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.

Full text

Article https://doi.org/10.1038/s41467-025-56562-x
Condensate droplet roaming on
nanostructured superhydrophobic surfaces
Cheuk Wing Edmond Lam
1,3
, Kartik Regulagadda
1,4
, Matteo Donati
1
,
Abinash Tripathy
1
, Gopal Chandra Pal
2
, Chander Shekhar Sharma
2
,
Athanasios Milionis
1
& Dimos Poulikakos
1
Jumping of coalescing condensate droplets from superhydrophobic surfaces
is an interesting phenomenon which yields marked heat transfer enhancement
overthemoreexploredgravity-driven droplet removal mode in surface con-
densation, a phase change process of central interest to applications ranging
from energy to water harvesting. However, when condensate microdroplets
coalesce, they can also spontaneouslypropelthemselvesomnidirectionallyon
the surface independent of gravity and grow by feeding from droplets they
sweepalongtheway.Hereweobserveandexplainthephysicsbehindthis
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 significantlyimprovedheattransferefficiency over con-
densate droplet jumping, the mechanism currently understood as maximum.
The phenomenon of water vapour condensation on a surface begins
with the formation of discrete liquid nuclei, which grow into droplets
that can coalesce with one another. If not removed periodically, such
droplets of condensate form a thick continuous film, which hinders the
removal of heat from the vapour through the surface. The pursuit for
efficient heat removal has strongly motivated surface engineering
research, with the central idea to minimise the residence time and
amount of the liquid condensate on the cooled surface1–10.
On superhydrophobic surfaces, it is possible for condensate
microdroplets to spontaneously depart in the direction normal to the
surface, by jumping upon coalescence, converting released surface
energy to kinetic energy11,12. Such jumping droplet departure sig-
nificantly reduces the size of droplets residing on the surface, further
improving heat transfer efficiency compared to conventional dropwise
condensation13,14. On superhydrophobic surfaces with micro-
structures, this spontaneous motion can also be at an angle, or even
tangential, instead of normal to the surface15–23. It has been postulated
that15,17–19,24, as the condensate droplets are at the same length scale as
the individual microfeatures, coalescence on the side walls of the
microstructure cavities triggers inclined jumping in random
Received: 15 May 2024
Accepted: 21 January 2025
Check for updates
1
Laboratory of Thermodynamics in Emerging Technologies, Department of Mechanical and Process Engineering, ETH Zurich, Zurich, Switzerland.
2
Ther-
mofluidics Research Laboratory, Department of Mechanical Engineering, Indian Institute of Technology Ropar, Rupnagar, Punjab, India.
3
Present address:
Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, MA, USA.
4
Present address: Department of Mechanical Engi-
neering, UC Berkeley, Berkeley, CA, USA. e-mail: dpoulikakos@ethz.ch
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directions. However, tangential movement of coalescing condensate
microdroplets is also observed on superhydrophobic surfaces equip-
ped solely with nanostructures25,26, which are orders of magnitude
smaller than the droplets in concern, with remarkable effects on
ensuing heat transfer augmentation. Here we explain this unexplored
droplet roaming coalescence mechanism, identify the conditions
under which roaming occurs, and determine its significant effect on
heat removal from a surface.
As in-plane roaming can span great lengths and coalesce with
other condensate microdroplets along the way25,comparedtoout-of-
plane jumping which is confined to a local cluster of droplets, it pro-
vides a pathway to continuously remove larger amounts of
condensate15. Frequent roaming exposes needed underlying surface
for new nucleation cycles, thus reducing droplet sizes against con-
ventional gravity-driven dropwise condensation, and ultimately
markedly improving heat transfer, even compared to jumping drop-
wise condensation.
Results and discussion
Roaming on solely nanostructured surfaces
To allow high-speed imaging of roaming, we prepare a reflective solely
nanostructured superhydrophobic surface by exposing flat aluminium
substrates to hot water to form boehmite nanowalls27–29,whichare
then coated with hydrophobic poly-(1H,1H,2H,2H-perfluorodecyl
acrylate) (pPFDA) using initiated chemical vapour deposition (iCVD)2,15
(Methods). The coating conforms to the nanowalls, and its thickness is
measured to be 3.5 nm with ellipsometry (Supplementary Informa-
tion S1). An image of the nanostructures with the pPFDA coating using
scanning electron microscopy (SEM) is seen in Fig. 1a. The advancing
contact angle and contact angle hysteresis are 162.5° ± 1.8° and 1.1°,
respectively (Methods).
All samples are tested in our condensation setup illustrated in
Fig. 1b. A transparent window separates the condensation chamber
environment and the atmosphere. During experiment, saturated
steam (30 mbar, 24.1 °C) continuously passes over and condenses on
the cooled surface of the sample. A microscope objective in front of
the window enables direct observation of microscale condensation
behaviour with a high-speed camera at a resolution of 4.5 µmperpixel,
and temperature sensors in the chamber allow the simultaneous
measurement of heat transfer performance. See Supplementary
Information S2.
