Possible Areas for PhD Projects

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I am happy to consider applications from students wishing to study for a PhD with me on any of my research interests. In addition, there may be specific projects for which I am keen to attract students. Details of these projects can be found below.

I am more than happy to talk to potential applicants, so please get in touch with me for more information. For instructions on how to make a formal application, please see the UEA Maths Research Degrees page.


Oscillations in Flow Through an Elastic-Walled Tube

Project Description

Flow-induced oscillations of fluid-conveying elastic vessels arise in many engineering and biomechanical systems. Examples include pipe flutter, wheezing during forced expiration from the pulmonary airways, and the development of Korotkoff sounds during blood pressure measurement by sphygmomanometry.

Experimental studies of flow in collapsible tubes are typically performed with a Starling resistor. A finite-length elastic tube is mounted between two rigid tubes and flow is driven through the system. The collapsible segment is contained inside a pressure chamber which allows the external pressure acting on the elastic tube to be controlled. If the pressure outside the tube becomes sufficiently large, it will buckle non-axisymmetrically. Once buckled, the tube is very flexible leading to strong fluid-structure interaction. Experiments show that in this buckled state, the elastic tube segment has a propensity to develop large-amplitude self-excited oscillations of great complexity when the flow rate is increased beyond a certain value.

This project aims to further our understanding of some of the mechanisms that can lead to this instability of flow through an elastic-walled tube. The fluid flow will be described by the Navier–Stokes equations, and an appropriate elastic model will be used for the tube wall. Whittaker et al (2010) developed a relatively simple model for small amplitude, long-wavelength, high-frequency oscillations. Work is currently underway on extensions to include shear effects, wall inertia and axial bending. This project will start by working to relax some of the remaining assumptions in the previous model, e.g. adding nonlinear effects and allowing for different cross-sectional shapes. The project will likely focus on developing reduced analytic models (which may need to be solved analytically or numerically) though there is also scope for conducting full-scale numerical simulations.

Funding

There is no specific funding allocated to this project. However, some funded studentships are available from the University to well-qualified students. Self-funded students can be considered too.

References

High-Frequency Self-Excited Oscillations in a Collapsible-Channel Flow
Oliver E. Jensen & Matthias Heil, 2003.
Annual Review of Fluid Mechanics 481, 235.
Biofluid Mechanics in Flexible Tubes
James B. Grotberg & Oliver E. Jensen, 2004.
Ann. Rev. Fluid Mechanics 36, 121.
Predicting the Onset of High-Frequency Self-Excited Oscillations in Elastic-Walled Tubes
Robert J. Whittaker, Matthias Heil, Oliver E. Jensen & Sarah L. Waters, 2010.
Proceedings of the Royal Society A 466 (2124), 3635–3657.
Fluid–Structure Interaction in Internal Physiological Flows
Matthias Heil & Andrew L. Hazel, 2011.
Annual Review of Fluid Mechanics 43, 141–162.

Further details of my work in this area can be found on my collapsible tubes research page.

Flow Prediction and Optimisation in a Microfluidic Device

This project is suitable for a graduate of applied mathematics, engineering or physics with a strong background in theoretical fluid mechanics, and an interest in modelling real-world problems.

Project Description

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.

Funding

There is no specific funding allocated to this project. However, some funded studentships are available from the University to well-qualified students. Self-funded students can be considered too.

References

Tracking lineages of single cells in lines using a microfluidic device
A. C. Rowat, et al., 2009
Proc Natl Acad Sci 106, 18149–18154.
Microhydrodynamics: Principles and Selected Applications
S. Kim & S. J. Karilla, 1991
Dover Publications, ISBN 0486442195.