Droplets impinging on solid substrates are encountered in a plethora of scenarios, including inkjet printing, bounded sprays and natural phenomena (e.g. raindrops interaction). For low impact velocities, droplets tend to simply spread across substrates, before potentially retracting, whereas for higher impact velocities droplets splash, breaking-up into a number of satellite droplets. The propensity of a droplet to splash is also affected by the droplet fluid properties, other pre-impact dynamics (e.g. direction and droplet shape), the surrounding gas dynamics, and substrate adhesive/cohesive forces (wettability). Understanding the conditions under which splashing occurs is often important (in e.g. printing, coating and contamination), usually to prevent the formation of smaller droplets with indiscriminate trajectories and unwanted aerosolisation of fluid.
We assess the effect of geometry on droplet splashing, focusing on the effect of substrate curvature. Using high-speed imaging, we study a uniquely wide range of dry curved substrates, from (convex) spheres of radius order 1 mm, through flat substrates, to concave lenses, in addition to a wide range of impact velocities. The precision of our experiments enables the transition between simple deposition and splashing to be precisely delineated across the range of curvatures considered, with the precise effect of droplet-sphere alignment determined. We also examine the spreading dynamics post-impact using image processing, including contact angles, making progress towards uncovering the physical mechanism underpinning splashing on substrates with curvature.