Mathematical Modelling of Rare Events in Nanoflows: A Feasibility Study

The 21st century has heralded a revolution in the miniaturisation of fluid-based technologies that parallels those achieved in electronics in the 20th century, with technologies on microfluidics length scales now fully commercialised (e.g. 3D printers). Naturally, focus has now turned to exploiting the tremendous potential of flows at the nanoscale (i.e. nanofluidics), where huge surface area to volume ratios create systems that are driven by surface/interfacial effects, so that tiny volumes of fluid can be manipulated in ways that are unimaginable at the scales we observe in our daily lives.

Our focus here is on the breakup of liquid volumes at the nanoscale, which are key to applications including nano-manufacturing (e.g. of thin-film solar cells), tear films and 'dry out' of the eye, bionic nano-devices for regenerative medicine and novel nano-particle drugs. Remarkably, at present, no scientific tools have been developed for these nanoflows as:
- Experimental techniques can only provide limited information, as the dynamics occur too fast.
- Theoretical approaches based on conventional fluid dynamics fail at the nanoscale, as thermal fluctuations ('noise' or 'Brownian motion') drive qualitatively new stochastic dynamics.

This feasibility study will explore a new mathematical approach to overcome these challenges based on new methods for rare events that were originally developed for quantum mechanics. If successful, this will provide a platform for a much broader programme of intra-/inter-disciplinary research into the mathematical modelling of practically relevant nano-systems that could put the UK at the forefront of this high-tech emerging area.