# A plate-type condenser platform with engineered wettability for space
applications

Tibin M. Thomas
Department of Mechanical Engineering
Indian Institute of Technology Madras
Chennai 600036, India
<EMAIL_ADDRESS>
&Pallab Sinha Mahapatra
Department of Mechanical Engineering
Indian Institute of Technology Madras
Chennai 600036, India
<EMAIL_ADDRESS>
###### Abstract

Vapor condensation is extensively used in applications that demand the
exchange of a substantial amount of heat energy or the vapor-liquid phase
conversion. In conventional condensers, the condensate removal from a
subcooled surface is caused by gravity force. This restricts the use of such
condensers in space applications or in horizontal orientations. The current
study demonstrates proof-of-concept of a novel plate-type condenser platform
for passively removing condensate from a horizontally oriented surface to the
surrounded wicking reservoir without gravity. The condensing surface is
engineered with patterned wettabilities, which enables the continuous
migration of condensate from the inner region of the condenser surface to the
side edges via surface energy gradient. The surrounding wicking reservoir
facilitates the continuous absorption of condensate from the side edges. The
condensation dynamics on different substrates with patterned wettabilities are
investigated, and their condensation heat transfer performance is compared.
The continuous migration of condensate drops from a superhydrophobic to a
superhydrophilic area can rejuvenate the nucleation sites in the
superhydrophobic area, resulting in increased heat transport. We can use the
condenser design with engineered wettability mentioned above for temperature
and humidity management applications in space.

_Keywords_ Condensation $\cdot$ patterning of wettability $\cdot$ horizontal
surface $\cdot$ microgravity $\cdot$ passive transport $\cdot$ wicking

##  1 Introduction

Condensation is an inevitable process in energy conversion [1], environmental
control [2], water harvesting [3], desalination [4], and thermal management
systems [5]. The overall efficiency of these systems has a greater dependence
on the condensation process, and the performance of the condensation process
is reliant on the mode of condensation, nucleation rate, and condensate
removal rate [6, 7]. These parameters are influenced by the surface
wettability, which can be engineered by both physical and chemical
modifications [8, 9, 10, 11]. The gravitational force plays a vital role in
facilitating the removal of condensate from a surface, which is necessary for
the continuous functioning of conventional condensers at optimum performance.
The transport of condensate over the surface and the removal of condensate
become challenging when a condenser surface is placed in a microgravity
environment (space) or horizontal orientation. In space applications, devices
such as heat pipes [12, 13], porous media based condensers [14], and other
complex condensing heat exchanger systems consisting of slurper bars and a
rotary separator [15, 16] are used as a replacement for conventional condenser
devices. Despite the fact that the wicking process ensures condensate
transport via capillary forces, the fundamental disadvantage of these devices
is their poor heat transfer performance due to film formation on the
condensing area. Because the heat transfer performance of the filmwise mode of
condensation during pure vapour conditions is one order of magnitude lower
than the dropwise mode [6]. It is challenging to design a plate type condenser
with superior performance that can be employed in space or in a horizontal
orientation with either a dropwise mode or a mix of both filmwise and dropwise
modes. The various techniques used for the self-transport of liquid on an open
surface without gravity aid are important for the development of condensers
that can efficiently remove the condensate from the surface for space
application.

Because of the exciting opportunities in micro-fluidics, lab-on-a-chip,
condensation, and spray cooling applications, self-transport of liquid on an
open surface has attracted a lot of attention in the last decade [17, 18, 19,
20]. Passive liquid transport on an open surface without gravity aid was
accomplished through engineered surface modification techniques such as
wettability gradient [21], superhydrophilic wedge surrounded by a hydrophobic
boundary [22], topological liquid diode [23], charge gradient [24], and so on.
On a wettability gradient surface, the difference in the Laplace pressure
between two opposite ends drives the droplet from the high contact angle
region to the low contact angle region [21]. Likewise, liquid transport occurs
from the narrower end to the wider end of a superhydrophilic wedge track due
to the Laplace pressure difference between the front and back end [22, 25].
The topological structure on the surface of a topological liquid diode breaks
the contact line pinning of the drop at the advancing edge while
simultaneously imparting a strong pinning force at the receding edge. This
converts excess surface energy to kinetic energy, propelling the droplets from
receding to advancing end [23]. On a charge gradient surface, droplets
transport from a higher charge density region to a lower charge density region
[24, 26].

