Droplets Sit and Slide Anisotropically on Soft, Stretched Substrates

Anisotropically wetting substrates enable useful control of droplet behavior across a range of applications. Usually, these involve chemically or physically patterning the substrate surface, or applying gradients in properties like temperature or electrical field. Here, we show that a flat, stretched, uniform soft substrate also exhibits asymmetric wetting, both in terms of how droplets slide and in their static shape. Droplet dynamics are strongly affected by stretch: glycerol droplets on silicone substrates with a 23% stretch slide 67% faster in the direction parallel to the applied stretch than in the perpendicular direction. Contrary to classical wetting theory, static droplets in equilibrium appear elongated, oriented parallel to the stretch direction. Both effects arise from droplet-induced deformations of the substrate near the contact line.

Figure 1

Droplets slide anisotropically on stretched substrates. (a) Droplets sliding parallel to the stretch (red) direction move faster than those sliding in the perpendicular (purple) direction and have clearly different shapes. (b) Measured droplet positions vs time for sliding in the two different directions. This shows the average for 9 droplets sliding parallel to stretch and 7 droplets sliding perpendicular to stretch; $\epsilon =23\%$. Shaded areas indicate 1 standard deviation to either side of the average. Note that the speed is essentially constant during our observations. Droplets do not undergo a transition to fast, lubricated sliding, indicating that un-cross-linked silicone chains in the substrate do not play a role here [21].

Figure 2

Droplet shapes become elliptical on soft, stretched substrates. (a),(b) Brightfield (top) and interferometry (bottom) images for two droplets of different sizes, when the substrate is relaxed (left) and after 56% stretch (right). The stretch direction is indicated by the arrows. (c) There is no observable contact line hysteresis for droplets. Droplets are the same shape regardless of whether they are applied to a soft, stretched substrate before it is stretched (green) or after (yellow). The inset histograms show the alignment of droplets with the stretch direction. (d) Droplets are essentially round (to pixel resolution) on unstretched, soft silicone (red circles) and stretched, stiff silicone (purple diamonds). The blue data show droplet shapes on soft silicone with a similar stretch for comparison. (e) $l-w$ for glycerol droplets on soft silicone substrates increases with droplet size and stretch. The inset histograms show the alignment of droplets with the stretch direction. (f) The data from (e) collapses onto a single curve, when each dataset is divided by the average slope $\alpha$ of the data for $(l+w)/2<20\mu \mathrm{m}$. The inset shows this collapse parameter $\alpha$ as a function of $\epsilon$.

Figure 3

The surface profile under a droplet on a stretched substrate ($\epsilon =60\%$) is very asymmetric. We measure the height profile of fluorescent nanobeads on the surface of the silicone gel under a glycerol droplet with confocal microscopy (e.g., Ref. [15]). The color is an interpolated surface profile.