Emergent Collective Motion of Self-Propelled Condensate Droplets

Recently, there is much interest in droplet condensation on soft or liquid or liquidlike substrates. Droplets can deform soft and liquid interfaces resulting in a wealth of phenomena not observed on hard, solid surfaces (e.g., increased nucleation, interdroplet attraction). Here, we describe a unique collective motion of condensate water droplets that emerges spontaneously when a solid substrate is covered with a thin oil film. Droplets move first in a serpentine, self-avoiding fashion before transitioning to circular motions. We show that this self-propulsion (with speeds in the $0.1–1\mathrm{mm}{\mathrm{s}}^{-1}$ range) is fueled by the interfacial energy release upon merging with newly condensed but much smaller droplets. The resultant collective motion spans multiple length scales from submillimeter to several centimeters, with potentially important heat-transfer and water-harvesting applications.

Figure 1

(a) Initial interdroplet attraction and coalescence on a cooled lubricated surface. (b) Coalescence and subsequent recondensation results in polydisperse droplet sizes. Scale bar is 2 mm. (c) Nonaxisymmetric menisci (dark regions around each droplet) as observed using reflection interference contrast microscopy. Scale bar is 0.1 mm. (d),(e) Time series for the two boxed regions in (b). Scale bars are 0.15 mm.

Figure 2

(a) Schematic and (b) IR imaging (2 mm scale bars) showing the self-propelled serpentine motion of condensate droplets on a cooled lubricated micropillar surface. Droplet size and position are tracked automatically using Hough transform [42]. Increase in (c) displacement and (d) radius with time for droplet A for the first 12 m of motion. $t=0\mathrm{m}$ corresponds to the start of droplet A motion which occurs after 27 m of cooling.

Figure 3

(a),(b) Enlarged view of droplet with radius $R$ sweeping through neighboring droplets of much smaller mean radius $⟨r⟩$ and local area coverage ${\varphi }_l$. Scale bar is 1 mm. $t=0\mathrm{m}$ corresponds to start of the droplet serpentine motion. (c) Velocity $U_{\mathrm{L}}$ and (d) normalized velocity $U_{\mathrm{L}}/(\gamma /\eta )$ as a function of droplet radius $R$ on lubricated surfaces with different viscosities. Circles and squares represent fluorinated and silicone oils, respectively. We used nanotextured and micropillar surfaces for hot and cooled experiments, respectively.

Figure 4

Self-similar serpentine and circular motions of condensate droplets. (a) IR imaging of self-similar serpentine droplet motions on cooled substrate. Scale bars are 2 mm and 1 mm for main figure and inset. (b) Multiple circular motions coexist with serpentine motions for hot vapor condensates on nanotextured surface lubricated with silicone oil ($\eta =2\mathrm{mPa}.\mathrm{s}$). Clockwise and anticlockwise motions (indicated by full and dashed circles, respectively) appear with equal probability. Scale bar is 2 mm. (c) Clockwise circular motion for one droplet ($R=0.5\mathrm{mm}$) in (b).