Making a deposit: towards real-world models for the coffee-ring effect
Qualification(s) available: PhD
- Entry requirements
- 2:1+
- Fees for 2026-27 (per academic year)
-
(Funded)UK: Fully fundedInternational: Fully funded
- Full-time
- 3 years
- Part-time
- 6 years
- Start date
- October 2026
- Application deadline
- 19 April 2026
- Project reference
- SCI26/MA/MM
- Location
- Loughborough
- Subject area(s)
- Mathematical Sciences
Project details
When you accidentally knock over your cup of coffee and spill a droplet onto the table, you may have noticed that the stain that remains after the liquid has evaporated is darker at its edges.
As the droplet evaporates, liquid flows from the centre of the droplet to its edge due to conservation of mass, carrying particles of coffee along with it.
This is known as the coffee-ring effect and, in fact, occurs widely in different situations with a liquid containing particles.
It can be advantageous – for example in printing micro-circuits or aligning DNA to map it easily – but can also be a drawback – for example in printing pixels on Q/OLED screens for electronic devices, where a uniform deposit is desired for a crisp image.
Due to its range of applications, the evaporation of colloidal droplets is a flourishing field. The long-term goal is to have a thorough grasp on the underlying physics in order to develop non-intrusive optimal control strategies that may be employed in an industrial or real-world setting to achieve a desired outcome, such as a uniform coating on your mobile phone screen.
Since the coffee-ring effect arises due to the complex interaction between evaporation, fluid dynamics and particle transport, classical treatment of the problem was restricted to only treating the simplest possible cases: relatively-flat, circular droplets in isolation. This has dramatically limited the applicability of mathematical models to real-world contexts.
In recent years, the project proposer Dr Madeleine Moore has worked alongside collaborators at Strathclyde, Glasgow and Oxford to help relax some of the simplifying assumptions, including work on the evaporation of non-circular droplets and droplet arrays; gravitational effects on particle transport; and substrate-particle interactions.
This project seeks to build on these advances by deriving mathematical models for the dynamic growth of the coffee ring as it forms as a small region of closely-packed particles at the edge of a non-circular droplet.
The successful candidate will develop both analytical (e.g. matched asymptotic analysis) and numerical techniques for solving partial differential equations and will compare results to existing data. There is wide scope for the latter parts of the project to be guided by the candidate’s interests and strengths, including the possibility of collaborating with experimental and industrial experts.
The project will provide the successful candidate an opportunity to develop sophisticated problem-solving and modelling skills, as well as analytical and computation techniques for tackling mathematical models. In addition, the candidate will get the opportunity to develop their programming skills (e.g. MATLAB, Maple, Python).
94% of Loughborough’s research impact is rated world-leading or internationally excellent. REF 2021
Supervisors
Primary supervisor: Dr Madeleine Moore
Entry requirements
Our entry requirements are listed using standard UK undergraduate degree classifications i.e. first-class honours, upper second-class honours and lower second-class honours. To learn the equivalent for your country, please choose it from the drop-down below.
Entry requirements for United Kingdom
Applicants should have or expect to achieve a minimum of a 2:1 Honours degree (or equivalent international qualification) in Mathematics, Engineering or a related discipline. A relevant Master's degree is desirable, but not required. Experience in mathematical modelling, partial differential equations or fluid dynamics is highly desirable.