In the presence of gravity, the condensate is removed from the vertically
oriented surface when the size of the condensate reaches the capillary length
scale, such that the gravity force of the condensate exceeds the surface
tension forces [6]. Condensate droplets can also be removed at a size smaller
than the capillary length scale via coalescence-induced droplet jumping from
non-wettable surfaces [27, 28], periodic wicking structures from a hydrophilic
surface [29, 30], and the application of an intermittent electrostatic
potential to a hydrophilic surface [31]. In addition, various techniques of
self-transport of liquid drops have been used in the condensation process to
achieve directional transport of condensates or to improve overall
condensation performance. On a surface with radially graded wettability,
condensate was observed migrating from the central region of a substrate to
the outer region [32, 33]. Many researchers have also proposed bio-inspired
structural graded structures that mimic spider silk, desert beetles, cactus
spines, pitcher plants, and other natural materials for water harvesting from
humid air via condensation and directional transport of condensate liquid [34,
35, 36, 37]. When a superhydrophobic surface is infused with high viscous oil,
condensate droplets can be seen levitating. Capillary force causes a meniscus
to form over a condensate drop on an oil-infused surface. The stretching of
the oil layer caused by droplet growth results in the droplets levitating
[38]. Different types of surfaces with patterned wettability have also been
proposed in the literature for directional condensate transport and to utilise
the advantages of both hydrophilicity and hydrophobicity during condensation
[39, 40, 41, 42, 43].

Previous research on condensation on a horizontally oriented substrate focused
on either condensation mechanisms like nucleation, drop growth, and drop-
coalescence, or passive droplet movement on the substrate with a radially
smooth wettability gradient [32, 33] or a charge density gradient [26].
Nonetheless, it is yet unclear how to employ these substrates as condenser
systems and how to continuously remove the migrating droplets from the
substrate in a microgravity environment. Additionally, previous studies on the
condensation process on a substrate with patterned wettability and the
effectiveness of their condensation heat transfer primarily looked at
vertically oriented or inclined substrates [39, 40, 44]. In such cases, the
gravity force aids the removal of condensate from the substrate irrespective
of the design of the various patterned wettabilities. On the other hand, when
condensation occurs on a horizontal surface or a condenser surface kept in a
microgravity environment, the condensate spreads and accumulates regardless of
the substrate wettability. In such cases, the removal of condensate from the
surface is challenging and condensate accumulates on the substrate with time.
To avoid liquid accumulation, condensate must be continuously removed from the
surface using either passive or active techniques.

The current study proposes proof-of-concept for a plate-type condenser
platform with patterned wettability as well as a novel method for the
continuous removal of liquid formed by condensation on a horizontally oriented
surface or the condenser surface in a microgravity environment via a wicking
reservoir. A substrate with patterned wettability was designed to allow the
passive transport of condensate droplets without external force or gravity.
The gradient in surface energies propels the condensate formed on the
substrate to the surface’s outer edges. The propelled condensate from the
outer edges is absorbed by the wicking reservoir, which is surrounded by the
substrate. Wherein, the wicking reservoir is not attached to the substrate,
and a tiny gap is maintained between them to prevent heat conduction. The
mechanism by which condensate is transported from the substrate to the wicking
reservoir is explored. The key features of this study are,

  * •

Different patterned wettable surfaces were used and a design is proposed
(pattern P4) as a best condensing surface for the condensate transport. The
proposed pattern P4 and the passive droplet transport process is novel. This
design showed better condensate collection during experiments and the
transport mechanism is explained through simulations.

  * •

A new approach to the experimental characterization of the condensation rate
from a horizontally oriented substrate by a wicking reservoir was established
in the present study.

  * •

Although, a lot of data on condensation heat transfer rate were available on
literature, however to the best of our knowledge, no data are available with
condensation on horizontal surface in presence of NCG.

