A liquid droplet impacting a dry solid substrate may, among other outcomes, simply spread across the substrate, or break-up and emit smaller satellite droplets (splashing). Not only are the dynamics of splashing fascinating from a fundamental perspective, but understanding the conditions under which splashing occurs is crucial in applications including spray processes, forensics, and inkjet printing; especially in cases where the aersolisation of potentially-hazardous fluids is to be avoided, or surface-finish quality is important. The propensity of an impacting droplet to splash depends on various parameters, including droplet fluid properties, the surrounding gas dynamics, and wettability, but also substrate geometry.

In this talk, we present a high-speed imaging study (featuring both shadowgraph and colour images) of droplet splashing dynamics on dry curved substrates, including both convex and concave surfaces. We first establish the key parameters involved and use these to precisely delineate the splashing threshold across a wide range of curved substrates and impact conditions. A physical mechanism underpinning the splashing threshold observed will be proposed, leading to a modification of existing state-of-the-art splashing theory to account for substrate curvature. Hence, we attain a consistent parameterisation of the splashing threshold across the whole range of concave, flat, and convex substrates studied. Whilst the results described above pertain to axisymmetric impacts, we will also discuss the influence of introducing a horizontal offset between the impacting droplet and substrate apex, both in relation to the proposed physical mechanism and the potential for splash suppression in this way.