Self-funded PhD opportunities

Multiscale modelling of lithium-ion batteries

  • Application end date: Saturday 1 July 2017
  • Funding Availability: Self-funded PhD students only
  • Department: Mathematics
  • PhD Supervisor: Jamie Foster, William Lee & Andrew Osbaldestin

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.

How to apply

To apply or make an enquiry, please visit postgraduate research: Mathematics and Physics

Applications should use our standard application forms and follow the instructions given under the ‘Research Degrees’ heading on the following webpage:

When applying please note the project code: MPHY3310217

Funding Notes: Home/EU applicants only. Please use the online application form and state the project code and studentship title in the personal statement section.

An appropriate first or upper second class honours degree of any United Kingdom university or a recognised equivalent non-UK degree of the same standard honours degree or equivalent in a relevant subject or a master’s degree in an appropriate subject. Exceptionally, equivalent professional experience and/or qualifications will be considered.

The ideal candidate would have some knowledge of the physics of electrical systems as well as some familiarity with asymptotic methods and scientific computing (e.g., in MATLAB). The successful applicant will have the benefit of taking part in meetings with both domestic and international industrial collaborators.