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Numerical modelling of non-Newtonian rising bubbles

   Cardiff School of Engineering

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  Dr Z Xie, Prof T N Phillips, Dr S Pan  No more applications being accepted  Funded PhD Project (European/UK Students Only)

About the Project

The student will join in the Hydro-environmental Research Centre (HRC) at the Cardiff School of Engineering. HRC is internationally known for modelling of hydrodynamics, water quality and sediment transport processes in marine, coastal, estuarine waters and river basins, as well as the research on marine renewable energy,


The dynamics of bubbles rising in viscoelastic liquids are characterised by several interesting phenomena. Experimentally, an abrupt increase in the rise velocity of an isolated bubble occurs at a critical value of its volume, under creeping flow conditions. This ‘velocity discontinuity’, in most experiments involving shear-thinning fluids, has been associated with the change of the shape of the bubble to an inverted teardrop with a cusp at its pole and/or the formation of the ‘negative wake’ structure behind it. The interconnectivity of these phenomena is not fully understood yet, making the mechanism of the ‘velocity jump’ unclear. This project will seek to predict this phenomena and to determine a physical explanation.

The project will explore the use of several constitutive laws for viscoelastic fluids that incorporate either shear-thinning or constant viscosity behaviour. A sophisticated 3D computational model will be developed that will allow the trademark cusp at the trailing end of a rising bubble as well as the formation of a negative wake to be predicted to a high resolution. These phenomena cannot be predicted using simpler models that use the irrotational assumption.

The numerical discretization will be based on an adaptive unstructured mesh modelling framework, which can modify and adapt unstructured meshes to better represent the underlying physics of multiphase problems and reduce computational effort without sacrificing accuracy. The numerical framework consists of a mixed control volume and finite element formulation, a ‘volume of fluid’ type method for the interface capturing based on a compressive control volume advection method and a force-balanced algorithm for the surface tension implementation. Careful attention will be given to the choice of multiphase technique to be implemented to ensure that numerical stability is preserved.


The student will:

- Attend the Applied & Computational Mathematics seminar series in the School of Mathematics, the Young Professional Network seminar series organised by the HRC at the School of Engineering.

- Receive training on numerical skills and attend workshops with collaborators in the UK, such as Imperial College London, University of Cambridge and University College London.

- Spend some time abroad at well-known research centres in multiphase flows, such as the Multiphase Research Group at the University of Tokyo, the State Key Laboratories in China.


You should have obtained, or be about to obtain, a First or Upper Second Class UK Honours degree, or the equivalent qualifications gained outside the UK.

Applicants with a Lower Second Class degree will be considered if they also have a master’s degree. Applicants with a minimum Upper Second Class degree and significant relevant non-academic experience are encouraged to apply.

Funding Notes

Full awards, including the Tuition fee and maintenance stipend (Approx. £14,777 in 2018/19), are open to UK Nationals and EU students who can satisfy UK residency requirements. To be eligible for the full award, EU Nationals must have been in the UK for at least 3 years prior to the start of the course for which they are seeking funding, including for the purposes of full-time education.


Applications should be made online at:

Please note the following when completing your online application:

The Programme name is Doctor of Philosophy in Engineering with an October 2019 start date.

In the "Research proposal and Funding" section of your application, please specify the project title, supervisors of the project and copy the project description in the text box provided.

Please select “No, I am not self-funding my research” when asked whether you are self-funding your research.

Please quote “ZX-ECR-2019/20” when asked "Please provide the name of the funding you are applying for".
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