Condensate droplet roaming on nanostructured superhydrophobic surfaces

Abstract

Jumping of coalescing condensate droplets from superhydrophobic surfaces is an interesting phenomenon which yields marked heat transfer enhancement over the more explored gravity-driven droplet removal mode in surface condensation, a phase change process of central interest to applications ranging from energy to water harvesting. However, when condensate microdroplets coalesce, they can also spontaneously propel themselves omnidirectionally on the surface independent of gravity and grow by feeding from droplets they sweep along the way. Here we observe and explain the physics behind this phenomenon of roaming of coalescing condensate microdroplets on solely nanostructured superhydrophobic surfaces, where the microdroplets are orders of magnitude larger than the underlaying surface nanotexture. We quantify and show that it is the inherent asymmetries in droplet adhesion during condensation, arising from the stochastic nature of nucleation within the nanostructures, that generates the tangential momentum driving the roaming motion. Subsequent dewetting during this conversion initiates a vivid roaming and successive coalescence process, preventing condensate flooding of the surface, and enhancing surface renewal. Finally, we show that the more efficient conversion process of roaming from excess surface energy to kinetic energy results in significantly improved heat transfer efficiency over condensate droplet jumping, the mechanism currently understood as maximum.

Fig. 1. Roaming on solely nanostructured superhydrophobic surfaces.

a SEM image of the boehmite nanowalls coated with pPFDA, a solely nanostructured superhydrophobic surface. Scale bar: 2 µm. Left inset: Water droplet being deposited at 2 µL s⁻¹, and wettability measurements of the advancing contact angle (ACA), contact angle hysteresis (CAH), and the static contact angle (SCA). Scale bar: 1 mm. Right inset: SEM image of the nanowalls at higher magnification. Scale bar: 100 nm. b Schematic of the condensation and observation setup. $T$ and $p$ refer to temperature and pressure measurements respectively. Gravity $g$ is in the +z-direction. c Roaming event during vapour condensation on boehmite nanowalls coated with pPFDA. Yellow dashed lines enclose the main droplet. Red arrow indicates the approximate trajectory of the roaming event. Also see Supplementary Movie 1. Subcooling: 2.6 K. Gravity is downwards. Scale bars: 100 µm. d Participating droplets distribution for the in-plane (xz) roaming event in (c). The line represents the trajectory of the main droplet (red arrow in c). Inset: Evolution of the shape of the main droplet. Every contour is 0.4 ms apart. Source data are provided as a Source Data file.

Fig. 2. Characteristics of roaming events.

a Participating droplet distribution of 13 selected roaming events (indicated by different colours), at different locations of the surface. Roaming events do not repeatedly occur at the same location over time. b Main droplet trajectories corresponding to the events shown in (a). Squares indicate starting location of the events. All events progress in in-plane directions, independent of downward gravity. c Distance travelled by the main droplet for all the events. Initial roaming velocity 0.18 m s⁻¹. d Circularity $\left(=4\pi \left(\mathrm{area}/{\mathrm{perimeter}}^2\right)\right)$ and Feret ratio ($=\mathrm{maximumcaliperdiameter}/\mathrm{minimumcaliperdiameter}$) of the main droplet from the events. Both approach unity at ≈ 5 ms. Source data are provided as a Source Data file.

Fig. 3. Heat transfer performance of roaming condensation.

a Heat transfer coefficients $h$ at steady state. Lines of constant heat flux $q″$ are shown in grey, from 25 to 275 kW m⁻² at intervals of 50. For a fair test, the 7 subcooling achieved for each surface correspond to 7 identical cooler back end temperatures (Supplementary Information S2). On the superhydrophobic surface, two modes of condensation are observed. Measurements on pristine boehmite match closely with the Nusselt model for filmwise condensation. b Snapshots of condensation behaviour for superhydrophobic boehmite. Transition is seen from jumping dropwise to roaming condensation. At the lowest subcooling (0.7 K), only jumping is observed and there are numerous droplets in the vapour, with darker appearance and out-of-focus contour. These droplets in the vapour travel in one general direction to the bottom left due to steam flow (leftward) and gravity (downward). At 1.3 K, the number of jumped droplets in the vapour is visibly reduced, and some are seen to return to the surface. After the transition subcooling (1.5 K), condensation is dominated by roaming. Red arrows are trajectories of roaming events. Roaming droplets travel in all in-plane directions. See Supplementary Movie 5 for the corresponding video. Scale bars: 500 µm. c Surface area renewal rate $S\prime$ from roaming (unit: m² of surface area renewed per m² of condensing surface per second) and critical nucleation diameter $d_{\mathrm{crit}}$ for 30 mbar saturated steam (top). As transition to roaming occurs at ≈1.5 K, the critical nucleation diameter lies below most nanostructure cavity sizes (bottom). The sizes are obtained from the square root of the projected area of each cavity (Supplementary Information S11). d When subcooling is increased past the transition, condensate nucleates within the nanostructures. Microdroplets on top of these nanostructures could then exhibit different wetting states. The asymmetric adhesion gives rise to substantial tangential momentum upon coalescence. e The high surface area renewal rate of roaming enables abundant renucleation. Frequent roaming also assists droplet growth to the required size of gravitational removal. Source data are provided as a Source Data file.