Afghanistan
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Masters | 95% | 85% | 70% |
Albania
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Diplomë e Nivelit të Pare (First Level (University) Diploma (from 2010) | 9.5 | 8.5 | 8 |
Algeria
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Licence (4 year) / Diplome d'Inginieur d'Etat / Diplôme d'Etudes Supérieures | 16 | 14 | 12 |
Argentina
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Licenciatura/ Licenciado (4 year) | 8.5 | 7.5 | 6.0 |
Armenia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Bakalavri Kochum required but typically a Magistrosi Kochum | 90% or 3.9 | 80% or 3.5 | 70% or 3.0 |
Australia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Honours degree (AQF level 8) | First Class, 80% | Upper Second, 70%, H2A | Lower Second, 60%, H2B |
| Ordinary degree - AQF Level 7 pass (mark 46 or 50) | High Distinction (80% or 85%) | Distinction (75% or 80%) | Distinction (70% or 75%) |
Austria
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Degree / Diplomstudium / Fachhochschuldiplom (Diplom (FH)) | A (or 1.5) mit Auszeichnungbestanden | 60% / B / (or 2) | 60% / B / (or 2) |
Azerbaijan
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Bakalavr Diplomu/ Diplomu (Specialist Diploma) | 4.5 or 90% | 4 or 80% | 3.5 or 70% |
Bahamas
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Degree from University of the West Indies only | 1st (GPA 3.6) | 2:1 (GPA 3.0) | 2:2 (GPA 2.5) |
Bahrain
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| GPA 4.0 scale | 3.5 | 3.0 | 2.5 |
Bangladesh
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 4 Year Bachelor of Science in Engineering (IEB and BAETE accredited courses up to 2024) Any 4 year Bachelor degree or BSc in Nursing (2025 onwards) |
1st (70%) / 3.5 | 2nd (60%) / 3.0 | 2nd (55%) / 2.75 |
| Masters (1-2 years) following a 3 or 4 year degree | 80% / 4.0 | 65% / 3.25 | 50% / 2.5 |
Belarus
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Specialist Diploma (5Yr) | 9 | 7 | 5 |
Belgium
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Bachelor degree/Licenciaat/Licencie | 80% or 17 | 70% or 14 | 60% or 12 |
Belize
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Degree from University of the West Indies only | 1st (GPA 3.6) | 2:1 (GPA 3.0) | 2:2 (GPA 2.5) |
Benin
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Maitrise | 18 | 15 or Bien | 12 or Assez Bien |
Bermuda
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Degree from University of the West Indies only | 1st (GPA 3.6) | 2:1 (GPA 3.0) | 2:2 (GPA 2.5) |
Bolivia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| A Licenciado, 4 years Private (public/private) | 85/78 | 75/66 | 67/55 |
Bosnia and Herzegovina
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Diploma Visokog Obrazovanja / Diplomirani | 10 | 9 | 8 |
Botswana
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Master's degree | A or 80% | B or 70% | C or 60% |
Brazil
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Brazil - 4 yr Bacharel or Licenciado/Licenciatura or Título Profissional | 8.5 | 7.5 | 6.5 |
Brunei
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Brunei | First | Upper Second (60%/B/3.1) | Lower Second (50% or C or 2.5) |
Bulgaria
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 5 yr Diploma za Zavarsheno Visshe Obrazovanie (Diploma of Completed Higher Education) | 6 | 5 | 4 |
Burundi
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Masters or Diplôme d'Études Approfondies or Diplôme Ingénieur (professional title) | 18 | 15/20 (Bien) | 12.5/20 (Assez Bien) |
Cambodia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Masters | 80% or B+ or 3.5 | 70% or B or 3.0 | 60% or C+ or 2.5 |
Cameroon
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Bachelor degree or Diplome d'Etudes Superiures de Commerce or Diplome d'Ingenieur or Diplôme d'Ingénieur de Conception or a Maitrise, 4 year Licence or Master 1 (M1) | 1st / 3.6 or 15/Tres Bien | 2:1 / GPA 3.0 or 14 / Bien | 2:2 / GPA 2.5 or 12.5/ Assez Bien |
Canada
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| GPA 4.0/Percentage | 3.7/85% | 3.3/75% | 2.7/68% |
| Out of 9 | 8 | 6 | 5 |
| Out of 12 | 10 | 8 | 6 |
Chile
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Grado de Licenciado / Título (Profesional) de [subject area] (4 years) | 6 | 5.5 | 5 |
China
Students are required to have a bachelor degree (4 years) for entry to a postgraduate programme. The University uses a tiered ranking system to identify the required final mark, as outlined on the table below.
You can search for your institution (university or affiliated college) via our look up tool.
| First class (70%) | Mid 2:1 (65%) | 2:1 (60%) | Mid 2:2 (55%) | 2:2 (50%) | |
|---|---|---|---|---|---|
| Tier 1 | 80% | 76% | 72% | 70% | 67% |
| Tier 2 | 83% | 79% | 75% | 73% | 70% |
| Tier 3 | 86% | 82% | 79% | 77% | 75% |
Students who do not meet the above requirements may occasionally be considered if they have a relevant degree, can show good grades in relevant subjects, and/or have substantial relevant work experience.
