The mathematical modelling of the production of bio-fuels from cellulosic materials. This project specifically considers the acid pretreatment and the enzymatic hydrolysis of bagasse (sugar cane fibre residue).
The mathematical modelling of electrochemical nano-dioides. These are nano-porous devices that rectify the passage of current in an electrolyte solution. This project considers electric double layer formation and interaction, charge transport in electrolyte solution using Poisson-Nernst-Planck and modified Poisson-Nernst-Planck models as well as discrete to continuum approaches for modelling low density flows.
The optimisation of metal-air batteries. This work involves a complementary experimental and mathematical modelling approach to provide decision support capabilities for the understanding and subsequent optimisation of lithium-air electrodes for secondary batteries.
The multiscale, mathematical modelling of periodic porous materials using a hybrid continuum/particle based approach. This projects considers the integration of microscopic scale particle based models (Smooth Particle Hydrodynamics, Lattice Boltzmann and Boundary Element) for high-dimensional Stokes flow with continuum flow (conservation of momentum and mass equations) at mesoscopic and macroscopic size scales.
Modelling the uptake of agrochemicals through the cuticular membranes of plant leaves. This project aims to develop novel mathematical models of chemical uptake in plants. It is envisaged that such models can then be utilised to better understand this process as well as develop more efficacious agrochemicals..
The Intermittent Microwave Convective (IMWC) Drying of food. This project is developing multiphase, multicomponent mathematical models of food materials that account for free and bound water transport and material deformation during drying.
Predicting the component gas concentrations of coal seam gas (CSG) reservoirs over time using a mathematical modelling approach. This project develops a population of models (PoMs) to predict the changing gas composition at a CSG compression facility. The individual reservoir models that feed into the PoMs are volume averaged unsaturated porous flow models that account for multicomponent liquid and gas transport within the matrix and cleat scales of individual coal seams.
Thermal Modelling of Large-Scale Biomass Stockpiles. This project addresses the important problem of preventing spontaneous combustion in large stockpiles of bagasse (sugar cane fibre residue). This will significantly extend its availability for renewable energy products.
Phase field modelling of Lithium Metal Phosphate Batteries. This project is looking at the development and numerical solution of mutliscale, high-dimensional, Cahn-Hilliard Reaction models to predict the phase change behaviour within secondary, lithium-ion batteries. Such model systems are notoriously difficult to solve accurately and novel numerical approaches have been developed to achieve this.
Industrial and applied mathematical modelling simulation
Investigation and development of virtual log models for Southern Pines will be based on analysis of data from the cores, peeled billets and approximately 60 sawn logs. We plan to predict log and stem wood properties from the breast height cores taken in the field study. Following this, applied mathematics will be used to investigate the processing of these virtual logs and predict properties for the virtual boards ‘sawn’ from these logs.
Invited talks, refereed proceedings and other conference outputs
Psaltis, S., Turner I., Farrell T., Carr E. J., Bailleres H., Kumar C., et al.
(2020). Prediction of sawn timber MOE from increment cores. The 20th Biennial Computational Techniques and Applications Conference (CTAC2020).
Greennwood, A. A., Zhang Z., O'Hara I. M., & Farrell T.
(2015). Limitations of a laboratory scale model in predicting optimal pilot scale conditions for dilute acid pretreatment of sugarcane bagasse. 37th Conference of the Australian Society of Sugar Cane Technologists. R. In Bruce. Australian Society of Sugar Cane Technologists Ltd.
Psaltis, S. T. P., Burrage K., & Farrell T.
(2015). Mathematical modelling of gas production in a Coal Seam Gas (CSG) field. Eleventh International Conference on CFD in the Minerals and Process Industries.
Tredenick, E. C., Farrell T., W. Forster A., & Psaltis S. T. P.
(2017). Nonlinear Porous Diffusion Modeling of Hydrophilic Ionic Agrochemicals in Astomatous Plant Cuticle Aqueous Pores: A Mechanistic Approach. Frontiers in Plant Science. 8, doi: 10.3389/fpls.2017.00746
Jiang, Z., Mariethoz G., Farrell T., Schrank C., & Cox M.
(2015). Characterization of alluvial formation by stochastic modelling of paleo-fluvial processes: The concept and method. Journal of Hydrology. 524, 367-377. doi: 10.1016/j.jhydrol.2015.03.007
Greenwood, A. A., Farrell T., Zhang Z., & O’Hara I. M.
(2015). A novel population balance model for the dilute acid hydrolysis of hemicellulose. Biotechnology for Biofuels. 8(1), doi: 10.1186/s13068-015-0211-5
Dargaville, S., & Farrell T.
(2015). A least squares based finite volume method for the Cahn–Hilliard and Cahn–Hilliard-reaction equations. Journal of Computational and Applied Mathematics. 273, 225-244. doi: 10.1016/j.cam.2014.06.020