We investigate roaming motion on solely nanostructured super-
hydrophobic surfaces and avoid the presence of microstructures
which canalter the motion of coalescing condensate microdroplets at
the similar length scale (Supplementary Information S3). A typical
roaming event is shown in Fig. 1c. After the first coalescence (Panel i),
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 depos-
ited at 2 µLs
−1, and wettability measurements of the advancing contactangle (ACA),
contact angle hysteresis (CAH),and the static contactangle (SCA). Scale bar: 1 mm.
Right inset: SEM image of the nanowalls at higher magnification. Scalebar: 100 nm.
bSchematic of the condensation and observation setup. Tand prefer to tem-
perature and pressure measurements respectively. Gravity gis in the +z-direction.
cRoaming 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. dParticipating dro-
plets 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.
Article https://doi.org/10.1038/s41467-025-56562-x
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there is a tangential motion to the right (Panel ii). The droplet coa-
lesces with other droplets along its way, roaming the surface (Panel iii),
before coming to rest (Panel iv). The corresponding video can be
found in Supplementary Movie 1. Evidently, roaming demonstrates in-
plane arbitrary directionality which spans across considerable time
and distance, and is distinct from localised multi-droplet
coalescence30,31, which is confined to a specific location and occurs
on shorter timescales (Supplementary Movie 2).
We observe the condensation behaviour as we increase the sur-
face subcooling ΔT=Tsteam Tsurf , the difference between the steam
temperature Tsteam and the surface temperature Tsurf.Asthesteamis
always at saturation, Tsteam equals the saturation temperature at our
operating pressure (Tsat at 30 mbar). Above a subcooling of ≈1.5 K,
roaming becomes frequent on the surface. We characterise roaming
events from two perspectives: (1) We measure the positionand time of
all visible droplets which coalesce and take part in the event (partici-
pating droplets, shown as circles in Fig. 1d); and (2) we track over time
the location and shape of the travelling droplet (main droplet, trajec-
toryandshapeshownininsetofFig.1d) which grows as it coalesces
with and absorbs the participating droplets. Details of image proces-
sing, and individual droplet measurement and tracking canbe found in
Supplementary Information S4.
Mechanism of roaming coalescence
Figure 2a, b displays the participating droplet distributions and the
corresponding trajectory of the main droplet of several roaming
events, out of a total of 28 observed at a subcooling of 2.2–2.6 K.
Roaming occurs in all in-plane directions, independent of gravity. This
can be explained with the Bond number Bo = ΔρgR2=σ,whereΔρis the
density difference of liquid water and its saturated vapour, gis the
gravitational acceleration, Ris the characteristic droplet length scale,
and σis the surface tension of liquid water. Substituting the mean main
droplet equivalent radius of 79± 28 µm as the length scale,
Bo = 0:0009 ≪1, indicating that roaming is dominantly a capillary
phenomenon. During our experiments, we have not seen roaming
events to repeatedly occur at fixed locations on the condensing sur-
face (i.e. the starting and terminating locations are random, see
Fig. 2b), indicating that it is not triggered by surface defects. Roaming
is also found to be independent of the form of nanostructures, as we
have observed its occurrence on titanium dioxide nanorods32 and
copper(II) hydroxide nanoneedles33 as well (Supplementary Informa-
tion S5). We have not found a specific nanomorphology which would
prohibit roaming of condensate droplets, and we believe that this
phenomenon is generic to nanostructured superhydrophobic sur-
faces. Occasionally, a roaming event can alter its direction as it pro-
gresses, resulting in an in-plane curved trajectory (Supplementary
Movie 3). Apart from coming to rest as in Fig. 1c, it can also terminate
by jumping (Supplementary Movie 4). Of the measured roaming
events, the mean duration is 5.3± 3.4 ms, with a mean travelled dis-
tance of 744 ± 334 µm, on average 37× of the mean participating dro-
plet diameter of the event.
Roaming requires significant generation of tangential momen-
tum. Figure 2c displays the distance travelled over time for the main
droplet of roaming events. Although the mass increase of the main
droplet varies significantly for different events (Supplementary Infor-
mation S6), it largely follows a constant initial velocity of ≈0.18 m s−1,
0 5 10 15 20 25
Time [ms]
0.5
0.6
0.7
0.8
0.9
1
Circularity of the main droplet [-]
1
1.5
2
2.5
3
3.5
Feret ratio of the main droplet [-]
0 5 10 15 20 25
Time [ms]
0
0.5
1
1.5
2
Distance travelled by
the main droplet [mm]
0.18 ms
-1
0 1000 2000 3000
x-coordinate [µm]
0
500
1000
1500
2000
2500
3000
z-coordinate [µm]
Participating droplets
g
0 1000 2000 3000
x-coordinate [µm]
0
500
1000
1500
2000
2500
3000
z-coordinate [µm]
Starting location
Main droplet trajectory
g
(a) (b)
(c) (d)
Fig. 2 | Characteristics of roamingevents. 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.
bMain 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. cDistance travelled by the main droplet for all the
events. Initial roaming velocity 0.18 m s−1.dCircularity ð=4πðarea=perimeter2ÞÞ and
Feret ratio ( = maximumcaliperdiameter=minimumcaliperdiameter) of the main
droplet from the events. Both approach unity at ≈5 ms. Source data are provided as a
Source Data file.
