The motion of a liquid droplet over a solid surface is a process that is commonly observed, for instance, with water dew on plant leaves or rain drops on a car's windshield. These scenarios are incredibly easy to visualise, yet, they are inherently complicated to study due to the competition of effects that operate across multiple scales and in the vicinity of the solid/liquid/vapour contact line. The understanding of such phenomena is crucial for the development of many technologies, such as within self-cleaning surfaces, DNA analysis, printing applications, hydrogen fuel cells, desalination and water harvesting systems for arid regions across the planet. Many of these technologies are developed based on intuition derived from an amalgamation of laboratory experiments, mathematical modelling, and computer simulations. Although impressive progress has been made in both software/algorithms and hardware, computer simulations may require days to complete on supercomputers, even when investigating relatively simple cases.

The combination of mathematical and data-driven modelling approaches can constitute an effective tool for the development of low-order, surrogate models, as a means to mitigate the computing requirements, and, importantly, to enhance our understanding of the key physics that drive droplet motion. In this project, the synergies between applied mathematical analysis, data-driven modelling approaches and large-scale simulations will be explored for wetting phenomena.

The development of novel modelling and computational tools in the form of open-source software will allow us to enhance our fundamental understanding of how to control droplet transport in complex environments, to investigate several industrially relevant scenarios, aspiring to contribute towards a more cost-effective development of new technologies and the optimisation of existing ones.