Droplet motion driven by humidity gradients during evaporation and condensation

The motion of droplets on solid surfaces in response to an external gradient is a fundamental problem with a broad range of applications, including water harvesting, heat exchange, mixing and printing. Here we study the motion of droplets driven by a humidity gradient, i.e. a variation in concentration of their own vapour in the surrounding gas phase. Using lattice-Boltzmann simulations of a diffuse-interface hydrodynamic model to account for the liquid and gas phases, we demonstrate that the droplet migrates towards the region of higher vapour concentration. This effect holds in situations where the ambient gradient drives either the evaporation or the condensation of the droplet, or both simultaneously. We identify two main mechanisms responsible for the observed motion: a difference in surface wettability, which we measure in terms of the Young stress, and a variation in surface tension, which drives a Marangoni flow. Our results are relevant in advancing our knowledge of the interplay between gas and liquid phases out of thermodynamic equilibrium, as well as for applications involving the control of droplet motion.