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before slowing and diverging at ~3–5 ms as viscous dissipation sets in
(compared to a viscous timescale tμ=ρR2=μ= 7 ms, where R=79μmis
the mean main droplet equivalent radius and μis the dynamic viscosity
of liquid water). We term this velocity of the travelling main droplet as
the apparent roaming velocity. Although roaming occurs in all in-plane
directions, including some against gravity, there is no visible effect on
the velocity, further indicating that it is dominated by capillarity
effects.
As the main droplet gains mass and size, perturbations from fur-
ther coalescence with upcoming participating droplets increasingly
contribute to the low-amplitude capillary waves at the liquid-vapour
interface, instead of bulk droplet motion. This is due to the increase in
the number of available oscillation modes in a larger main droplet34,35,
along with coalescence bridges becoming increasingly small com-
pared to the traversing main droplet. As viscous effects become
important, the roaming event slows and terminates. We quantify the
intensity of coalescence over the course of the multiple events by
describing the shape evolution of the main droplet in Fig. 2d. At the
transition time of ≈5 ms, its circularity and Feret ratio quickly
approach unity, indicating transition to a circular contour (also see
inset of Fig. 1d). At the same time, the ratio of participating droplet
sizes relative to the main droplet size drops below unity (Supple-
mentary Information S6).
The translational kinetic energy of roaming stems from the excess
surface energy due to the reduction of liquid-vapour interfacial area
upon coalescence. Instead of the absolute velocity, we compare and
normalise the roaming velocity with the theoretical maximum velocity
(i.e. ifall excess surface energy were converted to in-plane translational
kinetic energy) to quantify the efficiency of this energy conversion. We
employ initial velocities just after coalescence, as common in the lit-
erature of droplet-jumping studies, to exclude effects other than
capillarity. However, we note that even without tangential momentum
generation, there would be a shift in the location of the main droplet
after it coalesces with each participating droplet, due to the addition of
mass from the participating droplet to the main droplet away from its
location. Therefore, to account for this effect and extract the “real”
roaming velocity that is purely the result of tangential momentum
generation, we dynamically measure the increase in the distance
between the main droplet and the centre of mass of the system of
coalesced participating droplets. The real roaming velocity is 48 ± 14%
of the theoretical maximum. For out-of-plane droplet jumping, it is ≈
20%11,36. See Supplementary Information S7. Roaming better scavenges
the excess surface energy of coalescence, which would otherwise be
dissipated as heat, for condensate removal, improving heat transfer
efficiency.
Roaming condensation heat transfer and the transition
subcooling
The more efficient energy conversion and larger span of roaming than
jumping suggest heat transfer benefits. In Fig. 3, the heat transfer
performance and the condensation behaviour at different subcooling
are quantified. We first measure the heat flux q00 and the subcooling ΔT
(Supplementary Information S8) and compute the heat transfer coef-
ficient h=q00=ΔT(Fig. 3a). A surface with the same boehmite nanowalls
but without the pPFDA coating (pristine boehmite) is used as the
filmwise condensation control. Filmwise condensation measurements
are validated against the Nusselt model, as commonly found in
literature37 (Supplementary Information S2).
Overall, the superhydrophobic boehmite surface is superior:
When comparing the mean of all measurements from each surface,
there is an increase in the heat transfer coefficient of over 300% from
20.1 kW m−2K–1on pristine boehmite to 82.6 kW m−2K−1on the super-
hydrophobic surface. However, on the superhydrophobic surface
alone, there are two regimes of condensation mode, dependent on the
current subcooling. At low subcooling, condensation is dominated by
the jumping dropwise mode with a relatively lower heat transfer
coefficient (mean = 62.7 kW m−2K−1,first 3 points from the left in
Fig. 3a); but when subcooling increases, there is a transition and con-
densation is dominated by the roaming mode with an increased heat
transfer coefficient (mean = 97.5 kW m−2K−1, last 4 points from the left
in Fig. 3a). When compared to filmwise condensation at similar sub-
cooling (mean = 25. 4 kW m−2K–1,first two points from the left in
Fig. 3a), jumping dropwise condensation provides a 147% increase in
the heat transfer coefficient while roaming condensation provides a
284% increase. The synergistic effect of a higher heat transfer coeffi-
cient at a higher thermal driving force, i.e. subcooling, results in a 175%
higher heat flux for roaming condensation than jumping dropwise
condensation. The jumping-roaming transition can be seen in Fig. 3b
and Supplementary Movie 5. We quantify the transition in the top
subplot of Fig. 3c and show that when the subcooling increases past
the transition at ≈1.5 K, the surface area renewal rate S0from roaming
sharply increases. Remarkably, over 70% of the surface is renewed
every second by r oaming when it is the dominant mode. Lastly, most o f
the roaming events end as droplets at rest. Termination in jumping is
scarce when roaming first emerges at the transition subcooling; as
subcooling increases, droplet jumping of all kind all but vanishes. See
Supplementary Movie 5 and Supplementary InformationS9. A few rare
cases of jumping at subcooling higher than the transition can be seen
in Supplementary Movie 2. The gradual deceleration of a roaming
droplet until coming to rest (instead of an abrupt stop) on the surface,
as evident in Fig. 2c, indicates thatmotion is not terminated by pinning
at local adhesion points from condensate-filled nanostructures, but
rather by energy dissipation over time. A droplet coming to rest on the
surface after roaming is therefore likely in the Cassie state and rela-
tively mobile. This larger droplet is then available for further roaming
and coalescence. The entir e process significantly speeds up the growth
of droplets on the surface to attain the gravitational departure size
(Supplementary Information S9). Eventually, the condensate droplets
leave by gravity.
