Superhydrophobic frictions

Abstract

Contrasting with its sluggish behavior on standard solids, water is extremely mobile on superhydrophobic materials, as shown, for instance, by the continuous acceleration of drops on tilted water-repellent leaves. For much longer substrates, however, drops reach a terminal velocity that results from a balance between weight and friction, allowing us to question the nature of this friction. We report that the relationship between force and terminal velocity is nonlinear. This is interpreted by showing that classical sources of friction are minimized, so that the aerodynamical resistance to motion becomes dominant, which eventually explains the matchless mobility of water. Our results are finally extended to viscous liquids, also known to be unusually quick on these materials.

Keywords: dissipation; drops; friction; superhydrophobic; velocity.

Fig. 1.

Drops running down SH materials. (A) AFM picture of the material used in our experiments: x and y are the coordinates in the plane, and h is the depth. (B) AFM cross-sectional view along the red dotted line in A, around y = 200 nm. (C) Water drop descending a tilted SH plate in the regime where it reached its terminal velocity U = 66 cm/s. We superimpose colored images separated by 20 ms for a volume Ω = 100 µL, an equatorial radius R ∼ 3.7 mm and a tilt α = 2°. (See also Movie S1.) (D) Terminal velocity U of water–glycerol mixtures (Ω = 100 µL) as a function of their viscosity η. The tilt angle here is α = 2.3°, and the dashed line represents Eq. 3.

Fig. 2.

Mobility of viscous drops on SH materials tilted by an angle α. (A) Terminal velocity U as a function of the sine of α for a water–glycerol mixture with viscosity η ∼ 110 mPa∙s and Ω ∼ 100 µL (blue circles) or Ω ∼ 200 µL (red squares). (See also Movie S2.) (B) Terminal velocity U of viscous drops as a function of 1/η, the inverse of the viscosity, for α = 2.3° and Ω ∼ 100 µL. The linear fit (dashed line) has a slope of 3.35 mN/m.

Fig. 3.

Water drop mobility on SH inclines. In all plots, the drop volume is Ω = 100 μL, and dashed lines show Eq. 3. (A) Terminal velocity U as a function of the sine of the sliding angle α for water drops. (B) Terminal velocity U as a function of sinα for water drops in an atmosphere of air (light blue circles) or neon (red circles).