Geometry-driven jets underlie dispersal of plants and fungi by raindrops

The impact of droplets on concave surfaces is poorly understood, although it is relevant to a mode of dispersal of reproductive units that has evolved independently in several species of plants and fungi. This mode of dispersal relies on splash-cups, specialized organs that use raindrops to disperse reproductive units away from the parent organism. We investigated the impact of droplets on conical cavities that mimic splash-cups. We observed the formation of two types of jets, lateral and upward, which appear relevant to dispersal in plants and in fungi, respectively. We built a minimal kinematic model that explains jet formation, involving the motion of fluid particles along geodesics that geometrically focus on the cone surface. We used this model to predict cup angles that optimize jet formation and obtained two separate maxima for lateral and upward jets consistent with the geometries of natural splash-cups. Altogether, our work provides a geometric framework to study impact of droplets on nonflat surfaces and illustrates physical constraints underlying plant and fungal morphogenesis.