The roaming mode provides higher heat transfer efficiency than
the jumping dropwise mode despite a surface with more larger dro-
plets as seen in Fig. 3b. In condensation, most of the heat and mass
transfer is attributed to the initial droplet growth afternucleation38.On
a surface with a distribution of various condensate droplet sizes, the
majority of heat flows through the smallest droplets. When subcooling
increases, (1) the diameter at which nucleation occurs, i.e. the critical
nucleation diameter dcrit, decreases, and (2) the nucleation rate
(number of nuclei per area per time) increases39. Therefore, at elevated
subcooling, a renewed surface area is soon filled with a large number of
small condensate droplets idealfor heat transfer. The frequent renewal
of large surface areas (1) by roaming itself, and (2) from the increased
gravitational departure assisted by roaming, enable abundant renu-
cleation and ultimately maximise heat transfer. In addition, the higher
condensation rates when subcooling increases, inevitably translate to
more active condensation behaviour. For example, there is a higher
droplet density and thus a higher frequency of (roaming or localised)
coalescence events. Such collateral effects, together with the promi-
nent roaming motion of droplets over the entire surface, piece toge-
ther the overall roaming condensation mode with its high heat transfer
coefficients.
The emergence of roaming when subcooling increases provides a
clue about its origin. As dcrit is reduced with increasing subcooling and
becomes smaller than the nanocavity sizes, nucleation occurs sto-
chastically within the nanocavities. At the transition subcooling of
1.5 K, dcrit (≈23 nm) is below the majority of boehmite cavity sizes
(Fig. 3c). On the other hand, we find thaton surfaces with muchsparser
nanostructures and thus larger cavities such as copper(II) hydroxide
nanoneedles, the transition subcooling is notably reduced to 0.7 K
(Supplementary Information S10). In addition, at a subcooling of 1.3 K,
these sparser copper(II) hydroxide structures begin to flood as most of
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the nanocavities are filled with condensate. This jumping-roaming-
flooding transition evidently shows that roaming is closely related to
condensate filling of some nanocavities, producing some droplets on
the nanostructures which are in the partial-Wenzel state. It furthers
droplet growth and heat transfer as there is more droplet-substrate
contact than Cassie-state droplets40. Figure 3d, e summarises the
mechanism for roaming and its benefits to heat transfer, which we will
discuss in detail in the upcoming sections.
For a cavity to be filled, two competing factors are in
play. When subcooling increases, although the nucleation rate
increases, the volume of each nucleus reduces. To assess the
probability of cavity filling through nucleation, we define a volu-
metric nucleation rate as the product of the two. A substantial
increase in the volumetric nucleation rate is seen around the
transition subcooling at 1.5 K, indicating the increased likelihood
for the cavities to be filled. The timescale to fill the nanocavities
Fig. 3 | Heat transfer performance of roaming condensation. a Heat transfer
coefficients hat steadystate. Lines of constant heat flux q00 are shown in grey, from
25 to 275 kW m−2at intervals of50. For a fair test,the 7 subcoolingachieved for each
surface correspond to 7 identical cooler back end temperatures (Supplementary
Information S2).On the superhydrophobicsurface, two modes of condensationare
observed. Measurements on pristine boehmite match closely with the Nusselt
model for filmwise condensation. bSnapshots of condensation behaviour for
superhydrophobic boehmite. Transition is seen fromjumping dropwiseto roaming
condensation. Atthe lowest subcooling (0.7K), only jumping isobserved and there
are numerous droplets in the vapour, with darker appearance and out-of-focus
contour.These droplets inthe vapour travelin one general direction to thebottom
left due to steam flow (leftward) and gravity (downward). At 1.3 K, the number of
jumpeddroplets in the vapour is visibly reduced, and someare seen to returnto 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. cSurface area renewal rate S0fromroaming (unit: m2of surface
area renewed per m2of condensing surface per second) and critical nucleation
diameter dcrit for 30mbar saturated steam (top). As transition to roamingoccurs at
≈1.5 K, the critical nucleation diameter lies below most nanostructure cavity sizes
(bottom). The sizesare obtained fromthe square root of theprojected area of each
cavity (Supplementary Information S11). dWhen subcooling is increased past the
transition, condensate nucleates within the nanostructures. Microdroplets on top
of thesenanostructures couldthen exhibit differentwetting states.The asymmetric
adhesion gives rise to substantial tangential momentum upon coalescence. eThe
high surface area renewal rateof roaming enablesabundant renucleation.Frequent
roaming also assists droplet growth to the required size of gravitational removal.
