Multiscale modelling of lithium-ion batteries

PROJECT REF: MPHY3310217

Developing cheap and efficient means of providing energy storage is key to the low-carbon economy. The fastest growing battery type, lithium-ion batteries, are already produced in their billions each year and are ubiquitous in consumer devices because they exhibit a high energy density, no memory effects, and little self-discharge when not in use. Despite these promising characteristics, before they can be widely adopted by the automotive industry, hurdles must be overcome in peak current capabilities and cell lifetime.

The aims of this project are to carry out the mathematical modelling and analysis (both analytical and numerical) required to underpin and inform changes in the current design of cells that give rise to these desired characteristics.

Commercial lithium-ion cells are quintessential multiscale systems, where alterations in design at small, microscopic length scales have a large impact on cell characteristics at larger length scales relevant at the level of the whole cell. Useful mathematical models of these devices must therefore be able to ‘connect’ descriptions of the cell operation at the level of the microstructure to characteristics at the cell scale.

In the initial stages of the project, the mathematical tools to coherently and self-consistently connect these two disparate length scales will be developed. This will be done by leveraging an asymptotic technique in homogenisation known as the method of multiple scales. Then, both electrochemical and mechanical models, operating at the level of the microstructure will be proposed. These models will consist of systems of coupled nonlinear partial differential equations. Using the previously developed tools, these microstructural models will be ‘upscaled’ to the cell level. The resulting mathematical description will then be used to identify optimal designs for the cell microstructure that give rise to cells that are capable of higher discharge rates and are more durable.