Free-decay and resonant methods for investigating the fundamental limit of superhydrophobicity

The recently demonstrated extremely water-repellent surfaces with contact angles close to 180° with nearly zero hysteresis approach the fundamental limit of non-wetting. The measurement of the small but non-zero energy dissipation of a droplet moving on such a surface is not feasible with the contemporary methods, although it would be needed for optimized technological applications related to dirt repellency, microfluidics and functional surfaces. Here we show that magnetically controlled freely decaying and resonant oscillations of water droplets doped with superparamagnetic nanoparticles allow quantification of the energy dissipation as a function of normal force. Two dissipative forces are identified at a precision of ~ 10 nN, one related to contact angle hysteresis near the three-phase contact line and the other to viscous dissipation near the droplet-solid interface. The method is adaptable to common optical goniometers and facilitates systematic and quantitative investigations of dynamical superhydrophobicity, defects and inhomogeneities on extremely superhydrophobic surfaces.