##  2 Material and Methods

###  2.1 Fabrication of the substrate with patterned wettability and
characterization

The substrate material was an aluminium alloy of grade 6061 with dimensions of
40 $mm$$\times$ 40 $mm$$\times$ 3 $mm$. The substrate was first ultrasonically
cleaned for 10 minutes in a solution of deionized (DI) water, ethanol, and
acetone, and then dried with $N_{2}$ gas. Further, the substrate was
microtextured by dipping in 3$M$ $HCl$ (Merck-EMPLURA grade) for 5 minutes and
washed thoroughly with DI water. The microtextured substrate was immersed in
DI water at a temperature of 100 ${}^{\circ}C$ for 30 minutes to grow the
boehmite nanostructures above the microstructures [45]. These procedures
modified the polished aluminum substrate to a hierarchical rough
superhydrophilic surface with a contact angle of below 5∘. Further, the
superhydrophilic substrate was functionalized with 0.5 % vol/vol
1H,1H,2H,2H-Perfluoro-octyl-triethoxysilane (PFOTS) in ethanol solution by
dip-coating for 3 hours, followed by drying in a laboratory environment for 12
hours [46]. This procedure transformed the wettability of the substrate from
superhydrophilic (SHL) to superhydrophobic (SHB). To fabricate the substrate
with patterned wettability, the uniformly coated hydrophobic layer has been
selectively removed by laser ablation. A 60 $W$ $CO_{2}$ laser (Universal
Laser VLS3.60) having a spot size of 30 $\mu m$ was used for the laser
ablation. The power setting of the laser was 95 % of the total power and the
speed setting was 5 % of the total speed. After the laser ablation, the areas
that were exposed to the laser changed into SHL, while the areas that weren’t
exposed to the laser remained as SHB [19].

The morphology of the modified hierarchical surface textures was analyzed
using a high-resolution scanning electron microscope (Apreo- Thermofisher)
after the gold sputtering operation for 30 sec. The surface roughness was
measured using a surface profilometer (Nanomap 1000WLI). The dynamic contact
angles (advancing and receding) were measured by injecting/drawing out the DI
water at a flow rate of 0.2 $\mu L/sec$ to/from a sessile water drop of volume
5 $\mu L$ using a syringe pump [47].

###  2.2 Fabrication of the wicking reservoir

Figure 1: Design of the wicking reservoir (a) Illustration of wicking
reservoir (gray colour) placed surrounded to the condensing substrate. To
prevent heat transfer losses due to conduction between the wicking reservoir
and the substrate, a gap of 0.5 $mm$ was maintained. (b) Sectional view of
wicking reservoir, comprising of layers of filter papers, plastic layer
covering and nitrile foam insulation.

A wicking reservoir was used to passively remove the condensate from a
horizontal substrate. The wicking reservoir is made up of multiple layers of
Whatman filter papers of Grade 1 as interior layers and a thin plastic sheet
as top and bottom layers, as shown in Fig. 1. Each layer of filter paper was
cut according to the dimensions mentioned in Fig. 1a using a $CO_{2}$ laser at
a power setting of 5 % of total power and 3 % of total speed. The laser-cut
papers were then stacked, and the top and bottom sides of the stack were
covered with a laser-cut plastic sheet of the same dimension using double-
sided adhesive tape. To prevent mass loss of condensates collected from the
substrate, the lateral sides of the wicking reservoir were covered with
plastic tape. The top surface of the wicking reservoir was insulated with 3
$mm$ of thick nitrile foam to prevent water vapour condensation on the wicking
reservoir (see Fig. 1b).

###  2.3 Experimental procedures

Figure 2: Experimental setup for the condensation experiments on the
horizontally oriented substrate with patterned wettability. (a) Snapshot and,
(b) schematic representation.