Source data are provided as a Source Data file.
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of boehmite is in turn estimated to be 0.1–1 ms. See Supplementary
Information S11.
As roaming is not observed to repeatedly initiate at certain loca-
tions (Fig. 2b), and the surface can sustain roaming condensation at
steady state with no surface flooding over time, such stochastic locally
wetted cavities are expected to dewet in a roaming event, similar to
dewetting by condensate motion previously suggested11 for the case of
droplet jumping. On the other hand, hierarchical condensation41,in
which condensate nucleates within structure cavities under a droplet,
is very unlikely, due to the lack of low-resistance vapour flow paths
across the thin, dense and closed nanostructure (Supplementary
Information S3). After roaming renews the surface, the dewetted cav-
ities are again exposed to the vapour for another nucleation cycle.
The heat transfer coefficient can exhibit different trends with
subcooling for surfaces on which condensate appears in the form of
droplets4,13,42,43. When droplet removal is sufficiently efficient, it can
increase with subcooling4,42, due to higher nucleation rates and smaller
nucleation diameters. This important trend is also present in the
superhydrophobic boehmite heat transfer coefficients in Fig. 3a.
However, this trend sustains so long as the condensation mode allows
it, that is, there is limited flooding of structures or saturation of
nucleation sites because of the efficient droplet removal. The >70%
area renewed every second in roaming condensation enables ample
space for fresh nucleation, sustaining the trend. For structured sur-
faces, when the subcooling is high enough for nucleation to occur
within the cavities, apart from the increased nucleation rate from the
increase in subcooling, there is as well additional area available for
nucleation from the cavity walls. These higher rates are only sustain-
able when they are balanced with enhanced condensate removal from
the cavities to avoid flooding. Surface structures which promote the
ejection of droplets from within are often exploited to achieve this
goal44–48,anddelayflooding so that the abovementioned relationship
can be extended to higher subcooling levels for jumping dropwise
condensation. In our work, we show that as jumping subsides athigher
subcooling,roaming,whichnaturallyoccursonthesesuper-
hydrophobic surfaces, can further extend thetrend at high subcooling,
by providing an efficientpathway to employthe excess surface energy
of droplet coalescence for cavity dewetting. See Supplementary
Information S8 for additional discussion.
In summary, we have put forth roaming condensation as a readily
achievable state for a wide range of superhydrophobic surfaces. It is a
condensation mode in itself, and it occurs sustainably in the requisite
subcooling range, as a result of the collaborative effect of nucleation
diameters and nucleation rates. The lack of flooding, and the highest
heat transfer coefficients roaming yields compared to all other modes,
including jumping dropwise condensation, render it as a preferable
mode to be targeted in various heat transfer applications for m aximum
energy efficiency.
Generation of tangential momentum in roaming
The absence of roaming at the limit of low subcooling suggests that
this phenomenon is exclusive to condensate droplets—gently depos-
ited Cassie droplets do not roam upon coalescence. Indeed, no tan-
gential motion has been reported in the literature for deposited
droplets on solely nanostructured surfaces. As some nanocavities fill,
stochastic wetting at random locations across the surface promotes
the concurrent presence of Cassie and (partial-)Wenzel-state con-
densate droplets on superhydrophobic surfaces40. Their different
adhesion47 produces an adhesion asymmetry of the droplets for tan-
gential motion. See Fig. 3d. Without this, there is no apparent reason
for out-of-plane jumping to transition to in-plane roaming. Jumping is a
result of the reaction force from a rapidly growing droplet coalescence
bridge impinging on the surface, breaking the oscillation
symmetry49,50. The normal impingement of the bridge can only gen-
erate a normal reaction from the surface in the opposite direction. For
roaming, there is no symmetry-breaking surface for a tangential
reaction force to manifest as the condensate microdroplets are orders
of magnitude larger than the underlaying nanostructures. If the
increase in adhesion for all condensate droplets on the surface were
uniform when subcooling increases, i.e. no asymmetry, jumpingwould
gradually cease and transition to flooded condensation would be
directly evident without any intermediate in-plane roaming regime.
