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Continuum modelling of particulate flows in nature and industry

   Cardiff School of Mathematics

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  Dr Thomas Barker, Prof T N Phillips, Dr T C Hales  No more applications being accepted  Funded PhD Project (Students Worldwide)

About the Project

Fully Funded EPSRC DTP PhD Studentship in Applied and Computational Mathematics



Project Summary

So much of the natural and man-made world is composed of collections of discrete solid grains. However, there is currently no completely satisfactory theory to describe their motion, en masse, in the many complex flow scenarios which are important across industry and geophysics. Despite the challenges, a promising paradigm has been building over the last 20 years. Based around key experimental, mathematical and physical insights, continuum models for both the flow of dry grains and for particles suspended in a background fluid are beginning to mature.

In this project, the driving goal will be to develop a unified rheology spanning the many flow regimes that particulate materials can exhibit. Once this model begins to take shape, novel numerical methods will be developed to solve the resultant dynamical equations. This in-house code will then be applied to various test cases inspired by flows in nature, such as debris avalanches and subsea landslides, and in industry, such as hopper flows and drum mixers.

The work will be framed and motivated by key open questions such as "Is it useful in modelling to categorise particle flow dynamics into gas-like, liquid-like and solid-like behaviour?", "What is the most appropriate numerical method to solve multi-regime particulate flow equations?" and "How does the presence of liquid water modify the severity of natural hazards and the efficiency of industrial processes?".

Research Environment

Students undertaking this project will work in a dynamic field of research with many opportunities for innovation and impact. Success in the project will see the student gain ability and confidence in many areas of applied mathematics. In particular, the student will work at the forefront of continuum mechanics, computational fluid dynamics, granular rheology, discrete element modelling, geophysics and engineering.

Cardiff’s School of Mathematics is home to a world-leading Applied Mathematics group which has fostered an outstanding postgraduate research environment. The latest Postgraduate Research Experience Survey (PRES) ranks it 3rd in overall satisfaction and 1st (out of 22 in the UK) in professional development. With around 15 full-time staff and PhD students and weekly seminars by international experts, there will be many opportunities for knowledge exchange and guidance throughout the project.

The successful candidate will also become member of a vibrant postgraduate research community, which hosts the SIAM-IMA Student Chapter at Cardiff University, formed by the Society for Industrial and Applied Mathematics and supported by the Institute of Mathematics and its Applications. They will be provided with a desk and a computer, and access to state-of-the-art facilities in the School’s purpose-built new home, Abacws, where the School moved in September 2021.

Training and Development Opportunities

With the funding enabled by this studentship, students will have access to many conferences and workshops outside Cardiff. Of particular relevance in the coming years are the Particles 2023 conference in Milan, the 2024 Gordon Research Conference in Boston and Powders & Grains 2025 in India. These activities will encourage the general intellectual and personal development of the student, leading to many transferrable skills.

To expand their mathematical knowledge beyond that offered by their specific project, in addition to research work, in the first two years the student will attend a total of 100 hours of postgraduate lecture courses run by MAGIC (Mathematics Access Grid Instruction and Collaboration), which is jointly organised remotely by 20 UK Universities. Assignments to the MAGIC courses will be assessed by the course lecturers.


Applicants should apply through the Cardiff University online application portal, for a Doctor of Philosophy in Mathematics with an entry point of October 2023.

In the research proposal section of your application, please specify the project title and supervisors of this project. There is no requirement to submit a detailed research proposal.

In the funding section, please select "I will be applying for advertised funding from EPRSC DTP.


A 1st or upper 2nd class UK Honours degree (or equivalent) or a Master’s degree is required in mathematics or a related subject.


Applicants for whom English is not their first language must demonstrate proficiency by obtaining an IELTS score of at least 6.5 overall, with a minimum of 5.5 in each skills component. Further acceptable qualifications can be found at https://www.cardiff.ac.uk/study/international/english-language-requirements/postgraduate


·        Curriculum vitae

·        A personal statement

·        Two completed references

·        Degree certificates and transcripts

·        Proof of English language (if applicable)


EPSRC DTP studentships are available to home and international students. Up to 30% of our cohort can comprise international students, once the limit has been reached we are unable to make offers to international students.

International students will not be charged the fee difference between the UK and international rate. Applicants should satisfy the UKRI eligibility requirements. 

Cardiff University is committed to support students from a range of backgrounds and circumstances. Where needed, we will work with you to take into consideration reasonable project adaptations (for example to support caring responsibilities, disabilities, other significant personal circumstances) as well as flexible working and part‐time study requests, to enable greater access to a PhD. All our supervisors support us with this aim, so please feel comfortable in discussing further with the listed PhD project supervisor to see what is feasible.

 Cardiff University is committed to supporting and promoting equality and diversity and to creating an inclusive environment for all. We welcome applications from all members of the global community irrespective of age, disability, sex, gender identity, gender reassignment, marital or civil partnership status, pregnancy or maternity, race, religion or belief and sexual orientation.

We welcome applications for both full and part-time study and from candidates with non-traditional academic backgrounds. For further information about modes of study, please contact us.


 Applicants are reminded to submit all relevant documents (transcripts, supporting statement, etc) by the deadline. Due to the volume of applications received, incomplete applications will not be considered. Shortlisted applicants will be invited to interview early in March 2023.

Funding Notes

The studentship funded by the EPSRC DTP is for 3.5 years and covers tuition fees, an annual tax-free living stipend of in line with UKRI minimum rates (currently £17,668) and includes access to a Research Training Support Grant (currently £4000).
If you have a disability you may be entitled to a Disabled Students’ Allowance (DSA) on top of your studentship.

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