A thin layer of air, just a few millionths of a metre thick, can make raindrops bounce off each other instead of merging—and current computer models cannot predict when this happens. This Fellowship will build the first mathematical framework that can, by embedding the physics of these nanofilms into large-scale simulations. The problem is viciously multiscale: the same trapped gas that makes a droplet skate over a hot surface also governs whether cloud droplets collide and grow into rain. Existing computational fluid dynamics fails because it cannot resolve these submicron films, which generate powerful lubrication forces. If the models succeed, they will directly improve weather and climate prediction—extreme precipitation warnings can save lives and prevent financial damage. They will also help agricultural companies design crop sprays that reduce harmful drift, protecting biodiversity while maintaining food production. At its core, this is fundamental mathematical and computational science, connecting nanofluidics to cloud dynamics. Past work in this vein has reshaped entire fields; here, the payoff is a new ability to predict how trillions of droplets behave, from the espresso cup to the storm cloud.
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In our daily lives we routinely encounter small liquid drops; from the first shower of the day, through a rainy morning commute and onto the final drops of espresso completing a morning coffee. Usually, it is the interaction of these drops with other surfaces which concerns us – will the impacting drop bounce, merge, or shatter? The outcome is crucial to a spectacular range of processes, from the very small scale, where liquid drops form the building blocks of bespoke 3D-printed objects, up to to the vast scales on which clouds (composed of trillions of droplets) evolve. In the latter case, it is the collective interaction of droplets that dictates a cloud’s behaviour and thus impacts upon both weather and climate prediction. Remarkably, despite the existence of robust computational fluid dynamics (CFD) packages and rapid advances in experimental methods, predicting the outcome of droplet collisions remains a remarkably complex and currently-open problem. The complexity of drop collisions comes from the ubiquity of gas nanofilms, i.e. thin layers of fluid which are trapped between converging interfaces with a ‘height’ on the submicron scale, which usually cannot be resolved experimentally. These generate such strong lubrication forces that, for example, air nanofilms can cause water droplets to bounce from other droplets or to skate over solids. The effect is compounded by the presence of hot surfaces, held above the drop’s boiling temperature, which trigger the Leidenfrost effect, so that drops can bounce-off and levitate-on their own vapour film. It is the existence of flow-dictating nanofilms, that are governed by unconventional physics and create a viciously multiscale problem, that renders current CFD impotent. This Fellowship will develop the first framework capable of predicting droplet collision outcomes, their manipulation by complex environments and their collective effect on large-scale flows. To overcome fundamental flaws in existing modelling, it will harness and develop cutting-edge mathematical modelling techniques from scientific domains that are usually segregated. Our initial foci will be on how drop collision outcomes govern the dynamics of (i) clouds and (ii) sprays. For (i), we will collaborate with the leading meteorological services to improve models that affect both climate, i.e. the future of planet earth, and weather, where extreme precipitation warnings can prevent loss of life and financial damage. For (ii), we will work with a globally-prominent agricultural company on crop sprays, to ensure sustainable food whilst preserving biodiversity (that is damaged by ‘spray drift’). At its core, the fellowship will develop new mathematical and computational models embedded with nanofluidic information to understand the collision of droplets, their interaction with other free-surfaces and their collective behaviour. This will provide an injection of new ideas into a vibrant UK fluid dynamics scene and naturally stimulate new unforeseen connections between sub-fields therein. The Fellowship will drive and thrive-on naturally new collaborations across disciplinary boundaries that connect applied mathematics, experimentation and application; creating symbiotic feedback between these elements. Through partnerships and network-building activities, particularly workshops, it will build a new community of researchers, traditionally siloed at their own scales, ambitiously targeting crucial connections spanning from nanofilm to cloud dynamics.
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