PhD Studentship - Improving Continuum Modelling of Transport through Foams

The University of Manchester - Mathematics

Qualification Type:PhD Location:Manchester Funding for:UK Students, EU Students Funding amount:£20,780 - please see advert Hours:Full Time Placed On:26th February 2026 Closes:26th May 2026 Application deadline: All year round

Research theme: Applied Mathematics

How to apply: uom.link/pgr-apply-2425

This 3.5-year PhD project is fully funded and home students, and EU students with settled status, are eligible to apply. The successful candidate will receive an annual tax-free stipend set at the UKRI rate (£20,780 for 2025/26) and tuition fees will be paid. We expect the stipend to increase each year. The start date is October 2026.

We recommend that you apply early as the advert may be removed before the deadline.

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For 75 years, AWE has proudly played a role of critical national importance: helping deliver the UK’s nuclear deterrent. We are at the forefront of science, technology and innovation, protecting the UK and NATO allies from the most extreme threats to national security. AWE has pioneered advancements in areas including physics, engineering, materials science, and high-performance computing. Together we’ve helped shape the UK’s technological landscape, driving innovation that extends well beyond defence.

Foams are used across industries—from aerospace to packaging—providing cushioning during transit, thermal insulation, and structural reinforcement in a range of applications. However, the mechanisms underpinning transport and reactions within some of these materials are still not well understood and there is a lack of effective mathematical modelling. Therefore, significant efforts are being devoted to understanding possible mechanisms and their effective modelling, with the aim of predicting transport/reaction characteristics of foam materials. While it is often appropriate to model transport of inert mobile species through un-foamed polymers via a simple diffusion equation and Henry’s mode sorption model, complexities arise when foams and composite materials are considered, as well as non-inert mobile species such as water.

The PhD will focus on improving the mechanistic understanding of transport through foams, with the aim of increasing accuracy/reducing uncertainties associated with mathematical modelling approaches based on PDE (partial-differential equation) descriptions. It will also investigate how material structure and gas-material interactions result in continuum level mechanisms, and when they are expected to occur. This is vital in terms of being able to accurately simulate transport through materials and understanding when different mechanisms are expected to be important. The models produced by this PhD will be used to support: i) focusing experimental resource; ii) aiding with down-selection of candidate materials and iii) predicting material characteristics through their life.

This PhD will be structured by considering a collection of closely related sub-problems throughout the 3.5-year PhD, typically expecting to consider one topic area per year. Collectively, the work will progress the current continuum (PDE) models of ageing and compatibility for polymeric foams.

Applicants should have, or expect to achieve, at least a 2.1 honours degree or a master’s (or international equivalent) in a relevant science or engineering related discipline.

To apply, please contact the main supervisor; Prof Richard Hewitt - Richard.E.Hewitt@manchester.ac.uk. Please include details of your current level of study, academic background and any relevant experience and include a paragraph about your motivation to study this PhD project.