Droplet splashing on curved substrates

Droplets impacting dry solid substrates often splash above a certain threshold impact velocity. We hypothesise that substrate curvature alters splashing thresholds due to a modification to the lift force acting on the lamella at the point of breakup. We have undertaken high-speed imaging experiments of millimetric droplets impacting convex and concave surfaces to establish splashing thresholds and dynamics across a wide range of substrate geometries and impact conditions. Our findings indicate that the tendency of droplets to splash is proportional to the reciprocal of the substrate's radius of curvature, independent of whether the substrate is convex or concave, with it being harder for droplets to splash on small spheres. Moreover, we consistently parameterise the axisymmetric splashing threshold across all curved substrate geometries via a modification to the well-known splashing ratio. Finally, the splashing dynamics resulting from initial asymmetry between the impacting droplet and curved substrate are also elucidated.