Non-local interactions of elasto-capillary bridges

About the Project

Droplets are of fundamental scientific interest across a wide range of scientific disciplines and applications. For example, in fog harvesting, water is collected from the condensation of fog onto netting to provide water for local communities. Droplets also play a key role in nature, such as in the adhesion of insects to solid surfaces, which is mediated by an oily secretion produced under their feet. Better understanding of droplet behaviour can therefore unlock exciting new technologies in adhesion science, improvements in the utility and efficacy of manufacturing techniques, and comprehension of fundamental aspects of mechanics and biology.

A key force in these scenarios is surface tension, which becomes increasingly important at the small scales associated with droplets. When droplets of liquid contact soft solid materials, these forces can deform the solids. This phenomenon is called elasto-capillarity, and it has been exploited to create a whole range of novel physical behaviours, including causing water to climb against gravity in a vertical thin gap and clumping arrays of deformable pillars during the fabrication of microstructured surfaces.

The dynamics of individual droplets bridging between deformable solids have been well studied in recent years; however, questions remain over how these droplets interact. This project aims to study this using mathematical models of droplets to explore how multiple droplet bridges interact through surface deformations.

The project will involve mathematically modelling the interaction of multiple liquid bridges in a variety of settings, before adding further competing physical processes. The goal is to develop mathematical models that can quantify the dynamic interactions of these droplets in key scenarios, and extract practical principles for future applications.

The student will join an active and supportive cohort of PhD students within the Continuum Mechanics and Industrial Mathematics (CMIM) group in the Department of Mathematics and Statistics. There will be learning and training opportunities to support the student’s career development, as well as the opportunity to attend conferences and workshops.

Candidates are expected to be from a discipline with a high mathematical content. Knowledge of continuum mechanics, and mathematical methods for the solution of partial differential equations is desirable.

This project will start by 1st October 2026, and applications will be considered as they are received. Early application is strongly encouraged. Details on how to apply can be found here.

Funding Notes

The project is funded (Fees and Stipend) for 36 months commencing 1st October 2026.