Troy W. Farrell

Predicting Active Material Utilization in LiFePO4 Electrodes Using a Multiscale Mathematical Model

A mathematical model is developed to simulate the discharge of a LiFePO 4 cathode. This model contains three size scales, which match with experimental observations present in the literature on the multiscale nature of LiFePO 4 material. A shrinking core is used on the smallest scale to represent the phase transition of LiFePO 4 during discharge. The model is then validated against existing experimental data and this validated model is then used to investigate parameters that influence active material utilization. Specifically, the size and composition of agglomerates of LiFePO 4 crystals is discussed, and we investigate and quantify the relative effects that the ionic and electronic conductivities within the oxide have on oxide utilization. We find that agglomerates of crystals can be tolerated under low discharge rates. The role of the electrolyte in limiting (cathodic) discharge is also discussed, and we show that electrolyte transport does limit performance at high discharge rates, confirming the conclusions of recent literature.

Micropolar flow over a porous stretching sheet with strong suction or injection

We consider self-similar boundary layer flow of a micropolar fluid driven by a porous stretching sheet. For the limiting cases of large suction or injection, an order of magnitude analysis is used to obtain analytic results for the shear stress and the microrotation at the surface. Our analysis reveals how the wall shear stress is significantly affected by two of the parameters in the micropolar model and we indicate how our findings may be of use in technological applications involving micropolar flow.

Mathematical model for intermittent microwave convective drying of food materials

ABSTRACT Intermittent microwave convective drying (IMCD) is an advanced technology that improves both energy efficiency and food quality in drying. Modeling of IMCD is essential to understand the physics of this advanced drying process and to optimize the microwave power level and intermittency during drying. However, there is still a lack of modeling studies dedicated to IMCD. In this study, a mathematical model for IMCD was developed and validated with experimental data. The model showed that the interior temperature of the material was higher than the surface in IMCD, and that the temperatures fluctuated and redistributed due to the intermittency of the microwave power. This redistribution of temperature could significantly contribute to the improvement of product quality during IMCD. Limitations when using Lambert’s law for microwave heat generation were identified and discussed.

Primary Alkaline Battery Cathodes A Three‐Scale Model

A mathematical model for the galvanostatic discharge and recovery of porous, electrolytic manganese dioxide cathodes, similar to those found within primary alkaline batteries is presented. The phenomena associated with discharge are modeled over three distinct size scales, a cathodic (or macroscopic) scale, a porous manganese oxide particle (or microscopic) scale, and a manganese oxide crystal (or submicroscopic) scale. The physical and chemical coupling between these size scales is included in the model. In addition, the model explicitly accounts for the graphite phase within the cathode. The effects that manganese oxide particle size and proton diffusion have on cathodic discharge and the effects of intraparticle voids and microporous electrode structure are predicted using the model.

Comparing Charge Transport Predictions for a Ternary Electrolyte Using the Maxwell–Stefan and Nernst–Planck Equations

In this work, we investigate and compare the Maxwell–Stefan and Nernst–Planck equations for modeling multicomponent charge transport in liquid electrolytes. Specifically, we consider charge transport in the Li+/I−/I3−/ACN ternary electrolyte originally found in dye-sensitized solar cells. We employ molecular dynamics simulations to obtain the Maxwell–Stefan diffusivities for this electrolyte. These simulated diffusion coefficients are used in a multicomponent charge transport model based on the Maxwell– Stefan equations, and this is compared to a Nernst–Planck based model which employs binary diffusion coefficients sourced from the literature. We show that significant differences between the electrolyte concentrations at electrode interfaces, as predicted by the Maxwell–Stefan and Nernst–Planck models, can occur. We find that these differences are driven by a pressure term that appears in the Maxwell–Stefan equations. We also investigate what effects the Maxwell–Stefan diffusivities have on the simulated charge transport. By incorporating binary diffusivities found in the literature into the Maxwell–Stefan framework, we show that the simulated transient concentration profiles depend on the diffusivities; however, the simulated equilibrium profiles remain unaffected.

Primary Alkaline Battery Cathodes A Simplified Model for Porous Manganese Oxide Particle Discharge

A mathematical model for the galvanostatic discharge of a porous manganese oxide particle, similar to those found within primary alkaline battery cathodes, is presented. Asymptotic techniques are employed to obtain the leading order spatial and temporal behavior of the particle. It is found that there is an initial rapid transient adjustment within the crystals forming the particle followed by a prolonged relatively uniform discharge regime which leads finally to a faster, particle-based, nonuniform discharge behavior. Analytical solutions of the model are obtained which describe the majority of the particle behaviors under a wide range of industrially relevant discharge conditions. These solutions are supplemented by simple numerical solutions where required. A comparison of the results with those obtained by a previous, more complete and accurate model is presented. The analysis shows that the particle radius, the applied discharge current, and the solid phase conductivity are the critical parameters that dictate the utilization of active material across a wide range of discharge conditions. The effect of these parameters on particle utilization is also presented.

