Spontaneous Droplet Motion on a Periodically Compliant Substrate

Droplet motion arises in many natural phenomena, ranging from the familiar gravity-driven slip and arrest of raindrops on windows to the directed transport of droplets for water harvesting by plants and animals under dry conditions. Deliberate transportation and manipulation of droplets are also important in many technological applications, including droplet-based microfluidic chemical reactors and for thermal management. Droplet motion usually requires gradients of surface energy or temperature or external vibration to overcome contact angle hysteresis. Here, we report a new phenomenon in which a drying droplet placed on a periodically compliant surface undergoes spontaneous, erratic motion in the absence of surface energy gradients and external stimuli such as vibration. By modeling the droplet as a mass-spring system on a substrate with periodically varying compliance, we show that the stability of equilibrium depends on the size of the droplet. Specifically, if the center of mass of the drop lies at a stable equilibrium point of the system, it will stay there until evaporation reduces its size and this fixed point becomes unstable; with any small perturbation, the droplet then moves to one of its neighboring fixed points.