The excess surface energy from coalescence would no longer over-
come the increased adhesion and be dissipated instead. Droplets
would not depart at all, whether in-plane or out-of-plane, until they
attain the size when gravity dominates.
Moreover, any droplet size mismatch during coalescence cannot
explain the generation of tangential momentum as well. In our roam-
ing events, there is no observable trend in participating droplet sizes
(Fig. 2a). Additionally, for two size-mismatched coalescing droplets,
the reaction force from the symmetry-breaking surface would still
largely be normal to the surface. Numerical simulations (Methods)
confirm that the direction of jumping from the coalescence of two size-
mismatched droplets deviates <4° fromthe surface normal, in line with
previously reported results24. See Supplementary Information S12.
While nuclei within the nanostructure cavities may coalesce with
and effectively be absorbed by the microdroplets on top, we do not
expect any substantial motion of the microdroplet to result from such
coalescence. It is because the vast difference in size of the coalescing
droplets quickly dampens capillary waves before they are converted to
bulk droplet motion. Moreover, when subcooling increases, this
becomes increasingly difficult and improbable due to the high
nucleation rates within the structure cavities. Microdroplets with dif-
ferentwetting states will eventually form. Roaming is a consequence of
the adhesion asymmetryof droplets under different wetting states and
propagates by the dewetting of the partial-Wenzel state droplets.
Roaming condensation is stochastic and occurs on very actively
condensing surfaces under saturated steam, where isolation and
control of individual events are impossible. Current experimental
methods do not simultaneously possess sufficient spatial and temporal
resolution to visualise the pinned contact line of the adhered droplet,
or the ≲100 nm-thick wetted nanostructure layer below the droplet,
during coalescence. Therefore, to further support our conclusions
from the experimental findings above, we follow with numerical
simulations, which yield essential additional information on the coa-
lescence mechanism. Guided by the experiments, we set up simulation
cases to study the evolution of momentum and energies throughout
the process in a highly temporally resolved manner, which cannot be
obtained experimentally, to demonstrate motion resulting from the
wetting asymmetry of two participating droplets. See Fig. 4aand
Methods. Two equally sized droplets of 160 µm in diameter are first
placed on a substrate at a contact angle of 160°, and a symmetry plane
is specified at z= 0. To mimic the effect of a wetted nanostructure layer
below a droplet (D1 in Fig. 4a), we specify the contact angle only for its
base area as 2°.
Contour plots of static gauge pressure at the symmetry plane are
displayed in Fig. 4b. In the beginning, the low pressure at the coales-
cence bridge draws the liquid to it which rapidly expands (Panel i). The
span in the x-direction increases, followed by a recoil with a downward
tendency due to the higher curvature at the +yend than the bottom.
The recoil is asymmetric and biased towards -xas the higher wettability
below Droplet D1 restricts liquid motion (Panel ii). This x-recoil in turn
increases the span in the y-andz-directions. As the liquid body elon-
gates in the y-direction, the adhesion of the hydrophilic wetted region
below Droplet D1 creates a locally concave liquid-vapour interface
(Panel iii). The pressure difference from the asymmetric curvature
further draws the liquid towards -x, providing most of the tangential
momentum generation. This cycle repeats, and the liquid body recoils
in the other direction (z), biased towards -x, and experiences another
curvature asymmetry (not shown in Fig. 4b). See Supplementary
Article https://doi.org/10.1038/s41467-025-56562-x
Nature Communications | (2025) 16:1167 6
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Information S13. Maximum x-displacement is reached at ≈1ms (Panel
iv). In the current case, we do not specify any dewetting step. The
liquid body then swings back towards +x.
The complete event for a duration of 2ms is shown in Supple-
mentary Movie 6, together with the reference case when both Droplets
D1 and D2 are in the Cassie state. The evolution of momentum and
centre-of-mass displacement in the x- and y-directions is plotted in
Fig. 4c against the reference case. In the latter, x-momentum and dis-
placement remain zero whereas y-displacement increases con-
tinuously owing to droplet jumping. In the former, where the base of
Droplet D1 is wetted, the absolute x-momentum reaches a maximum at
≈0.5 ms as the centre of mass of the system approaches the wetted
region, ceasing tangential momentum generation. This mechanism
reveals how wetting asymmetry due to increased adhesion of one
droplet can serve as a hinge24 to generate tangential momentum.
Lastly, we vary the diameter and thus area of the wetted region as a
percentage of the total base area below Droplet D1 and obtain the
maximum tangential momentum generated for each percentage
(Fig. 4d). A sharp transition at ≈20% reveals that a slightly wetted base
area can already generate substantial tangential momentum. See
Fig. 4e for a summary of the numerical model and simulation cases.
Dewetting and procession of roaming
After generating tangential momentum from asymmetric droplet
adhesion, to be able to roam, the droplet hasto dewet and detach from
its location. In Fig. 5a, we dewet the surface by reverting the specified
contact angle of the wetted region (2°) back to the original (160°) at
179 µs (Panel i), when the force exerted on it in the +y-direction is at
maximum. After recoiling in the z-direction (Panel ii), the coalesced
droplet departs with a substantial tangential component (Panel iii).
