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How do “hedgehogs” flow under pressure? S&T80

  • School: School of Science and Technology
  • Study mode(s): Full-time / Part-time
  • Starting: 2022
  • Funding: UK student / EU student (non-UK) / International student (non-EU) / Fully-funded


NTU's Fully-funded PhD Studentship Scheme 2022

Project ID: S&T80

Not all liquids flow like the water from our taps. Small pollutants aside, water comprises a huge collection of H2O molecules, each of which can be thought of as a small sphere. As anyone who has played in a ball pit as a child (or as an adult!) will know, the spherical shape of these water molecules means that they flow over one another rather easily in all directions. Physicists refer to liquids such as water which are made up of approximately spherical molecules as isotropic liquids.

However, there are many interesting liquids which are made up of long, rod-like molecules. On the molecular level, you can idealise such a liquid as an empty ball pit which is then filled with dry spaghetti. Importantly, the large aspect ratio of these rod-like molecules means that they do not flow over one another quite as easily, and in turn tend to arrange themselves locally in distinguished directions. Physicists refer to these kinds of liquid as anisotropic liquids, as their physical properties depend on the direction in which their molecules align locally.

Anisotropic liquids (such as nematics) have important and lucrative technological applications due to the manner in which they interact with light and, more recently, how they interact with biological systems. Of particular interest to mathematicians, physicists, and engineers alike are the defect structures that occur in anisotropic liquids. In the case that the constituent rod-like molecules arrange themselves in a spike ball-type configuration, we refer to such a configuration of molecules as a hedgehog defect. Understanding how hedgehog defects move when the anisotropic liquid flows – especially under pressure – is a challenging and important problem. Its solution, amongst other applications, can aid scientists who work in the display technology industry.

In this PhD project, which lies in the area of mathematical condensed matter physics, we shall study the flow behaviour of hedgehog defects in anisotropic liquids using the so-called Q-tensor theory of the Nobel Prize-winning physicist Pierre-Gilles de Gennes. The project will also involve collaboration with experimental physicists in the Physics Department at NTU. The concrete aim of the project is to formulate, solve, and interpret the solutions of the partial differential equations which govern the evolution of hedgehog defects in anisotropic liquids. It would be considered beneficial if interested candidates had a background in mathematical analysis, differential equations, and fluid dynamics. A willingness to work closely with experimental physicists is required.

School strategic research priority

The proposed research is very well aligned with the IMEC (Imaging, Materials, and Engineering Research Centre).

Entry qualifications

For the eligibility criteria, visit our studentship application page.

How to apply

For guidance and to make an application, please visit our studentship application page. The application deadline is Friday 14 January 2022.

Fees and funding

This is part of NTU's 2022 fully-funded PhD Studentship Scheme.

Guidance and support

Download our full applicant guidance notes for more information.

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