Colombia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Licenciado / Título de [subject area] | 4.5 | 3.75 | 3.2 |
Costa Rica
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Licenciado | 9 | 8 or 80 | 7 or 75 |
Croatia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Baccalaureus / Prvostupnik | 4.5 | 3.8 | 3.0 |
Cuba
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 4-year Titulo de Licenciado / Licenciatura | 5 | 4 | 3 |
Cyprus
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Cyprus | 8.5 | 7.0 | 6.5 |
Czech Republic
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Bakalár (after 2001) 6 yr integrated Magistr | 1 | 1.5 | 2 |
Denmark
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 5 year Candidatus/Candidata Magisterii or Bachelor degree (7 point scale) | 12 | 10 | 7 |
Dominican Republic
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 4 year Licenciado or Título de [subject area] | 3.8 | Magna Cum Laude or 3.5 or 85% | Cum Laude or 3.2 or 82% |
Ecuador
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Título de Licenciado / Título de [subject area] | 8.5 / 85% | 8 / 80% | 7 / 70% |
Egypt
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Egypt | 3.5 | 3.2 | 2.8 |
| Universities only | BA 90%, BSc 85% | BA 80%, BSc 75% | BA 65%, BSc 65% |
El Salvador
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 5 year Licenciado, Título de Ingeniero/Arquitecto | 8.5, 85% | 7.5, 75% or Muy Bueno | 6.5, 65% or Bueno |
Estonia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Bakalaureusekraad or Magister or Magistrikraad | 5 or 91% or A | 4 or 81% or B | 3 or 71% or C |
Ethiopia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Masters (up to 2025) | A / GPA 4.0 | A / GPA 3.5 | B / GPA 2.8 |
| 4-year Bachelor degree with thesis (from 2024) | A / GPA 4.0 | A / GPA 3.5 | B / GPA 2.8 |
| 5-year Bachelor degree (from 2025) | A / GPA 4.0 | A / GPA 3.5 | B / GPA 2.8 |
Finland
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Kandidaattii/Kandidat or the Maisteri/Magister | 3 (out of 3) or 4.5 (out of 5) | 2 (out of 3) or 3 (out of 5) | 1 (out of 3) or 2.5 (out of 5) |
France
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Licence (3 years)/ Maitrise/ Diplôme d'Ingénieur | 14 | 13 | 11 |
Georgia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 4-year degree (% = new system) | 5 (95%) | 4.0 (85%) | 3.5 (75%) |
Germany
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| German Bachelor/ Diplom, Magister Artium / Zeugnis über den Zweiten Abschnitt der Ärztlichen Prüfung | 1.5 | 2.5 | 3.0 |
Ghana
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Ghana | 65% / 3.4 GPA | 57% / 3.0 GPA | 50% / 2.5 GPA |
Greece
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Universities | 8.5 | 7.0 | 6 |
| TEI and non-University Institutions | 8.5 | 7 | 6.5 |
Grenada
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Degree from University of West Indies - classification | 1st, 70% (GPA 3.6) | 2:1, 60% (GPA 3.00) | 2:2, 50% (GPA 2.5) |
| Degree from University of West Indies - grade / percentage | A | B / 75% | C / 55% |
| Degree from University of West Indies - GPA | 3.6 | 3.0 | 2.0 |
Guatemala
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Liceniado / Titulo de (subject area) - 4 years | 90% (public university) / 95% (private university) | 80% (public university) / 85% (private university) | 60% (public university) / 70% (private university) |
Guyana
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Master's | GPA 4 | GPA 3.5 | 3.0 |
Honduras
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Título de Licenciado / Grado Académico de Licenciatura (4 year degree) - GPA out of 5 | GPA 5 or 90% | GPA 4 or 80% | GPA 3.5 or 70% |
Hong Kong
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Bachelor degree (Honours) | 1st or 3.5/4 | 2:1 or 3/4 | 2:2 or 2.5/4 |
Hungary
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Alapfokozt or Egyetemi Oklevel / Bachelor | 4.5 | 3.5 | 3 |
Iceland
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Baccalaurreatus degree or Kandidatsprof/Candidatus Mag | 8.5 | 7.5 | 6.5 |
India
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Institutions listed on the National Institutional Ranking Framework | 61% | 55% | 50% |
| All other Indian institutions | 68% | 62% | 57% |
Indonesia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Sarjana I (S1) from accredited Universities | 3.2 | 3.0 | 2.8 |
Iran
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Iran | 17 | 15 | 13 |
Iraq
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Iraq | 80% | 75% | 70% |
