Ewch i’r prif gynnwys

Numerical modelling of non-Newtonian rising bubbles

This research project is available as part of the EPSRC Doctoral Training Partnership (DTP). Find out more information about the DTP and how to apply.

Start date: 1 October 2019

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 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.

Project aims and methods

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 supervisory team has extensive experience in computational fluid dynamics (CFD) and a proven track record in all key elements of the project. The main supervisor and joint main supervisor have published over 30 and 70 journal papers respectively on developing, testing and applying advanced CFD methods for engineering applications (see publications). The joint main supervisor is an expert in non-Newtonian fluids and is also the President of British Society of Rheology. He is also the Fellow for the Institute of Mathematics and Its Applications, the Learned Society of Wales. The additional co-supervisor is the Director of our CDT Centre at Cardiff.  All these will help the student to complete within 3.5 years.

You will receive training courses and develop following key knowledge and skills in:

  • knowledge of fluid mechanics, rheology and complex fluids
  • knowledge of applied mathematics and numerical methods
  • experience in developing models, numerical tools, and writing computer programs to implement numerical methods to solve partial differential equations
  • numerical skills for scientific computing by using high performance computing cluster Supercomputing Wales (one of the largest supercomputers in the UK).

This project is multidisciplinary research and will enable you to develop a broad range of areas of interest during the PhD study. Opportunities for collaboration with numerical experts (at Imperial College London, University of Cambridge and University College London) and experimental collaborators (at Chinese State Key Laboratories) will be available during the project. You will gain research experience and collaborations through regular meetings/workshops in the School and within GW4 programmes, as well as national and international conferences such as: Annual Meeting of the American Physical Society Division of Fluid Dynamics, International Conference on Multiphase Flows, Annual Meeting of The Society of Rheology, International Congress of Theoretical and Applied Mechanics.


Zhihua Xie

Dr Zhihua Xie

Lecturer - Teaching and Research

+44 (0)29 2087 9375
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Yr Athro Tim Phillips

Head of School

+44 (0)29 2087 4194


Professor Shunqi Pan

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