Droplet Friction on Superhydrophobic Surfaces Scales With Liquid-Solid Contact Fraction

It is generally assumed that contact angle hysteresis of superhydrophobic surfaces scales with liquid-solid contact fraction, however, its experimental verification has been problematic due to the limited accuracy of contact angle and sliding angle goniometry. Advances in cantilever-based friction probes enable accurate droplet friction measurements down to the nanonewton regime, thus suiting much better for characterizing the wetting of superhydrophobic surfaces than contact angle hysteresis measurements. This work quantifies the relationship between droplet friction and liquid-solid contact fraction, through theory and experimental validation. Well-defined micropillar and microcone structures are used as model surfaces to provide a wide range of different liquid-solid contact fractions. Micropillars are known to be able to hold the water on top of them, and a theoretical analysis together with confocal laser scanning microscopy shows that despite the spiky nature of the microcones droplets do not sink into the conical structure either, rendering a diminishingly small liquid-solid contact fraction. Droplet friction characterization with a micropipette force sensor technique reveals a strong dependence of the droplet friction on the contact fraction, and the dependency is described with a simple physical equation, despite the nearly three-orders-of-magnitude difference in liquid-solid contact fraction between the sparsest cone surface and the densest pillar surface.