 μm for the standard scaffolds. This increase in the depth of infiltration occurred as early as 24 h post-seeding and remained constant over 7 days.

Design optimisation of ironless motors based on magnet selection

This paper considers the design of a radial flux permanent magnet iron less core brushless DC motor for use in an electric wheel drive with an integrated epicyclic gear reduction. The motor has been designed for a continuous output torque of 30 Nm and peak rating of 60 Nm with a maximum operating speed of 7000 RPM. In the design of brushless DC motors with a toothed iron stator the peak air-gap magnetic flux density is typically chosen to be close to that of the remanence value of the magnets used. This paper demonstrates that for an ironless motor the optimal peak air-gap flux density is closer to the maximum energy product of the magnets used. The use of a radial flux topology allows for high frequency operation and can be shown to give high specific power output while maintaining a relatively low magnet mass. Two-dimensional finite element analysis is used to predict the air-gap flux density. The motor design is based around commonly available NdFeB bar magnet size