How water droplets evaporate on a superhydrophobic substrate

Evaporation of water droplets on a superhydrophobic substrate, on which the contact line is pinned, is investigated. While previous studies focused mainly on droplets with contact angles smaller than 90${}^{°}$, here we analyze almost the full range of possible contact angles (10${}^{°}$–150${}^{°}$). The greater contact angles and pinned contact lines can be achieved by use of superhydrophobic carbon nanofiber substrates. The time evolutions of the contact angle and the droplet mass are examined. The experimental data are in good quantitative agreement with the model presented by Popov [Phys. Rev. E 71, 036313 (2005)], demonstrating that the evaporation process is quasistatic, diffusion-driven, and that thermal effects play no role. Furthermore, we show that the experimental data for the evolution of both the contact angle and the droplet mass can be collapsed onto one respective universal curve for all droplet sizes and initial contact angles.

Figure 1

Side view (a) and top view (b) of a 8 $\mu$L droplet on a CNF substrate in the initial moments. Parts (c) and (d) show the same droplet in the last moments before being completely evaporated. Note that the contact line remains perfectly circular and completely pinned until almost the end of the process.

Figure 2

Scanning electron microscopy (SEM) images of the CNFs used as superhydrophobic substrates. Tilted side view (left) and augmented top view (right).

Figure 3

(a) Droplet volume vs time for initial droplet volumes of 1.6 $\mu$L (blue filled circles), 2.1 $\mu$L (red squares), 2.9 $\mu$L (green diamonds), 4.6 $\mu$L (magenta upward triangles), 6.2 $\mu$L (cyan downward triangles), and 6.9 $\mu$L (brown unfilled circles). The error bars are deduced from the elliptical fit to the data. The measurements were performed with a time resolution of 1 s, but for clarity we show the data with a 30-s resolution. (b) The dimensionless droplet mass plotted against the dimensionless time. The black solid line represents the theoretical prediction according to the Popov model. The experimental data are scaled according to (6). The time is set to 0 at the end of the droplet life (see text).

Figure 4

(a) The rate of mass loss of the droplet (derived from the measured droplet volume) vs the contact angle. Colors and markers are as in Fig. 3. (b) The same data, but now scaled according to (6). Predictions from the Popov model (black solid line) and the model of Hu and Larson (purple dashed line) are shown.

Figure 5

(a) The evolution of the contact angle over time. The experimental data ($•$) can be described very well by the theoretical model of Popov (—) by adjusting the drop radius according to its experimental value (see Sec. 5). The error in the experimental data is not shown, since it is below 1$\%$. (b) The same data, but with the time scaled according to (6), and set to 0 at the end of the droplet life (see text). The black solid line represents the theoretical prediction according to the Popov model. Colors and markers are as in Fig. 3.

Figure 6

The droplet radius vs time. Significant depinning of the contact line is observed during the final 4% of the droplet lifetime. Data are shown with 15-s time resolution. During the depinning, a resolution of 5 s is used. Colors and markers are as in Fig. 3.