Probing the physical origins of droplet friction using a critically damped cantilever

Previously, we and others have used cantilever-based techniques to measure droplet friction on various surfaces, but typically at low speeds U < 1 mm s^-1; at higher speeds, friction measurements become inaccurate because of ringing artefacts. Here, we are able to eliminate the ringing noise using a critically damped cantilever. We measured droplet friction on a superhydrophobic surface over a wide range of speeds U = 10^-5-10^-1 m s^-1 and identified two regimes corresponding to two different physical origins of droplet friction. At low speeds U < 1 cm s^-1, the droplet is in contact with the top-most solid (Cassie-Baxter), and friction is dominated by contact-line pinning with F_fric force that is independent of U. In contrast, at high speeds U > 1 cm s^-1, the droplet lifts off the surface, and friction is dominated by viscous dissipation in the air layer with F_fric ∝ U^2/3 consistent with Landau-Levich-Derjaguin predictions. The same scaling applies for superhydrophobic and underwater superoleophobic surfaces despite their very different surface topographies and chemistries, i.e., the friction scaling law derived here is universal.