Droplet motion on designed microtextured superhydrophobic surfaces with tunable wettability

Superhydrophobic surfaces have shown promising applications in microfluidic systems as a result of their water-repellent and low-friction properties over the past decade. Recently, designed microstructures have been experimentally applied to construct wettability gradients and direct the droplet motion. However, thermodynamic mechanisms responsible for the droplet motion on such regular rough surfaces have not been well understood such that at present specific guidelines for the design of tunable superhydrophobic surfaces are not available. In this study, we propose a simple but robust thermodynamic methodology to gain thorough insight into the physical nature for the controllable motion of droplets. On the basis of the thermodynamic calculations of free energy (FE) and the free-energy barrier (FEB), the effects of surface geometry of a pillar microtexture are systematically investigated. It is found that decreasing the pillar width and spacing simultaneously is required to lower the advancing and receding FEBs to effectively direct droplets on the roughness gradient surface. Furthermore, the external energy plays a role in the actuation of spontaneous droplet motion with the cooperation of the roughness gradient. In addition, it is suggested that the so-called "virtual wall" used to confine the liquid flow along the undesired directions could be achieved by constructing highly advancing FEB areas around the microchannels, which is promising for the design of microfluidic systems.