Stability of Soap Films and Foams (WHITTAKERR2_U26EMP)

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 us 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 ad-hoc mechanics of the Plateau border were added too.

Theoretical results were compared with simulations conducted using the 'Surface Evolver' software. In this project you will continue the 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