The departure angle is sensitive to the dewetting time, as dewetting
20 µs later already results in entirely tangential departure. See Sup-
plementary Movie 7 and Supplementary Information S14. The actual
momentfordewettingdependsonwhenboth(1)staticfrictionofthe
contact line51 and (2) the adhesion work on the nanostructures are
overcome.
Fig. 4 | Generation of tangential momentum. a Computational d omain. Two
droplets with diameter 160µm are placed on a no-slip wall aty=0,specified with a
contactangle. A symmetryplane is at z=0.bContour plots of static gaugepressure
at the symmetry plane. The entire base area of Droplet D1 is wetted. Vectors are
velocities. Scale bars: 50µm. Yellow referencevelocity vector:2 m s−1.cMomentum
(pxand pyon the left y-axis) and centre-of-mass displacement (Δxcm and Δycm on
the right y-axis) in the x-andy-directions, for the case in which the base area of
DropletD1 is wetted and thecase in which bothDroplets D1 andD2 are in the Cassie
state. dMaximumtangential momentum generated, px,gen =max px




,forvarying
wetted fractions of the base area of Droplet D1 (top), and the corresponding x-
centre-of-massdisplacement(bottom). In candd, the momentum reported reflects
full spherical droplets, taking domain symmetry into account. eNumerical 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 keptat 160°, the sameas the outer surface. Source data
are provided as a Source Data file.
Article https://doi.org/10.1038/s41467-025-56562-x
Nature Communications | (2025) 16:1167 7
Content courtesy of Springer Nature, terms of use apply. Rights reserved

We plot the variation of momentum and displacement in Fig. 5b
for the first 0.5 ms. After dewetting, tangential momentum generation
ceases, but recovers in the normal direction. The kinetic energy of the
translational motion of the centre of mass50 compared to the total
kinetic energy is expressed in Fig. 5c(i). Although the total kinetic
energy of our dewetting and the reference cases are similar, the former
exhibits a higher centre-of-mass translational kinetic energy, indicat-
ing a higher efficiency in producing centre-of-mass motion instead of
oscillatory viscous dissipation. This applies to other dewetting times as
well (Supplementary Fig. 32). The adhesion keeps the liquid body close
to the surface, resulting in stronger and more instances of symmetry
breaking than droplet jumping (Fig. 5c(ii)). The symmetry breaking is
converted into motion with a substantial tangential component using
the adhesion asymmetry as a hinge, providing most of the in-plane
momentum in roaming (Supplementary Information S14). In these
simulations, we have selected the simplest case, the coalescence of
binary droplets, such that the two cases (tangential and out-of-plane
momentum generation) only differ in the presence of an adhesion
asymmetry. We then showed how the generation of tangential
momentum under such asymmetry can be more efficient than that of
out-of-plane momentum observed in experiments, where more dro-
plets are involved.
Finally, we demonstrate the dewetting experimentally in Fig. 5d.
Coalescence can be seen at 0.2 ms. At 1.7 ms (Panel iii), the main
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 Drop let 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.bMomentum (pxand pyon the left y-axis) and
centre-of-mass displacement (Δxcm and Δycm on the right y-axis) in the x-andy-
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 KEcm and the total kinetic energy KE tot for
the two cases. The momentum and kinetic energy reported in band 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 momen-
tum. In jumping, the liquid body leaves early and oscillate s int he 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. dExperimental 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 down-
wards. Scale bars: 100 µm. Source data are provided as a Source Data file.
Article https://doi.org/10.1038/s41467-025-56562-x
Nature Communications | (2025) 16:1167 8
Content courtesy of Springer Nature, terms of use apply. Rights reserved

droplet is slightly lifted from the surface with a change in droplet
reflection while maintaining significant tangential momentum. It
is then intercepted by droplets on the surface and returns to the
surface at 3.2 ms. In this event, we observe another dewetting at
5.5 ms (Panel v), before returning at 9.0 ms. See Supplementary
Movie8formoreexamples.Thesechangesinreflection appear
when the droplet is slightly lifted from the surface during
dewetting, much like the simulation shown in Fig. 5a. However,
depending on the dewetting time, the droplet may adopt a more
tangential motion (Supplementary Fig. 31b) and result in less
prominent lifting and reflection changes. See Supplementary
Information S14 for further discussion in interception.
