Drop dynamics on hydrophobic and superhydrophobic surfaces

We investigate the dynamics of micron-scale drops pushed across a hydrophobic or superhydrophobic surface. The velocity profile across the drop varies from quadratic to linear with increasing height, indicating a crossover from a sliding to a rolling motion. We identify a mesoscopic slip capillary number which depends only on the motion of the contact line and the shape of the drop, and show that the angular velocity of the rolling increases with increasing viscosity. For drops on superhydrophobic surfaces we argue that a tank treading advance from post to post replaces the diffusive relaxation that allows the contact line to move on smooth surfaces. Hence drops move on superhydrophobic surfaces more quickly than on smooth geometries.