Mathematical modelling of diffusion-driven oxidation in metals

Lead Research Organisation: University of Manchester
Department Name: Mathematics


This industrially-sponsored project is aimed at providing a predictive quantitative description of the formation of a protective oxide layer on a metal surface. Oxidation in pure oxygen, pure moisture, and mixtures of the two (e.g. humid air) are of interest. The kinetic properties of these oxidation reactions have been studied extensively in the past, and a large number of models describing the rates of reaction have been proposed. However, with just a few notable exceptions, these models have been empirical by their nature rather than mathematical descriptions of plausible underlying physical mechanisms. Oxidation in the absence of moisture is dominated by migration of oxygen anions through the oxide substrate towards the metal, while in the presence of moisture it is likely that ionic diffusion of hydroxyl anions is the rate limiting step. The overall process is thus one of combined temperature- and time-dependent chemical and ionic diffusion within a growing substrate of variable composition. It is vital that the dominant physical mechanisms are well modelled to provide both qualitative understanding and a quantitative predictive capability for long-term material ageing.


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Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509565/1 01/10/2016 30/09/2021
1782145 Studentship EP/N509565/1 04/09/2016 31/03/2020 Monisha Natchiar Subbiah Renganathan
Description Metals corrode (oxidise) when placed in most environments of practical interest. The precise details of this corrosion process are fundamentally tied to the chemistry of the particular metal, the surrounding gas state, and how the ambient gas/air diffuses through the metal material. Although models are established for some choices of material and environment these tend to be empirical fits, and there remains a stark lack of (chemical/physical) mechanistic models that predict how uranium oxidises in air. For the first time, this work proposes such a model, which notably for moist-air ambient conditions predicts the presence of a thin propagating hydride layer, which arises as part of the oxidation -- such a thin layer has been very recently observed via novel experimental methods by other researchers.
Publications from this study:
1. Asymptotics of coupled reaction-diffusion fronts with multiple static and diffusing reactants: uranium oxidation in water vapour. (Published;

Publications that will result from this study:
1. Hydride prediction during late-stage oxidation of uranium in a water-vapour environment (In preparation).
2. Mathematical modelling of oxidation of uranium in dry air (In preparation).
Exploitation Route We have put forward a diffusion-reaction-advection model for the prediction of uranium corrosion in a variety of cases. This model relies on a small number of key (measurable) physical constants. Although some of these values can be approximated from existing empirical data, there is an opportunity to now focus future experiments on those values that are of most quantitative significance, as highlighted by the theory. The current approach provides guidance on the ranges of values to be expected for good agreement with measured data sets. Ultimately, this study combined with the relevant future studies will help the industry personnel to re-evaluate their safety standards as the material studied can be hazardous if its corrosion exceeds a certain limit. The mathematical modelling of the oxidation kinetics of this material under different environments will help the industry personnel understand the material ageing, and thereby put into place policies and procedures governing its storage and disposal.
Sectors Aerospace, Defence and Marine,Energy

Description This approach has developed new modelling skills for the industrial collaborator, which can be applied to models of materials ageing. This modelling approach can span a range of materials, but remain underpinned by the same fundamental physical modelling, and asymptotic simplifications developed for this particular sub-case. By increasing modelling capability, we reduce the need for costly experimental programmes, while continuing to meet operational and safety standards when using these materials.
Description Visit to University of Bristol (School of Physics) 
Form Of Engagement Activity A formal working group, expert panel or dialogue
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Schools
Results and Impact Discussion of the research done by me and by another PhD student from the University of Manchester (working on a related topic in the same field) with a research group in the School of Physics, University of Bristol headed by Prof. Tom Scott. The meeting was intended to identify areas of collaboration and sharing of research data between the groups. We had a detailed discussion of the potential areas of interaction and possible collaboration that could result. Ideas were exchanged between the groups on the current projects undertaken by each of the groups.
Year(s) Of Engagement Activity 2017