Ireland
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Republic of Ireland | First (70%) | Upper second (60%) | Lower second (50%) |
Israel
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 3 yr Bachelor Degree | 90% | 80% | 70% |
Italy
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Diploma di Laurea | 109/110 | 100/110 | 90/110 |
Ivory Coast
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Diplome d'Etude Approfondies, Diplome d'Etude Superieures or Diplome d'Etude Superieures | 16 | 14 (Bien) | 12 (Assez Bien) |
Jamaica
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| For degrees studied at The University of West Indies or degrees accredited by UCJ and CCCJ | 1st (GPA 3.6) | 2:1 (GPA 3.0) or B | 2:2, 50% (GPA 2.5) |
Japan
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Gakushi – GPA 4.0 scale | 85% or A or 3.5 | 80% or B or 3.0 | 70% or C or 2.0 |
Jordan
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| GPA 4.0 scale | 3.5 | 3 or 3.5/5 or 75% | 2.5 (or 3.0/5) / 63% |
Kazakhstan
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| GPA 5.0/percentage scale | 4.5 or 90% | 4 or 85% | 3.5 or 80% |
| GPA 4.33 scale | 3.9 | 3.7 | 3.2 |
| GPA 4.0 scale | 3.7 | 3.4 | 3 |
Kenya
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Kenya | First / 70% / A | Upper second / 60% / B | Lower second / 50% / C |
Kosovo
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Kosovo | 10 | 9 | 8 |
Kuwait
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| GPA 4.0 scale | 3.6 | 3.0 | 2.6 |
Latvia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Latvia | 9 | 7 | 6 |
Lebanon
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| American | 85% (3.5) | 75% (3.0) | 62% (2.6) |
| French | 18 | 15 | 12 |
Liberia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Master's | 4.0 or 90% | 3.5 or 85% | 3 or 80% |
Libya
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| BSc Engineering, Architecture, Medicine | 85 (3.6) | 75 (3.0) | 65 (2.5) |
| Other bachelor's degree from a university | 90 (4.0) | 85% (3.6) | 75% (3.0) |
Lithuania
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Lithuania | 9 | 8 | 7 |
Luxembourg
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Luxembourg | 18 (excellent) | 16 (tres Bien) | 14 (bien) |
Macau
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Macau | 1st or GPA 3.7 | 2:1 or GPA 3.0 | 2:2 or GPA 2.5 |
Macedonia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Magistar Дипломиран / Баццалауреус / Баццалауреа (Bachelor degree) | 10 | 9 | 8 |
Malawi
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Master's only | MSc 75% | MSc 70% | MSc 65% |
Malaysia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Classification | First Class | 2.1 | GPA 2.5 |
| GPA 4.0 scale | 3.5 | 3.0 | 2.8 |
Malta
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Malta | 1st (80%) | 2:1 (70%) | 2:2 (55%) |
Mauritius
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Mauritius | 1st or 70% | 2:1 or 60% | 2:2 or 50% |
Mexico
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Licenciatura / Licenciado/ Título (Profesional) de [subject area] | 8.5 | 8 | 7 |
Moldova
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Diploma de Licenţă (Diploma of Licentiate) | 9 | 8 | 7 |
Mongolia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Диплом Специалиста (Specialist Diploma) | 90% or 3.5 | 80% or GPA 3.2 | 70% or GPA 3.0 |
Montenegro
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Diploma of Completed Undergraduate Studies or Diploma of Professional Undergraduate Studies | 10 (or 5.0) | 9 (or 4.5) | 8 (or 4.0) |
Morocco
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Diplôme d'Ingénieur d'État, Diplôme d'Écoles Nationales de Commerce et de Gestion, Licence / Licence d'Études Fondamentales / Licence Professionnelle | 16 | 14 | 12 |
Mozambique
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Mestrado/ Grau de Mastre | 16 | 14 | 12 |
Myanmar (Burma)
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 2 year Master's degree | 5 or 85% | 5 or 75% | 4.5 or 65% |
Namibia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 4-year Bachelor Honours (post 2008) or Masters | 80% or A | 70% or B | 60% or C |
Nepal
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 4 -year professional degree or Masters (after 3-year Bachelor degree) | 80% or 3.7 GPA | 65% or 3.3 GPA | 60% or 3.0 GPA |
Netherlands
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Netherlands | 8 | 7 | 6 |
New Zealand
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 4 Year Honours degree (480 credits) - Level 8 | First (7.0) | Upper Second (6.0) | Lower Second (4.0) |
