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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. [ABSTRACT FROM AUTHOR]

Superhydrophobicity plays a pivotal role in numerous applications. Recently, we have demonstrated the potential of auxetic metamaterials in creating superhydrophobic materials with unique wetting properties. However, the superhydrophobic properties are lost when the liquid penetrates into the surface structure. Understanding the conditions for droplet penetration is crucial for advancing wetting control. Here, we experimentally identify the transition from droplet suspension to full-penetration on an auxetic bowtie/honeycomb lattice membrane. We develop a comprehensive physical model surface representing different states of strain, ranging from auxetic to conventional lattice membranes, and consider the wetting as the liquid surface tension is varied using water/ethanol mixtures. By examining the interplay between contact angle and lattice structure, we gain valuable insights into the conditions for droplet suspension and full-penetration. Additionally, we develop a simple touch test to discern whether a droplet has effectively fully penetrated the structure, providing a practical and efficient means of distinguishing the different wetting states (suspended or partially penetrating vs fully penetrating). [ABSTRACT FROM AUTHOR]

The breakup of a slender filament of liquid driven by surface tension is a classical fluid dynamics stability problem that is important in many situations where fine droplets are required. When the filament is resting on a flat solid surface which imposes wetting conditions the subtle interplay with the fluid dynamics makes the instability pathways and mode selection difficult to predict. Here, we show how controlling the static and dynamic wetting of a surface can lead to repeatable switching between a toroidal film of an electrically insulating liquid and patterns of droplets of well-defined dimensions confined to a ring geometry. Mode selection between instability pathways to these different final states is achieved by dielectrophoresis forces selectively polarising the dipoles at the solid-liquid interface and so changing both the mobility of the contact line and the partial wetting of the topologically distinct liquid domains. Our results provide insights into the wetting and stability of shaped liquid filaments in simple and complex geometries relevant to applications ranging from printing to digital microfluidic devices. [ABSTRACT FROM AUTHOR]