Actuating water droplets on liquid infused surfaces: A rickshaw for droplets

We investigate the dynamics of millimeter-sized droplets moved on a liquid infused surface. The motion of the droplet is driven by a small spherical bead, whose trajectory is precisely controlled, which acts as a carrier. We first characterize the strength of the contact that maintains the adhesion between the droplet and the bead as a function of the ratio $R/r$ of their radii. When the bead is moved at a fixed velocity, the droplet follows its trajectory until a critical value of the velocity is reached at which the bead and the droplet lose contact. The critical velocity is rationalized as a balance between the capillary contact force and the friction acting on the droplet where it is in contact with the substrate. Experimental results are in good agreement with the model proposed. This study highlights a very efficient actuation method for millimetric droplets.

Figure 1

(a) Representation of the system on an inclined plane. Two images taken from above in the reference frame of the substrate for $\theta =0$ (b) and at the critical inclination ${\theta }_c$ (c), respectively ($r=0.5$ mm and $R=2$ mm).

Figure 2

$K$ analysis in experiments and simulation. (a) $sin\left({\theta }_c\right)$ as a function of $R^{-3}$ in experiments for beads of radius 0.5 (black circles), 1 (red squares), and 1.5 mm (green diamonds). Proportionality relations are displayed by solid lines. (b) Same data with $sin\left({\theta }_c\right)$ as a function of $\gamma r/\rho g{R}^3$ with $\gamma =55$ mN ${\mathrm{m}}^{-1}$. (c) Snapshots from the simulation for $\theta =0^{\circ }$ and ${42}^{\circ }$, respectively. (d) $K$ as a function of $r/{\lambda }_c$ for both experiments and simulations. In simulation, each point corresponds to one value of $r/{\lambda }_c$ and roughly 100 values of $R/{\lambda }_c$, whose effect is quantified by the error bars.

Figure 3

(a) Rotating setup designed to determine the critical velocity. (b) Snapshots taken for two velocities (the lower one is taken just prior to detachment). (c) Critical velocity $V_c$ as a function of $R/r$. Inset: log-log scale. The solid line is a power-law interpolation (exponent $-3/2$, prefactor 0.85 $\mathrm{m}{\mathrm{s}}^{-1}$).

Figure 4

Image sequence of a complex trajectory performed by a millimetric droplet. The circuit has a figure of eight shape and its length of about 10 cm is traveled in about 2 s. See movies in the Supplemental Material [45].