| 3 Year degree (360 credits) - Level 7 | A+ (9.0) | A- (7.0) | B+ (6.0) |
Nicaragua
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Licenciatura (4 year) | 90% | 80% | 70% |
Nigeria
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 7 point Scale | 6 | 5 | 3.0 (on 5 point scale) |
| 5 point scale | 4 | 3.4 | 2.7 |
| 4 point scale | 3.5 | 3 | 2.5 |
Norway
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Norway | A / 1.8 | B / 2.3 | C / 3.0 |
Oman
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| GPA 4.0 scale | 3.5 | 3.0 | 2.5 |
Pakistan
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 4 Year degree only (the higher of the 2 options) | A- or GPA 3.7 | B or GPA 3.0 | C+ or GPA 2.6 |
| 2 or 3 year Bachelor plus Masters | 1st (60%) plus GPA 3.7 | 2nd (55%) plus GPA 3.0 | 2nd (50%) plus GPA 2.6 |
Palestine
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Bachelor (4-years) | (85%) 3.5 | (80%) 3.0 | (70%) 2.5 |
Panama
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 4 Year Licenciado / Título de [subject area] | 91 (A) | 81 (B) | 71 (C) |
Papua New Guinea
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Bachelor (Honours) Degree | 1st | 2:1 | 2:2 |
Paraguay
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 4 Year Título de Licenciado / Título de [subject area] | 4.5 (85%) | 4 (80%) | 3.5 (75%) |
Peru
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 4 Year Título de Licenciado / Título de [subject area] | 14 | 13 | 12 |
Philippines
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Degree from prestigious state universities or Centres of Excellence (COE) | Summa Cum Laude 4.0 / 96% / 1.0 | Magna cum Laude 3.5 / 92% / 1.5 | Cum Laude 3.0 / 87%/ 2.0 |
Poland
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Bachelor Degree (post 2003) Magister (pre- 2003) | 5 | 4.5 | 4 |
Portugal
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Diploma de Estudos Superiores Especializados (DESE) or Licenciado | 18 | 16 | 14 |
Qatar
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| GPA 4.0 scale | 3.5 | 3.0 | 2.8 |
Romania
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Diploma de Licenta/ Diploma de Inginer | 9 | 8 | 7 |
Russia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Bakalavr/Specialist Diploma/Magistr | 4.5 | 4.0 | 3.5 |
Rwanda
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 4 year bachelor (Hons) degree (480 credits) | 1st, 16/20 (80%) | 2:1,14/20 (70%) | 2:2, 12/20 (60%) |
Saudi Arabia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| GPA 4.0 scale | 3.5 | 3.0 | 2.5 |
| GPA 5.0 scale | 4.5 | 3.75 | 3.0 |
Senegal
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Maitrise, Diplome d'Etude Approfondies, Diplome d'Etude Superieures or Diplome d'Etude Superieures Specialisees | 16/20 or Tres Bien | 14/20 or Bien | 12/20 or Assez Bien |
Serbia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Diplomirani/ Bachelor's degree | 9 | 8 | 7 |
Sierra Leone
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Honours degree or masters | 1st (70%) | 2:1 (60% or B) | 2:2 (50% or C) |
Singapore
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Bachelor (Hons) | First | Upper second | Lower second |
| GPA 4.0 scale | 3.7 | 3.0 | 2.7 |
| GPA 5.0 scale | 4.5 | 3.5 | 3.0 |
Slovakia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Bakalár (from 2005) Magister / Inzinier | 1.5 or B | 2.0 or C | 2.5 or C/high D |
Slovenia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| University Diplom | 9 | 8 | 7 |
South Africa
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Bachelor (Honours) or B Tech after 4 yrs study | 1st or 75% | 2:1 or 70% | 2:2 or 60% |
South Korea
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| GPA out of 4.5 | 3.8 / B+ | 3.2 / B | 2.8 / C+ |
| GPA out of 4.3 | 3.8 / B+ | 2.9 / C+ | 2.7 / C+ |
Spain
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Licenciado / Título de Ingeniero / Título de Arquitecto | 8.5 | 7 | 6.5 |
| UCM grading | 3.0 | 2.0 | 1.5 |
Sri Lanka
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 4 year Professional degree or Bachelor Special or Honours degree | 90%, GPA 3.70 | 80%, GPA 3.30 | 70%, GPA 3.0 |
Sudan
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 4 year degree | 1st, 70%, B+ | 2:1, 66% | mid 2:2, 60%, B |
Sweden
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Kandidatexamen or Magisterexamen | Overall grade of VG with a minimum of 120 credits at VG | B or Overall grade of VG with a minimum of 90 credits at VG | C or Overall grade of G with a minimum of 90 credits at G |
