Droplet splashing on curved substrates

Abstract

It is well-known that the propensity for an impinging droplet on a solid substrate to splash is affected by the droplet fluid properties, pre-impact dynamics, the surrounding gas dynamics, and substrate wettability. Understanding the conditions under which splashing occurs is crucial in natural and industrial situations (e.g. coating and inkjet printing), usually to prevent the formation of smaller droplets with indiscriminate trajectories and unwanted aerosolisation of fluid. In nature and applications, high-speed droplets often impact concave or convex substrates and particles (such as in spray drying), but the influence of substrate geometry on droplet splashing is not well understood. Previous experimental studies for droplets impacting spheres have generally considered wet substrates, either by design or because droplets impinged continuously leaving behind a thin and variable film of fluid, with contradictory results regarding the influence of curvature on the splashing threshold.
We present a high-speed imaging study of droplet impact onto curved substrates covering a wide range of Weber numbers, encompassing simple deposition through to corona splashing. The substrate was thoroughly dried between successive depositions. We consider a uniquely wide range of curved substrates, from spheres of radius on the order of 1mm, through flat substrates, to concave lenses. Two high-speed cameras positioned perpendicularly simultaneously captured the impact dynamics, enabling the effect of droplet-sphere alignment to be studied, and axisymmetry ensured when desired. The precision of our experiments enables the transition between simple deposition and splashing to be precisely delineated across the range of curvatures considered. We also examine the spreading dynamics post-impact, using image processing to extract contact angles during spreading (amongst other quantities) and consider a mathematical treatment of our experimental results to make progress towards uncovering the fundamental mechanism of splashing on curved substrates.