The condensation experiments on horizontally oriented surfaces were performed
in an environmental chamber (Espec-PR2J), as shown in Fig. 2. A peltier
(TeTech-CP061HT) was used to cool the test substrate, which was placed on a
vertical stage in a horizontal orientation. A copper block of dimension 40
$mm\times$ 40 $mm\times$ 10 $mm$ was attached to the middle of the peltier
cold plate using double-sided thermal conductive tape (3M Tape) of a thickness
of 0.25 $mm$. The remaining area of the peltier top plate was covered with a
10 $mm$ thick nitrile foam as thermal insulation. Then, the substrate was
attached above the copper block using thermal conductive double-sided tape (3M
Tape of 0.25 $mm$). A wicking reservoir was placed around the substrate to
wick the condensate from the substrate. To prevent heat transfer loss by
conduction, direct contact between the wicking reservoir and the substrate was
avoided, and a gap of 0.5 $mm$ was kept between the substrate and the wicking
reservoir (see Fig. 1). Thus, in order to initiate wicking, the liquid-vapor
interface of the condensate must crosses the gap and reach up to the side
edges of the wicking reservoir. The overall condensation performance of the
different substrates was measured from the weight difference of the wicking
reservoir before and after the condensation experiments in a controlled
environment for a duration of 1-2 hours. The mass of the wicking reservoir was
measured with a micro-balance (Ohaus-SPX622) of 10 $mg$ accuracy. A sheathed
T-type thermocouple (Tempsens) of diameter 0.6 $mm$ was inserted through the
lateral side of the substrate by making a drilled hole of diameter 0.8 $mm$.
The temperature of the substrate was measured using a data acquisition system
(Keysight-970A) at a recording rate of 1 data/minute. The time lapse images of
the condensation dynamics on the substrate were recorded at every minutes
using a DSLR camera (Nikon-D750) with a zoom lens (24-85 $mm$ Nikon lens), at
a focal length of 85 $mm$.

##  3 Results and Discussions

###  3.1 Surface morphology and engineered wettability

Figure 3: Surface morphology and wettability. (a-c) SEM, and (d) profilometer
micrographs of the SHB surface. Contact angle images of the water drop (e)
before and, (f) after hydrophobic functionalization on textured aluminum
substrate. The scale bars in the contact angle images are 1 $mm$.

Figure 3(a-c) shows the SEM images of the fabricated SHB surface at different
resolutions. It is evident from the SEM micrographs that the rationally
modified surface consists of $Al_{2}O_{3}$ blade-shaped nanostructures and
flower-shaped microstructures [46]. The length and width of the blade shaped
nanostructures were in the range of 100-300 $nm$ and 15-30 $nm$ respectively.
The size of the flower-shaped microstructures was in the range of 0.5-1 $\mu
m$. The physical structure of the SHB surface is identical to the surface
morphology of the textured surface before the silane functionalization, since
the self-assembled monolayer could only make a layer of negligible thickness
of 30 $\AA$ [48]. The average macroscopic roughness of the textured surface
was $\sim$4.2 $\mu m$. The textures on the modified rough surface were random,
and the peak height and valley depth were in the order of $\sim$10 $\mu m$ and
$\sim$15 $\mu m$ respectively (see Fig. 3d). The contact angle of the sessile
water droplet before the hydrophobic coating was nearly zero. The hydrophobic
coating changed the surface wettability of the textured surface to
superhydrophobicity, as shown in Fig. 3(e-f). The magnitudes of the advancing
($\theta_{A}$) and receding ($\theta_{R}$) contact angles on the SHB surface
were $159\pm 2^{\circ}$ and $155\pm 2^{\circ}$ respectively. The contact angle
hysteresis (CAH) is defined as the difference between advancing and receding
contact angles, and the magnitude of the CAH for the SHB surface was $4\pm
2^{\circ}$. The wettability patterns on the substrate were fabricated by
selective etching of the hydrophobic coating using a $CO_{2}$ laser. As a
result, the laser exposed area on the substrate transitioned to
superhydrophilic with a contact angle of below 5∘.

Figure 4: A plate type condenser substrate with patterned wettability
comprising of SHL and SHB wettability regions (a) Pattern P1 - rectangular
strip: full, (b) Pattern P2 - rectangular strip: half, (c) Pattern P3 - wedge,
(d) Pattern P4 - hybrid (wedge + rectangular strip). The red shaded region
represents the SHL area and the blue region represents the SHB area. Here, the
SHB region promotes the dropwise mode of condensation and the SHL region
promotes the filmwise mode of condensation. The SHL tracks facilitate the
transport of condensate from the inner region of the substrate to the side
edge region. The units of all dimensions mentioned in this figure are in $mm$.

