Effect of groove curvature on droplet spreading

Capillary transport of droplets through channels and tubes is a well known problem in physics. Many different behaviors and dynamics have been reported so far depending mostly on the geometry of the system. In nature, curved grooves are observed on water-transporting organs of self-watering plants. However, less attention has been dedicated to the curvature effects of the channel transporting the liquid. In this work, we focus on this aspect by experimentally studying droplet spreading on 3D printed grooves with different curvatures. We prove that the sign of the curvature has a major effect on the shape and droplet dynamics. In all cases, the spreading dynamics follow a power law x = ct. For a concave groove, called hypocycle, the power p = 1/3 and the prefactor c increases if the groove's radius decreases. For a convex groove, called epicycle, p = 1/2 and c is independent of the groove radius. Two models are proposed to describe the scaling laws. The spreading of a droplet is much faster inside an epicycle groove than in a hypocycle groove, opening ways to develop applications.