This page lists potential PhD projects in biological and industrial mathematics, offered by faculty members of the School of Mathematics. For further details of the School's research in this area, please see the pages for Mathematical Biology Research and Industrial Mathematics Research. For further information about an individual project, please contact the listed supervisor. For information about submitting an application, please see our Research Degrees page.

Flow Prediction and Optimisation in a Microfluidic Device Flow Prediction and Optimisation in a Microfluidic Device

Supervisor: Dr Robert Whittaker

The project will involve working on fluid mechanics modelling as part of an interdisciplinary team, involving members of the School of Mathematics at UEA and the Institute of Food Research (IFR) on the Norwich Research Park. The project is to help analyse the flow in a micron-sized chamber for isolating and testing single bacterial spores. These microfluidic traps will allow microbiologists at IFR to gain insight into the development of foodborne botulism from germination and growth of single spores of C. botulinum in foods.

For 20 years, the food industry has adhered to a 10-day shelf-life rule in the UK for chilled, prepared foods to minimise the outbreak risk of food-borne botulism. Insight gained from studying single spores can contribute towards extending the 10-day rule with the concurrent benefits of reducing food waste and saving energy.

At IFR, microfluidic devices have been fabricated for isolating a single living bacterial cell at ambient temperature. The ability to subject these devices to a thermal shock that increases the temperature from ambient to about 80°C is also being explored and this will make the device ideal for generating information that is suitable for risk assessment.

A mathematical formulation of the fluid dynamics within the microfluidic device will be studied in this project, utilising both analytical and numerical techniques. These will include scaling analysis, asymptotic solutions, and boundary-integral methods. A variety of model problems will be considered to help understand how the device operates and the predict the effects of changes to geometry and operating conditions. From these calculations, it will be possible to optimise the design of the device to provide better functionality and more robust results.

As well as helping with the design of the device, results from the mathematical modelling will facilitate the interpretation of biological measurements made using the device and, potentially, will enable further developments in the experimental approach. Currently, microfluidic technology is relatively empirical. A mathematical formulation of the flow device will help provide a rational basis for integrating the observed behaviour of single spores with quantitative risk assessment.


  • A. C. Rowat, et al. (2009) Tracking lineages of single cells in lines using a microfluidic device, Proceedings of the  National Academy of Science 106, 18149–18154.
  • S. Kim & S. J. Karilla (1991). Microhydrodynamics: Principles and Selected Applications, Dover Publications, ISBN 0486442195.

For further information, please contact Dr Robert Whittaker.