Modelling hydrogels and fractal materials

PGR-P-309

Key facts

Type of research degree: PhD
Application deadline: Ongoing deadline
Project start date: Wednesday 1 October 2025
Country eligibility: International (open to all nationalities, including the UK)
Funding: Competition funded
Source of funding: University of Leeds
Supervisors: Dr David Head
Schools: School of Computer Science
Research groups/institutes: Computational Science and Engineering

<h2 class="heading hide-accessible">Summary</h2>

There is growing interest in the importance class of materials known as hydrogels, which are formed by the aggregation of small building blocks until they gel (or percolate) across the sample. This imbues the sample with rigidity, but also leaves pores which can be useful for e.g. drug delivery, diffusion of metabolites/nutrient for tissue engineering applications, and so on. Biopolymer-based hydrogels, such as those built from proteins which are a subject of experimental research in the School of Physics, are particularly appealing for healthcare applications due to their high biocompatibility. The mechanical properties of hydrogels are often crucial to their function. For instance, materials for wound healing must have a minimum strength, and substrates for tissue engineering can alter the cell types that derive from embedded stem cells. However, understanding and predicting the mechanical (and time-dependent mechanical, or viscoelastic) properties of hydrogels is challenging because of the way they form. Not only are they disordered, but they are typically fractal up to a characteristic size, both of which reduce the range of modelling tools that can be brought to this important class of material. This PhD project will be about developing mathematical and/or computational models to predict the viscoelastic response of hydrogels and/or general fractal materials, using the non-invasive characterisation to understand trends and make predictions for future materials and applications. The style of project will depend on the applicant's abilities and interests, but may take the form of (a) Developing molecular dynamics code, or similar, to simulate the formation of fractal structure with hydrogels, and use the same code to predict the resulting gel's viscoelasticity, along with other important metrics such as porosity. This mainly computational project will likely include contact with the nearby protein hydrogel experimental group in Physics. Alternatively, (b) Develop a range of schematic fractal systems in an attempt to fully characterise and elucidate the relationship between fractality and viscoelasticity. Mathematical and/or computer tools will be used to predict the viscoelastic response and explain the observed trends. This more mathematical project will apply to hydrogels, but also fractal-cut materials such as kirigami.

<h2 class="heading">How to apply</h2>

Formal applications for research degree study should be made online through the <a href="https://www.leeds.ac.uk/research-applying/doc/applying-research-degrees">University's website</a>. Please state clearly in the Planned Course of Study section that you are applying for PHD Computer Science FT, in the research information section that the research degree you wish to be considered for is Modelling hydrogels and fractal materials as well as <a href="https://engineering.leeds.ac.uk/staff/542/Dr_David_Head">Dr David Head</a> as your proposed supervisor and in the finance section, please state clearly the funding that you are applying for, if you are self-funding or externally sponsored. If English is not your first language, you must provide evidence that you meet the University's minimum English language requirements (below). As an international research-intensive university, we welcome students from all walks of life and from across the world. We foster an inclusive environment where all can flourish and prosper, and we are proud of our strong commitment to student education. Across all Faculties we are dedicated to diversifying our community and we welcome the unique contributions that individuals can bring, and particularly encourage applications from, but not limited to Black, Asian, people who belong to a minority ethnic community, people who identify as LGBT+ and people with disabilities. Applicants will always be selected based on merit and ability. Applications will be considered after the closing date. Potential applicants are strongly encouraged to contact the supervisors for an informal discussion before making a formal application. We also advise that you apply at the earliest opportunity as the application and selection process may close early, should we receive a sufficient number of applications or that a suitable candidate is appointed. Please note that you must provide the following documents in support of your application by the closing date of Monday 3 March 2025 if applying for Leeds Doctoral Scholarship or Tuesday 1 April 2025 for Leeds Opportunity Research Scholarship. If you are applying with external sponsorship or you are funding your own study, please ensure you provide your supporting documents at the point you submit your application: <ul> <li>Full Transcripts of all degree study or if in final year of study, full transcripts to date</li> <li>Personal Statement outlining your interest in the project</li> <li>CV</li> </ul>

<h2 class="heading heading--sm">Entry requirements</h2>

Applicants to research degree programmes should normally have at least a first class or an upper second class British Bachelors Honours degree (or equivalent) in an appropriate discipline. The criteria for entry for some research degrees may be higher, for example, several faculties, also require a Masters degree. Applicants are advised to check with the relevant School prior to making an application. Applicants who are uncertain about the requirements for a particular research degree are advised to contact the School or Graduate School prior to making an application.

<h2 class="heading heading--sm">English language requirements</h2>

The minimum English language entry requirement for research postgraduate research study is an IELTS of 6.5 overall with at least 6.5 in writing and at 6.0 in reading, listening and speaking or equivalent. The test must be dated within two years of the start date of the course in order to be valid. Some schools and faculties have a higher requirement.

<h2 class="heading">Funding on offer</h2>

Self-Funded or externally sponsored students are welcome to apply. UK – The <a href="http://phd.leeds.ac.uk/funding/138-leeds-doctoral-scholarship-2025-faculty-of-engineering-and-physical-sciences#:~:text=Key%20facts&text=One%20Leeds%20Doctoral%20Scholarship%20is,rata%20for%20part%2Dtime%20study.">Leeds Doctoral Scholarship</a> (closing date: Monday 3 March 2025) and <a href="https://phd.leeds.ac.uk/funding/234-leeds-opportunity-research-scholarship-2022">Leeds Opportunity Research Scholarship</a> (closing date: Tuesday 1 April 2025) are available to UK applicants. <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds. Non-UK – The <a href="https://phd.leeds.ac.uk/funding/48-china-scholarship-council-university-of-leeds-scholarships-2021">China Scholarship Council - University of Leeds Scholarship</a> is available to nationals of China (now closed for October 2025 entry). The <a href="https://phd.leeds.ac.uk/funding/73-leeds-marshall-scholarship">Leeds Marshall Scholarship</a> is available to support US citizens. <a href="https://phd.leeds.ac.uk/funding/60-alumni-bursary">Alumni Bursary</a> is available to graduates of the University of Leeds. You will be responsible for paying the overtime fee in full in your writing up/overtime year (£320 in Session 2024/25), but the scholarship maintenance allowance will continue to be paid for up to 6 months in the final year of award. Important: Please note that that the award does not cover the costs associated with moving to the UK. All such costs (<a href="https://www.leeds.ac.uk/international-visas-immigration/doc/applying-student-visa">visa, Immigration Health Surcharge</a>, flights etc) would have to be met by yourself, or you will need to find an alternative funding source. Please refer to the <a href="https://www.ukcisa.org.uk/">UKCISA</a> website for information regarding Fee Status for Non-UK Nationals.

<h2 class="heading">Contact details</h2>

For further information about your application, please contact PGR Admissions by email to <a href="mailto:EMAIL@leeds.ac.uk">p</a><a href="mailto:phd@engineering.leeds.ac.uk">hd@engineering.leeds.ac.uk</a> For further information about this project, please contact Dr David Head by email to <a href="mailto:D.Head@leeds.ac.uk">D.Head@leeds.ac.uk</a>