Figure 4 illustrates the design of the different substrates with patterned
wettabilities used in the present study. The pattern P1 consists of fourteen
parallel SHL rectangular strips with a width of 1.2 $mm$ and a length of 40
$mm$ laid on a SHB background (see Fig. 4a). Wherein, the spacing between the
wettability transition lines of two consecutive SHL strips is set at 1.6 $mm$.
For pattern P2, every SHL track in the pattern P1 is divided from the centre
such that each of these tracks is converted to two rectangular tracks, as
shown in Fig. 4b. Hence, the total number of SHL tracks became twenty-eight in
the pattern P2 with a strip length of 19 $mm$. The central spacing between two
in-line SHL strips is set at 2 $mm$. In pattern P3, rectangular strips of
pattern P2 were replaced with wedge-shaped tracks having a wedge angle of
$8^{\circ}$ (see Fig. 4c). Wherein, the width of the wedge at its widest end
was 3 $mm$, the narrower end was 0.35 $mm$ and the pitch between two
consecutive parallel wedges was 4.5 $mm$. On pattern P3, the distance between
the wettability transition lines of two consecutive SHL wedges ranges from
4.15 $mm$ at the narrower end to 1.5 $mm$ at the wider end. The wedge angle of
8∘ is chosen in the design such that successful transport of a drop with a
diameter greater than 1.8 $mm$ (equal to the departure diameter for a
hydrophobic surface in vertical orientation [49]) from the superhydrophobic
area to the surrounding wicking reservoir is achievable once the drop has
merged with the liquid at the narrower end of the wedge. In our earlier study,
we described the rationale behind selecting the various parameters in the
proposed pattern of wettability. [19] The total number of SHL tracks in the
pattern P3 was reduced to eighteen compared to pattern P2 since the width of
the tracks in the pattern P3 was increased to 3.01 $mm$ compared to 1.2 $mm$.
To increase the total number of SHL tracks, pattern P4 was designed by
combining patterns P2 and P3. The various design parameters for pattern P4
were selected so that the total fractional area of the superhydrophilic track
of the surface was kept in the range between 30–35%, like in pattern P3. Each
SHL track in pattern P4 consists of a shorter wedge compared to the wedge in
pattern P3, and the narrower end of the wedge was connected with a rectangular
strip of width 0.6 $mm$ and a length of 9 $mm$, as shown in Fig. 4d. The total
number of SHL tracks on Pattern P3 increased to twenty-six. The width of the
wider end of the wedge was 2 $mm$, the narrower end of the wedge was 0.6 $mm$,
and the pitch between the two consecutive tracks was 3.2 $mm$. As a result,
the distance between the wettability transition lines of two consecutive SHL
tracks on pattern P4 was shortened in comparison to pattern P3, ranging from
2.6 $mm$ at the narrower end to 1.2 $mm$ at the wider end.

###  3.2 Condensation observation

Figure 5: Macroscale condensation snapshots of different substrates with
patterned wettability at different times. The red-coloured contour represents
the shape of the SHL track in each patterned substrate. $t_{0}$ denotes the
time when the temperature of the substrate reaches $T_{s}$. The scale bar is 5
$mm$.

Condensation is a complex phenomenon that consists of various processes such
as drop nucleation, droplet growth, and coalescence [7]. Typically, condensate
that forms on a surface drains away when the gravity force of the condensate
becomes higher than the force of surface adhesion. However, in a microgravity
environment, the generated condensate on a homogeneous surface coalesces and
accumulates over the surface as multiple bulges, further transitioning to a
thick film. The removal of condensate from a surface before the formation of a
larger sized liquid bulge is necessary for the continuous operation of a
condenser at a desired heat transfer rate. The wicking reservoir of the
proposed platform helps to remove the condensate from the substrate. The
liquid-vapor interface of the condensate must overcome the gap between the
substrate side edges and the wicking reservoir in order to start wicking. The
condensate transport mechanism and its performance on four different
substrates with patterned wettability in a controlled humid air environment
are compared in this study. Figure 5 depicts the snap-shots of the
condensation phenomena on the horizontally oriented substrates having
different patterned wettabilities at an interval of 30 minutes. The
experiments were carried out in an environmental chamber with a temperature
($T_{env}$) of 40 ${}^{\circ}C$, a relative humidity (RH) of 80 % and a
substrate temperature ($T_{s}$) of 4$\pm$1 ${}^{\circ}C$. At the initial stage
of condensation, the substrates showed a dropwise mode of condensation on the
SHB area and a filmwise mode of condensation on the SHL area. On pattern P1,
the amount of condensate liquid increased in the rectangular SHL tracks and
formed a liquid bulge with time since the condensate was not removed from the
substrate. This liquid bulge grew with time, and the liquid interface of the
bulge coalesced with either the neighbouring bulge or the neighbouring SHL
rectangular track. After a few more coalescences, the liquid bulges over the
centre region of the substrate and floods (see Fig. 5a). These liquid bulges
prevent the effective spread of condensate through the SHL tracks and resist
the continuous removal of condensate through the substrate side edges by
wicking. The formation of larger sized liquid bulges was also observed on the
substrate with pattern P2. The total volume and the total number of bulges
were found to be higher on pattern P2 than on pattern P1. The central SHB area
on pattern P2 avoids the merging of liquid bulges formed on the SHL tracks
found on the opposite sides, as shown in Fig. 5b. Interestingly, flooding of
the condensate was not observed on patterns P3 and P4 (see Fig. 5c and d).
This indicates that the nucleated condensate was being removed continuously
from these substrates with patterned wettability P3 and P4.