Primary Alkaline Battery Cathodes

A mathematical model for the galvanostatic discharge of a porous manganese oxide particle, similar to those found within primary alkaline battery cathodes, is presented. Asymptotic techniques are employed to obtain the leading order spatial and temporal behavior of the particle. It is found that there is an initial rapid transient adjustment within the crystals forming the particle followed by a prolonged relatively uniform discharge regime which leads finally to a faster, particle-based, nonuniform discharge behavior. Analytical solutions of the model are obtained which describe the majority of the particle behaviors under a wide range of industrially relevant discharge conditions. These solutions are supplemented by simple numerical solutions where required. A comparison of the results with those obtained by a previous, more complete and accurate model is presented. The analysis shows that the particle radius, the applied discharge current, and the solid phase conductivity are the critical parameters that dictate the utilization of active material across a wide range of discharge conditions. The effect of these parameters on particle utilization is also presented.

Investigation of intermittent microwave convective drying (IMCD) of food materials by a coupled 3D electromagnetics and multiphase model

ABSTRACT Intermittent microwave convective drying (IMCD) improves energy efficiency and the product quality during drying of agricultural products. However, the physical mechanism of heat and mass transfer involved in IMCD is poorly understood due to lack of a comprehensive and realistic mathematical model of this process. A multiphase porous media model considering coupled electromagnetics and multiphase transport phenomena in porous media can potentially provide fundamental details of underlying mechanisms of IMCD. The aim of this study is to develop a mathematical model for IMCD considering electromagnetics using Maxwell’s equations coupled with multiphase porous media in 3D and validate the model against experimental results. The results show that the temperature distribution is uneven in the material, which redistributes during the tempering period. The water and vapor fluxes showed asymmetric profile along the diameter of the sample due to the non-uniformity of microwave heating. A clear understanding of these transport mechanisms in IMCD will lead to the development of appropriate drying process for improved food quality, energy efficiency, and optimization of the IMCD process.

A novel population balance model for the dilute acid hydrolysis of hemicellulose

BackgroundAcid hydrolysis is a popular pretreatment for removing hemicellulose from lignocelluloses in order to produce a digestible substrate for enzymatic saccharification. In this work, a novel model for the dilute acid hydrolysis of hemicellulose within sugarcane bagasse is presented and calibrated against experimental oligomer profiles. The efficacy of mathematical models as hydrolysis yield predictors and as vehicles for investigating the mechanisms of acid hydrolysis is also examined.ResultsExperimental xylose, oligomer (degree of polymerisation 2 to 6) and furfural yield profiles were obtained for bagasse under dilute acid hydrolysis conditions at temperatures ranging from 110°C to 170°C. Population balance kinetics, diffusion and porosity evolution were incorporated into a mathematical model of the acid hydrolysis of sugarcane bagasse. This model was able to produce a good fit to experimental xylose yield data with only three unknown kinetic parameters ka,kb and kd. However, fitting this same model to an expanded data set of oligomeric and furfural yield profiles did not successfully reproduce the experimental results. It was found that a “hard-to-hydrolyse” parameter, α, was required in the model to ensure reproducibility of the experimental oligomer profiles at 110°C, 125°C and 140°C. The parameters obtained through the fitting exercises at lower temperatures were able to be used to predict the oligomer profiles at 155°C and 170°C with promising results.ConclusionsThe interpretation of kinetic parameters obtained by fitting a model to only a single set of data may be ambiguous. Although these parameters may correctly reproduce the data, they may not be indicative of the actual rate parameters, unless some care has been taken to ensure that the model describes the true mechanisms of acid hydrolysis. It is possible to challenge the robustness of the model by expanding the experimental data set and hence limiting the parameter space for the fitting parameters. The novel combination of “hard-to-hydrolyse” and population balance dynamics in the model presented here appears to stand up to such rigorous fitting constraints.

Modeling the Stepped Potential Discharge of Primary Alkaline Battery Cathodes

A novel model for the potentiostatic discharge of primary alkaline battery cathodes is presented. The model is used to simulate discharges resulting from the stepped potential electrochemical spectroscopy (SPECS) of primary alkaline battery cathodes cathodes, and the results are validated with experimental data. We show that a model based on a single (or mean) reaction framework can be used to simulate multi-reaction discharge behaviour and we develop a consistent functional modification to the kinetic equation of the model that allows for this to occur. The model is used to investigate the effects that the initial exchange current density, i00, and the diffusion coefficient for protons in electrolytic manganese dioxide (EMD), DH+, have on SPECS discharge. The behaviour observed is consistent with the idea that individual reduction reactions, within the multi-reaction, reduction behaviour of EMD, have distinct i00 and DH+ values.