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

Abstract

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.