Figure 6: The coalescence between drop and film causes the capillary-driven
pumping of condensate from the SHB region to the SHL region on pattern P1 and
P2. The red solid line represents the border line between the SHB and SHL
areas. The yellow arrow line represents the liquid transport from drop to
film. The scale bar is 3 $mm$.

Condensate appeared as distinct drops with a size ranging from several
nanometers to millimetres in the SHB area. Whereas, condensate was observed in
the form of a liquid film on the SHL tracks. The condensate drops from the SHB
region were passively transported to the SHL tracks by coalescence driven
capillary pumping [44, 40]. The nucleated drop in the SHB region grew with
time, and it coalesced with the nearest condensate film in the SHL region once
the liquid interface of the drop was in contact with the wettability
transition line, as shown in Fig. 6. This liquid transport occurs due to the
difference in the Laplace pressure acting at the liquid-vapor interface
between the drop and the film. The higher interfacial Laplace pressure of the
drop compared to the liquid film having an infinite radius of curvature causes
the transport of liquid from the drop to the film in the SHL track. After the
coalescence, the liquid-vapor interface of the liquid film in the SHL region
crosses the wettability transition line (see Fig. 6c) due to inertia, and
finally the liquid volume from the drop is spread out over the SHL track.

Figure 7: An illustration of the passive transport of condensate through an
SHL wedge and the transport of condensate from substrate to wicking reservoir
in the pattern P3. The red solid line represents the border line between the
SHB and SHL areas. The yellow arrow line represents the direction of liquid
transport. The violet-coloured shaded region represents the side end of the
wicking reservoir. The scale bar is 3 $mm$.

Figure 7 demonstrates the transport of a liquid drop from the SHB region to
the wicking reservoir via the SHL wedge on substrate P3 during condensation.
Wherein, the SHL track is completely filled with the condensate before the
drop-film coalescence event. The drop from the SHB region is transported to
the SHL region once the liquid interface of the drop is in contact with the
liquid film present in the SHL track due to capillary pumping [44, 40].
Thereafter, the liquid is transported inside the wedge track from the narrower
end to the wider end by a Laplace pressure gradient arising due to the
curvature difference between the front and back end [21, 22]. The magnitude of
the pressure gradient of the liquid bulge in the SHL track is calculated based
on scaling arguments [22],

$\frac{dP}{dx}\approx
2\sigma_{lv}sin\theta_{avg}\frac{\alpha}{2\delta(x)^{2}}$ (1)

where $\sigma_{lv}$ is the interfacial surface tension, $\theta_{avg}$ is the
average of the front and back end apparent contact angles of the liquid bulge,
$\alpha$ is the included angle of the wedge track, and $\delta(x)$ is the
track width of the wedge at a local position of $x$ from the narrower end in
the direction of liquid transport (see Fig. 7a). Wherein, the SHL track is not
completely filled with the condensate prior to drop-film coalescence. The
transported liquid accumulated in the wider region of the wedge due to the
substrate edge resistance. The size of the accumulated liquid bulge inside the
SHL track increases with time, and the liquid interface of the bulge merges
with the surrounded wicking reservoir. Thereafter, the wicking reservoir
absorbs condensate from the substrate by wicking.

Figure 8: Illustration of liquid transport from the thin rectangular track to
the wider end of the wedge in the pattern P4. The red solid line represents
the border line between the SHB and SHL areas. The yellow arrow line
represents the direction of liquid transport. The violet-coloured shaded
region represents the side end of the wicking reservoir. The scale bar is 3
$mm$.

