Substrate curvature affects droplet splashing thresholds

Understanding the conditions under which droplets splash when impacting dry substrates is crucial in a variety of 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 potentially-hazerdous fluids. Whilst splashing propensity is known to depend on various parameters, including droplet fluid properties, the surrounding gas dynamics, and substrate wettability, the influence of substrate geometry is not well understood. In our high-speed imaging study, we precisely delineate splashing thresholds for axisymmetric impacts across a wide range of dry curved substrates and impact conditions. By quantitatively assessing the post-impact spreading dynamics, including extracting dynamic contact angles, we propose a physical mechanism to underpin the curvature-induced modification of the splashing threshold seen. Under the framework of our proposed physical mechanism, we present a consistent parameterization of the threshold observed across the whole range of concave, flat, and convex substrates studied.