[Langmuir] Spontaneous Droplet Motion on a Periodic 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 is 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.
Tianshu Liu, Nichole K. Nadermann, Zhenping He, Steven H. Strogatz, Chung-Yuen Hui, and Anand Jagota Langmuir, Just Accepted Manuscript DOI: 10.1021/acs.langmuir.7b01414 Publication Date (Web): April 27, 2017 Copyright © 2017 American Chemical Society