Radu Cimpeanu

From bouncing to making a splash: Mathematical modelling of liquid impact

Whether we notice them or not, phenomena related to liquid impact are commonplace in our daily lives - from falling raindrops to manufacturing processes, from smart printing applications to aircraft landing on water. This talk is dedicated to the mathematics of impact and fluid-structure interaction in this context, as well as the impact of the mathematics in question.

We will start with the canonical system of a millimetre-sized sphere impacting on the free surface of a quiescent bath, which can be propelled back into the air by capillary effects and dynamic fluid forces, whilst transferring part of its energy to the fluid. Experiments, simulations and asymptotic analysis reveal trends in the rebound metrics, uncover new phenomena at both ends of the Weber number spectrum, and collapse the datasets (Galeano-Rios et al., JFM 912, 2021). We then shift gears towards the much more violent regime of high-speed impact resulting in splashing, where a combination of matched asymptotic expansions grounded in Wagner theory and direct numerical simulations allow us to produce theoretical predictions for the location and velocity of the ejected liquid jet, as well as its thickness (Cimpeanu and Moore, JFM 856, 2019). While the early-time analytical methodology neglects effects such as surface tension or viscosity (focusing on inertia instead), corrections and adaptations of the technique (Moore et al., JFM 882, 2020) will also be presented and validated against an associated computational framework, bringing us even closer to efficiently providing information of interest for applications such as inkjet printing and pesticide distribution.

The last few minutes will be dedicated to lessons learned from interactions with commercial and industry partners in this wider area, touching upon the role of the modern applied mathematician in the current research landscape.