In this work, we have focused on solely nanostructured
superhydrophobic surfaces to eliminate the effects from micro-
structures. However, roaming on hierarchical surfaces might be
possible (Supplementary Information S16). Roaming events in our
work travel over distances below 1 mm, suggesting that roaming
might also be possible on highly curved surfaces. The tangential
momentum generation of coalescing condensate microdroplets
on solely nanostructured superhydrophobic surfaces is attributed
to the stochastic wetting state of the condensing droplets. The
simultaneous presence of droplets at different wetting states
results in adhesion asymmetry during coalescence, effectively
converting excess surface energy to tangential kinetic energy as
coalescence occurs. The ability of the coalesced droplet to dewet
from the surface triggers roaming while preventing condensate
flooding of the surface. This frequently renews the surface for
fresh nucleation. Remarkably, this process significantly improves
heat transfer compared to other condensate removal modes, as it
takes over as the dominant mechanism with jumping dropwise
condensation subsiding at higher subcooling.
Methods
Formation of boehmite nanowalls27–29
All aluminium substrates are of EN AW-1050A. The substrates are
sonicated in acetone, isopropanol, deionised water for 10 min
respectively, followed by sonication in 0.25M sodium hydroxide
solution for at least 10min, before rinsing with deionised water and
drying with nitrogen. The samples are then placed in hot water at
≈96 °C for 10 min and dried with nitrogen.
pPFDA coating with iCVD2,15
The samples are first treated with oxygen plasma (Femto, Diener
electronic) at 0.6 mbar for 10 min, followed by coating with tri-
chlorovinylsilane (Sigma-Aldrich, CAS No.: 75-94-5) in a custom CVD
chamber (saturated silane vapour at room temperature,≈60 Torr ). The
samples are then placed in an iCVD system (iLab, GVD), to form a
pPFDA coating at 100 mTorr using tert-butyl peroxide (Sigma-Aldrich,
CAS No.: 110-05-4) as the initiator and 1H,1H,2H,2H-perfluorodecyl
acrylate (Sigma-Aldrich, CAS No.: 27905-45-9) as the monomer. The
stage and filament temperatures are set to 40°C and 300°C respec-
tively. When applied on a pristine silicon wafer, the coating gives an
advancing contact angle, contact angle hysteresis, and static contact
angle of 124.2° ± 0.4°, 12.5° ± 2.1° and 119.2 ° ± 1.5°, respectively.
Contact angle goniometry
Advancing and receding contact angles are measured with a goni-
ometer (OCA 35, DataPhysics Instruments). Deionised water is
deposited and withdrawn at a rate of 2 µLs
−1. The sample is blown dry
with nitrogen before depositionof every droplet. Threemeasurements
are taken before and after condensation. No significant change in
wettability is observed. The static contact angle is computed from the
mean of advancing and receding contact angles as a single droplet
cannot be stably deposited.
Numerical simulations
Cases are set up and computed with Ansys ICEM CFD and Ansys Fluent
using the volume of fluid method. Saturation properties at 30 mbar are
specified for the fluids. Postprocessing is performed in Tecplot 360 EX
and MATLAB (MathWorks). See Supplementary Information S15 for
details.
Data availability
Experimental and simulation data are provided as a Source Data file
with this paper and in the repository figshare (https://doi.org/10.6084/
m9.figshare.28147487). Source data are provided with this paper.
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Acknowledgements
We thank Tobias Neef for his assistance with the iCVD process, and Jovo
Vidic and Peter Feusi for their assistance in the construction of the
condensation setup. We thank Henry Lambley and Jonathan Boreyko for
helpful discussions; and Thibaut Delafosse and Mithulan Vasan for
assisting in preliminary experiments. We thank Jiayu Song for preparing
the titanium samples. We thank the Cleanroom Operations Team of the
Binnig and Rohrer Nanotechnology Center (BRNC) for their help and
support. Unless otherwise specified, fluid properties are obtained with
CoolProp (www.coolprop.org)52. This project has received funding from
the European Union’s Horizon 2020 research and innovation pro-
gramme under grant number 801229 (HARMoNIC). C.W.E.L. acknowl-
edges funding from the Croucher Foundation during revision of this
manuscript.
Author contributions
C.W.E.L. and D.P. conceived the research. D.P. supervised all aspects of
the research and provided scientific guidance. C.W.E.L. designed and
constructed the condensation setup, conducted the experiments, per-
formed the simulations, and analysed the data. C.W.E.L. prepared the
aluminium samples. M.D. prepared the copper samples. C.W.E.L., K.R.,
and A.T. applied the pPFDA coatings. G.C.P. assisted in the simulations.
D.P., K.R., C.S.S., and A.M. provided scientific guidance for the various
aspects of the research. C.W.E.L. and D.P. wrote the manuscript with
contribution from all other authors.
Funding
OpenaccessfundingprovidedbySwiss Federal Institute of Technology
Zurich
Competing interests
The authors declare no competing interests.
Article https://doi.org/10.1038/s41467-025-56562-x
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Additional information
Supplementary information The online version contains
supplementary material available at
https://doi.org/10.1038/s41467-025-56562-x.
Correspondence and requests for materials should be addressed to
Dimos Poulikakos.
Peer review information Nature Communications thanks Xianming Dai,
and the other, anonymous, reviewers for their contribution to the peer
review of this work. A peer review file is available.
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