Megan Richards

Background: I graduated in 2020 from Durham University with a BSc in Mathematics. I then completed a Masters in Computational Applied Mathematics at The University of Edinburgh. For my MSc dissertation, I worked with the Swain Lab Group to focus on mathematically modelling ion regulation in yeast cells.

Why I chose the CDT in Fluid Dynamics: Overall, the structure of the CDT programme really appealed to me. In particular, the opportunity to learn about fluid dynamics on a broad spectrum and consolidate knowledge before deciding my project will be extremely useful. Also, I found that the CDT places emphasis on a collaborative environment. This is important to me as I enjoy working with other people, so I liked the cohort structure of the programme.

PhD Project Title: Theoretical analysis of fluid flow in microfluidic biomedical devices

Microfluidics has been recognised as an area of potential for the development of cancer treatment methods. In particular, new microfluidic “lab-on-a-chip” devices show a promising capacity to revolutionise the field by considerably reducing the disadvantages associated with existing treatments. The microbubbles produced by such devices are becoming a viable option for use as targeted drug delivery vehicles. This method increases efficacy in the region of disease and eradicates unwanted side effects in the healthy tissue.

Upon arrival at the tumour, ultrasound is used to rapidly contract and expand the bubble in resonance, destroying the bubble and triggering drug release. In order for the ultrasound to successfully resonate the bubble and induce its collapse, it is essential to know the size of bubble as it reaches the target tissue. This is complex to predict as the size of bubbles produced by microfluidic devices are influenced by many parameters including those associated with device geometry as well as the properties of the immiscible fluids in the device. Additionally, gas can diffuse out of the bubble as it moves through the body. Whilst surfactants in the bubble shell can be used to reduce this effect, diffusion will still cause the bubble to shrink so that it is smaller upon arrival at the tumour than it was when it was first produced.

Many open challenges remain in the design and optimisation of microfluidic devices. In particular, there are fundamental questions relating to the effect of the channel wall on the flow through the device at microscopic scales.  Most of the work on the low-Reynolds number viscous fluid flow associated with the devices has evaded rigorous fundamental mathematical analysis and instead most current work used to direct the device design is based on experiments. Consequently, there is an opportunity for the development of new theory to describe the process of microbubble production, and to establish multi-phase equations for the dynamics of bubble aggregates as they travel to tumours.

The first aim of my project is to develop a theoretical model to predict how the shape of a fluid-fluid interface evolves over time for a confined bubble in a tube under general surface tension. My goal is to develop a time dependent solver for this interface as the bubble moves through a straight channel. Once established, this will act as a benchmark for confined bubble geometries which are more complex and closer to the confinement associated with microfluidic flow focusing devices.