Fig. 4. Generation of tangential momentum.

a Computational domain. Two droplets with diameter 160 µm are placed on a no-slip wall at $y=0$, specified with a contact angle. A symmetry plane is at $z=0$. b Contour plots of static gauge pressure at the symmetry plane. The entire base area of Droplet D1 is wetted. Vectors are velocities. Scale bars: 50 µm. Yellow reference velocity vector: 2 m s⁻¹. c Momentum ($p_{\mathrm{x}}$ and $p_{\mathrm{y}}$ on the left y-axis) and centre-of-mass displacement (${\mathrm{\Delta }x}_{\mathrm{cm}}$ and ${\mathrm{\Delta }y}_{\mathrm{cm}}$ on the right y-axis) in the x- and y-directions, for the case in which the base area of Droplet D1 is wetted and the case in which both Droplets D1 and D2 are in the Cassie state. d Maximum tangential momentum generated, $p_{\mathrm{x},\mathrm{gen}}=\max \left(∣p_{\mathrm{x}}∣\right)$, for varying wetted fractions of the base area of Droplet D1 (top), and the corresponding x-centre-of-mass displacement (bottom). In c and d, the momentum reported reflects full spherical droplets, taking domain symmetry into account. e Numerical model and simulation cases. (i) Simultaneous presence of droplets at different wetting states. (ii) To mimic the effect of wetted nanostructures, the contact angle for the base area of D1 is set to 2°. (iii) The size of the wetted area of D1 is varied, and the remaining base area of D1 is kept at 160°, the same as the outer surface. Source data are provided as a Source Data file.

Fig. 5. Dewetting in roaming.

a Contour plots of static gauge pressure at the symmetry plane after dewetting at 179 µs. Initially the entire base area of Droplet D1 is wetted, similar to Fig. 4b. Vectors are velocities. If the droplet had dewetted at a different time, the x-component of the resultant motion would have been different as well (dashed arrows, also see Supplementary Fig. 31b). Scale bars: 50 µm. Yellow reference velocity vector: 2 m s⁻¹. b Momentum ($p_{\mathrm{x}}$ and $p_{\mathrm{y}}$ on the left y-axis) and centre-of-mass displacement (${\mathrm{\Delta }x}_{\mathrm{cm}}$ and ${\mathrm{\Delta }y}_{\mathrm{cm}}$ on the right y-axis) in the x- and y-directions, for the case in which the original base area of Droplet D1 is subsequently dewetted at 179 µs, and the case in which it remains wetted. c (i) Kinetic energy of the translational motion of the centre of mass ${\mathrm{KE}}_{\mathrm{cm}}$ and the total kinetic energy ${\mathrm{KE}}_{\mathrm{tot}}$ for the two cases. The momentum and kinetic energy reported in b and c (i) reflect full spherical droplets, taking domain symmetry into account. c (ii) Schematic illustrating the symmetry breaking in jumping and roaming motions. When two droplets coalesce, the liquid body oscillates (numbered 1–4, 3 omitted in roaming for clarity). The interference with the surface breaks symmetry and generates momentum. In jumping, the liquid body leaves early and oscillates in the vapour. In roaming, the liquid body remains close to the surface. Oscillations interfere stronger with the surface repeatedly. The hinge then converts the symmetry breaking in the normal direction to a tangential direction. d Experimental observation of dewetting as roaming progresses. Coalescence is seen at 0.2 ms (Panel ii). Dewetting is seen at 1.7 ms (Panel iii) and 5.5 ms (Panel v) as indicated by the change in reflection of the main droplet. Black dashed lines enclose the main droplet. Red arrow indicates the approximate trajectory of the roaming event. Subcooling: 2.0 K. Gravity is downwards. Scale bars: 100 µm. Source data are provided as a Source Data file.