Droplet spreading on a two-dimensional wicking surface

The dynamics of droplet spreading on two-dimensional wicking surfaces were studied using square arrays of Si nanopillars. It was observed that the wicking film always precedes the droplet edge during the spreading process causing the droplet to effectively spread on a Cassie-Baxter surface composed of solid and liquid phases. Unlike the continual spreading of the wicking film, however, the droplet will eventually reach a shape where further spreading becomes energetically unfavorable. In addition, we found that the displacement-time relationship for droplet spreading follows a power law that is different from that of the wicking film. A quantitative model was put forth to derive this displacement-time relationship and predict the contact angle at which the droplet will stop spreading. The predictions of our model were validated with experimental data and results published in the literature.

Figure 1

(a) SEM picture of Si nanopillars. Scale bar represents 2 μm. (b) Schematic diagram of setup employed to track droplet spreading over time.

Figure 2

(a) Top view and (b) side view a droplet spreading on a 2D wicking surface. The solid arrow points to the droplet while the dashed arrow points to the wicking film. Scale bar represents 1 mm. (c) Representative plot of $a$ vs $t$ for the droplet edge and wicking front. The vertical dashed line marks $t$ = 10 ms and the green curve represents the function $a$ ∝ t${}^{1/2}$.

Figure 3

Schematic diagram showing a droplet spreading on a wicking film imbibed between the nanopillars. The sides, but not the top, of the nanopillars are wetted by the wicking film. The size of the precursor film has been exaggerated for clarity.

Figure 4

Plots of Eq. (5) (solid lines) and Eq. (6) (dashed lines) for various values of θ. Experimental data (for θ = 56.3°) are plotted as diamonds.

Figure 5

(a) A representative plot of $t$ versus $X$. (b) Plot of gradient, 3μ/δγ, versus $r$. Dashed line shows the average value of the data points.

Figure 6

Plot of $a$ vs $t$. The different lines show the binomial approximation in Eq. (9) carried out to different number of terms respectively.