Doctoral research
If you are interested in joining our group then there are plenty of possibilities. We currently invite applications to the following opportunities:
1) DPhil in Industrial Mathematics Studentship
More details.
2) Microscale coiling and wrapping in nature and technology
This project is in collaboration with
Dominic Vella,
and
Janine Nunes who is based in the Complex Fluids Group at Princeton University.
Micro- and nanoscale coiling and wrapping phenomena find themselves in many natural scenarios, from the functionality of a spider web to the packing of RNA within virus capsids. Similar behaviour is at play in manufacturing technologies including soft robotics, flexible electronics devices like bendable smartphones, and in multifunctional soft materials for bioengineering and healthcare applications, such as materials for tissue engineering. The successful manufacture of such soft devices, however, depend on our understanding of the wrapping phenomena and our ability to control it to engineer such products at small length scales.
In this project we will study the mathematics of microscale wrapping using combinations of deformability, fluid flow, electrostatics and surface tension. Our work will be underpinned by two example cases: one inspired by nature and one in technology. The first example case we will study concerns the internal wrapping of fibres in droplets in spider webs. Some spider's webs consist of long threads that are held taught by small scale droplets on them: the surface tension of these droplets is strong enough to 'spool' additional thread within them. This ensures that excess length is reeled into the droplets and the thread remains taut but may also be unravelled if the fibre in the web is stretched (for example when an insect flies into the web). It is thought the presence of droplets also helps to dissipate the fly's kinetic energy without too much stretching.
In this project, we will study the unravelling and reel-back process in spider-web droplets. The second case concerns the external wrapping of microscale charged fibres around oppositely charged soft particles through mutual electrostatic attraction. As they attract one another, the fibre will wrap around the particle, squeezing it and deforming its shape as it does so. The initial configuration and subsequent rate of wrapping have been observed to dictate the shape of the particle and the configuration when the fibre ceases to wrap. In this project, we will investigate the wrapping process and dependence on the deformability of the particle and the fibre, the strength of the electrostatic interaction, and its dependence on the initial configuration.
The mathematical models we derive in both of these example cases will be used to compare and contrast the wrapping dynamics and dependence of the behaviour and resulting configurations on the forces that are involved.
(left) A fibre is spooled by a droplet; (right) A fibre wraps around a microscale particle via electrostatic interaction.
Less details
3) Engineering liquid-crystal-based platforms for rapid sensing of biomolecules
More details.
4) DPhil in the Mathematical Institute
More details.
