How nanorough is rough enough to make a surface superhydrophobic during water condensation?

Nanostructured surfaces which manifest superhydrophobic properties during water condensation have a potential to dramatically enhance energy efficiency in power generation and desalination systems. Although various such surfaces have been reported, their development has been fortuitous, not driven by an understanding of the underlying physical processes. In this work, we perform a comprehensive study of microscale water condensation dynamics on nanostructured superhydrophobic surfaces made using a variety of synthetic methods. We demonstrate that the growth mechanism of individual water microdroplets on these surfaces is universal and independent of the surface architecture. The key role of the nanoscale topography is confinement of the base area of forming droplets, which allows droplets to grow only through contact angle increase. The nearly spherical droplets formed in this fashion become highly mobile after coalescence. By comparing experimentally observed drop growth with interface free energy calculations, we show that the minimum observed confined microdroplet base diameter depends directly on the nanoscale surface roughness and degree of interfacial wetting. Specifically, we show that the microscale condensation mechanism depends on the height of a liquid film with volume equal to the fill volume between the nanostructures. This introduced roughness length scale is a universal metric that allows for facile comparison of arbitrarily complex surface architectures. We use this new fundamental insight to develop quantitative design guidelines for superhydrophobic surfaces intended for condensation applications.