Droplet impact and the transition to splashing

Thesis

Droplet impact onto a variety of surfaces is a familiar everyday experience: from a dripping tap to spray painting or droplets ejected during a sneeze. An underappreciated question, but often of great importance, is what happens to the droplet after impacting a surface, be it solid or another liquid. For sufficiently high speed impacts the droplet can break up into several smaller droplets in what we define as a splash. In the case of impact onto a liquid pool the pool itself can be sufficiently deformed such that it breaks up into droplets meaning there could be a splash originating from either droplet or pool.

Whether or not a droplet impact results in a splash is often a consequence of the very early time dynamics. What happens in these earliest times is of great importance to understanding and potentially even predicting the outcome of the impact. Whilst some insights have been found for the case of impact onto smooth flat solids the dynamics are much more intricate in the more complex cases considered here.

In this thesis we investigate the early time dynamics of droplet impact onto liquid pools, curved solids, and liquid films floating on pools using a combination of high speed imaging experiments, high resolution direct numerical simulations, and mathematical modelling. First we analyse the early time motion of the common interface between an impacting droplet and a liquid pool. Building upon previous results that only considered the case of identical liquids to a general multi-fluid case we find an explicit equation for the speed of the interface. Furthermore, we extend this to the case of a floating film on top of a deep pool, investigating the motion of both the upper droplet-film interface and the lower film-pool interface.

We then investigate the variation of the threshold to splash in two different cases. The first case is the impact of a droplet onto a deep immiscible viscous pool to examine how the splashing threshold depends on the pool viscosity. We identify two different regimes where the splashing threshold shows a different variation with the pool viscosity. Applying the earlier result (penetration speed) we explain the observations and derive an equation for the splashing threshold in the case of high pool viscosity, as well as the composition of the splashed liquid. Finally we investigate the impact of a droplet onto both concave and convex curved surfaces, finding a consistent change in the splashing threshold for both cases, and explaining these results in the context of recent theoretical models.

Authors: Fudge, BD

• DOI: 10.5287/ora-4rrnrm62e
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Language: English
• Keywords: droplet impact; basilisk; experimental fluid dynamics; fluid dynamics; computational fluid dynamics
• Subjects: Computational fluid dynamics; Drops; Fluid dynamics