In pattern P4, the hybrid SHL track was designed by superimposing the wedge
pattern on a rectangular striped pattern. The condensate transported to the
rectangular stripe region from the SHB area spreads into the rectangular
shaped region of the hybrid SHL track with time, as shown in Fig. 8. The
transport of condensate is resisted at the merging region between the
rectangular and wedge SHL tracks. The maximum accumulation in the rectangular
region drives the transport of condensate from the rectangular region to the
narrower region of the wedge. Further, the liquid from the narrower end is
transported to the wider end by a difference in Laplace pressure, and the
accumulated condensate in the wider region of the wedge is absorbed by the
surrounded wicking reservoir, similar to pattern P3. The total volume of the
liquid that can be accommodated within a single SHL track on pattern P3 is
higher as compared to pattern P4.

The superhydrophilic tracks in the patterned substrate act as an intermediate
reservoir before the condensate is removed to the wicking reservoir placed
outside of the condenser plate. The drops from the superhydrophobic region can
coalesce with the liquid film at different locations on the substrate. After
the coalescence, the area occupied by the coalesced drop in the
superhydrophobic region will become dry, and further drop nucleation will
occur. The time scale of the liquid transport within the superhydrophilic
track is depend on the volume of the condensate occupied in the track and the
location of the drop when it connected with the wettability transition line.
Condensate wicking from the substrate can occur only when the superhydrophilic
track is completely filled with condensate and the liquid interface of the
bulge bridges the gap between the substrate and wicking reservoir. The time
scale for the transport process of the nucleated drops from the
superhydrophobic region to the superhydrophilic region is influenced by the
pitch between the superhydrophilic track and the total length of the
wettability transition line. The total length of the wettability transition
line was $\sim$0.7 $m$, and $\sim$1 $m$ for the patterned surfaces P3 and P4,
respectively. Hence, the probability for the occurrence of drop to film
coalescence process is higher for pattern P4 than pattern P3 due to 42%
increase in the wettability transition line for the pattern P4.

###  3.3 Droplet transport on wettability engineered superhydrophilic tracks

Figure 9: Steady state droplet shape on different patterned superhydrophilic
tracks. (a-c) The shape and size of the various superhydrophilic track
patterns (Patterns P2, P3, and P4, respectively). The wettability outside of
the track is superhydrophobic. All dimensions are in $mm$. (d-f) The droplet’s
initial condition on a patterned superhydrophilic rectangular track (pattern
P2), wedge-shaped track (pattern P3), or combined rectangular and wedge track
(pattern P4). (g) The final steady-state shape of the droplet on a rectangular
track. The bulge is formed near the initial droplet location. (h) The droplet
was transported to the end of the wedge track and the bulge formed near the
wider end of the track. (i) The droplet was transported efficiently and a
larger-sized bulge formed at the end of the track. The units of all dimensions
mentioned in this figure are in $mm$.

To identify the differences in the droplet transport behaviors on the
different patterned wettability surfaces, steady-state simulations are
performed using the HyDro droplet simulation solver [50]. Matsui et al. [50]
developed HyDro using hybrid energy minimization techniques to identify the
equilibrium shape of a droplet placed on a surface. In the simulations, only
the transport of a single droplet on smooth patterned wettable surfaces is
shown. The actual condensing scenarios are much more complex, with multiple
droplet coalescence, droplet-to-film coalescence, and hierarchical surface
roughness. To mimic the bulge formation on the superhydrophilic tracks
observed during condensation, we have placed a droplet of volume 10 $\mu L$ on
different patterned wettable surfaces, as shown in Fig. 9. Here the
superhydrophilic tracks are laid on a superhydrophobic background. Therefore,
when a droplet is placed at the start of the track, the droplet spreads till
the end of the track. However, the mechanism of droplet transport in the
different tracks or patterns is different. The droplet spreads on the
rectangular track (pattern P2) due to the surface’s high energy. After the
liquid had spread to the end of the track, a bulge formed near the initial
droplet location (see Fig. 9g). On the wedge track (pattern P3), the liquid
spreads due to the net capillary force caused by the difference in curvature
between the droplet’s front and back [51]. As the liquid is pumped due to the
capillary force, the bulge formation occurs near the wider end of the track
(see Fig. 9h). However, the bulge is spread over a longer distance. On the
combined rectangular and wedge track (pattern P4), the droplet transport takes
place initially on the rectangular track and then reaches the wedge region
through the capillary transport on the wedge track. This transport is very
efficient, as the liquid can move forward easily through the capillary
transport but cannot go back to the rectangular track due to the requirement
of extra pressure (working like a natural valve). Hence, the liquid bulge
forms near the end of the wedge track (see Fig. 9i). The formation of liquid
bulges on the various superhydrophilic tracks observed during experiments is
identical to the results obtained from steady-state simulations (see Fig. 5,
Fig. 7d, and Fig. 8c).

