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Stability of Soap Films and Foams (WHITTAKERR_U23SF)

   School of Mathematics

About the Project

Foams, comprising thin liquid films surrounding many small gas bubbles, have many domestic and industrial applications. These often rely on properties such as a high interfacial area, surface activity and yield stress. Foams can also be used as proxies for the structure of more complicated biological systems. The structure of a foam is largely determined by the minimization of the interfacial surface area. For relatively dry foams, this is dominated by the surface films, but there is also a contribution from the joins – known as Plateau borders – between the surfaces.

In any application, the stability of the foam will be important. We may want to promote either a stable long-lived foam, or an unstable foam that quickly breaks down. Previous work by the supervisor and a collaborator has investigated the stability of a single twisted Plateau border. Initially, just the effects of the connected surfaces were considered, and then some simple mechanics of the Plateau border were added too. Theoretical results were compared with simulations conducted using the ‘Surface Evolver’ software.

In this PhD project you will investigation of the stability of foams using theoretical mathematical modelling techniques. The starting point will be to develop a model for the mechanics of the Plateau border, to correctly account for restoring forces in response to extension, bending and twisting. Further work will look at integrating models for a single Plateau border to determine the bulk stability properties of a whole foam.

For more information on the supervisor for this project, please visit the UEA website:

The start date is in October 2023.

Entry Requirements

An acceptable first degree in Mathematics (with significant fluid mechanics and/or modelling content). The standard minimum entry requirement is 2:1 (Hons).

Funding Notes

This PhD project is offered on a self-funding basis. It is open to applicants with funding or those applying to funding sources. Details of tuition fees can be found at View Website
A bench fee is also payable on top of the tuition fee to cover specialist equipment or laboratory costs required for the research. Applicants should contact the primary supervisor for further information about the fee associated with the project.


i) Instability of Stretched and Twisted Soap Films in a Cylinder, SJ Cox & SA Jones, 2014, Journal of Engineering Mathematics, 86, 1-7.
ii) Stability of a Helicoidal Surface Inside a Cylinder with Pinned Diameters, RJ Whittaker & SJ Cox, 2015, Quarterly Journal of Mechanics and Applied Mathematics, 68 (1), pp23–52.
iii) Stability of Twisted Plateau Border with Line Tension and Bending Stiffness, RJ Whittaker & SJ Cox, 2019, IMA Journal of Applied Mathematics, 84(2), pp385–415.
iv) The Surface Evolver, K Brakke, 1992. Experimental Mathematics, 1(2), pp 141-165.

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