PhD Studentship: Mathematical and Computational Modelling of Diffusion-Driven Material Ageing

This 3.5 year project is funded by an external industrial sponsor. Tuition fees will be paid and you will receive a tax free stipend set at the UKRI rate (£18,622). This is for home students only.

This project will consider systems of reaction-advection-diffusion equations both computationally and analytically. These find application to modelling corrosion/ageing in materials, where diffusion of a reactant into the bulk material and its subsequent reaction leads to the growth of unwanted corrosion products. The project will therefore contribute tools and techniques that support material ageing and compatibility models, considering physical processes such as diffusion, solubility and corrosion site nucleation and growth.

For example, when uranium is exposed to hydrogen, the hydrogen diffuses through a protective (thin) oxide surface layer into the bulk material. Once the hydrogen concentration exceeds a critical value in the bulk, hydride sites will begin to nucleate and grow. Eventually these nucleated sites can grow sufficiently large that they rupture through the oxide layer, further facilitating the flow of more hydrogen into the bulk.

Attempts to model this phenomenon often rely on deterministic partial differential equation (PDE) based methods. Whilst these methods can quickly and accurately simulate some aspects of the reaction, they cannot directly account for the stochastic nucleation process. Alternatively, a global stochastic simulation can deal with nucleation, but is currently prohibitively slow to apply to larger domains (i.e. of the order of cm). The first aim of the project is thus to seek efficiencies in the modelling, perhaps by considering a hybrid deterministic-stochastic approach, whilst attempting to validate/fit the model against available data.

Further aims of the project include:

• Continued development of existing mathematical models of corrosion/ageing.
• Development of models of reactive transport through polymer foams.
• Development of a model of competitive solubility when a polymer is exposed to a range of gases.

Relevant skills:

• Mathematical modelling, continuum mechanics, analytical and computational approaches to partial differential equations.

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.

Before you apply please contact the supervisor, Prof Richard Hewitt: richard.hewitt@manchester.ac.uk

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