Switzerland
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Bachelor Degree, Diplom or Lizentiat (10/6/5) | 10 / 5.5 / 1 | 8 / 5 / 2 | 6 / 4 / 3 |
Syria
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| State universities 4 years of study | 80% | 70% | 60% |
| Private universities 4 years of study | 90% | 80% | 70% |
Taiwan
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 4 year degree | 76% 3.0 GPA |
70% 2.8 GPA |
65% 2.6 GPA |
Tajikistan
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Диплом специалиста - Specialist Diploma | 5 | 4.5 | 4 |
Tanzania
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Tanzania | 1st | 2:1 | 2:2 |
Thailand
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| GPA 4.0 scale | 3.2 | 2.8 | 2.6 |
Trinidad and Tobago
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| For degrees studied at The University of West Indies or degrees accredited by ACTT | 1st or GPA 3.6 | 2:1 or GPA 3.0 | 2:2 or GPA 2.5 |
Tunisia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Licence, Maîtrise, Diplôme National d'Ingénieu | 16 (tres bien) | 14 (bien) | 11 (assez bien) |
Turkey
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Lisans Diplomasi or a Műhendis Diplomasi | 3.3 | 2.9 | 2.4 |
Turkmenistan
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 4 Yr Bakalavr, Specialist Diploma or Magistr | 5 | 4.5 | 4 |
Uganda
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Uganda | 1st or 4.4 | 2:1 or 3.8 | 2:2 or 3.0 |
Ukraine
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Dyplom Magistra or a Bachelors degree (11 / 5) | 4.5 | 4.0 | 3.5 |
United Arab Emirates
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| GPA 4.0 scale | 3.5 | 3.0 | 2.6 |
United States of America
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| GPA 4.0 scale | 3.5 | 3 | 2.6 |
Uruguay
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Licenciado (4 year) | 9 | 8 | 7 |
Uzbekistan
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Majistr Diplomi / Diplomi (Specialist Diploma) | 90% or GPA 4.5 | 80% or GPA 4.0 | 70% or GPA 3.5 |
Venezuela
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Licenciado/Professional title. (4 year) | 18/20 or 8/9 | 16/20 or 7/9 | 14/20 or 6/9 |
Vietnam
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 10-point scale | 8.0 | 7.0 | 6.0 |
| 4-point scale | 3.2 | 2.8 | 2.4 |
Zambia
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| Master's | A or 4.0 or 80% | B+, 3.5 or 70% | B or 3.0 or 60% |
Zimbabwe
| First-class honours (70%) | Upper second-class honours (60%) | Lower second-class honours (50%) | |
|---|---|---|---|
| 3/4 year degree | 1st or 75% | 2:1 or 65% | 2:2 or 60% |
English language requirements
Applicants must meet the minimum English language requirements. Further details are available on the International website.
Fees and funding
Tuition fees for 2026-27 entry
UK fee
Fully funded Full-time degree per annum
International fee
Fully funded Full-time degree per annum
Fees for the 2026-27 academic year apply to projects starting in October 2026, February 2027 and July 2027.
Tuition fees cover the cost of your teaching, assessment and operating University facilities such as the library, IT equipment and other support services. University fees and charges can be paid in advance and there are several methods of payment, including online payments and payment by instalment. Fees are reviewed annually and are likely to increase to take into account inflationary pressures.
The studentship is for 3 years and provides a tax-free stipend of £21,805 per annum for the duration of the studentship plus university tuition fees.
Please note that studentships will be awarded on a competitive basis to applicants who have applied to this project and other advertised projects starting with advert reference ‘SCI26’ in the School of Science. Successful candidates will be informed during May 2026.
Funding for this studentship is awarded on a competitive basis and is not guaranteed; availability will depend on the outcome of the selection process and subject to final approval by the University.
How to apply
All applications should be made online. Under Campus, please select ‘Loughborough’ and select Programme ‘Mathematical Sciences’. Please quote the advertised reference number SCI26/MA/MM in your application.
To avoid delays in processing your application, please ensure that you submit the minimum supporting documents. The following selection criteria will be used by academic schools to help them make a decision on your application.