Figure 10: The variation in liquid height at the central plane ($Y=0$) of the
different shaped patterns along the track length of the superhydrophilic
track. $X=0$ $mm$ represents the initial position of the drop and $X=19$ $mm$
represents the side edge of the substrate.

Figure 10 depicts the height of the liquid on the central plane ($Y=0$) of the
superhydrophilic track from the start ($X=0$ $mm$) to the end ($X=19$ $mm$)
position. On pattern P2, the liquid height increases from the initial position
and reaches a maximum value at $X=4.75$ $mm$ and further the height reduces
till $X=8.5$ $mm$. Thereafter, the liquid height is maintained as constant,
and a sharp reduction occurs at the end of the track. For pattern P3, a smooth
increase in the liquid height was observed till $X=16.5$ $mm$ and it further
reduced at the track end. The liquid height in the wedge region of the pattern
P4 first increases upto $X=16.5$ $mm$ and then reduces till the end of the
track. Interestingly, in the case of pattern P4, the liquid height in the
rectangular region of the track is quite small and the magnitude was $0.06$
$mm$. Thus, the liquid forms a thin film on the rectangular region of the
track and a big bulge near the end of the wedge region of the track. Due to
the larger bulge at the end of the track, the liquid in the superhydrophilic
track of pattern P4 can easily come into contact with the wicking material
placed on the sides of the condenser plate.

###  3.4 Condensation performance

The condensation experiments on the horizontally oriented substrates were
performed under two different conditions: Case (A) $T_{env}=30$ ${}^{\circ}C$,
RH= 80 %, and $T_{s}$= 1.5$\pm$0.5 ${}^{\circ}C$, and Case (B) $T_{env}=40$
${}^{\circ}C$, RH= 80 %, and $T_{s}$= 4$\pm$1 ${}^{\circ}C$. The dew point
temperature of Case (A) is $T_{dew}=26.1$ ${}^{\circ}C$ and Case (B) is
$T_{dew}=35.8$ ${}^{\circ}C$. The difference in the mass of the wicking
reservoir before and after the condensation experiments was calculated to
compare the condensation performance of different substrates with patterned
wettability. The pattern P2 showed the lowest and the pattern P4 showed the
highest condensation removal rate in both environmental conditions, as shown
in Fig. 11a. The formation of larger-sized liquid bulges observed on both
sides of the pattern P2 substrate caused the delay in the condensate transport
to the wicking reservoir. However, the wicking occurs when the liquid
interface of the liquid bulge crosses the side edge of the substrate. Pattern
P4 with hybrid SHL tracks has shown a better condensation removal rate
compared to pattern P3 with wedge-shaped SHL tracks.

Figure 11: Comparison of condensation performance on different substrates
engineered wettability. (a) The average rate of condensate collection by the
wicking reservoir on different substrates with patterned wettability. (b)
Average heat transfer coefficients of various substrates.

The effective condensation heat transfer coefficient (CHTC) of the substrate
is defined as [40],

$h=\frac{\dot{m}h_{fg}}{T_{dew}-T_{s}}$ (2)

where $\dot{m}$ is the total mass collected by the wicking reservoir, $h_{fg}$
is the latent heat absorbed by the substrate during condensation, $T_{dew}$ is
the dew point temperature, and $T_{s}$ is the substrate temperature. The
accurate collection of condensate without any mass losses is important for
predicting the CHTC accurately. As the mass collection system is kept in a
humid environment, evaporation of the collected condensate occurs and can lead
to the underprediction of the CHTC. In the present study, condensate
collection is achieved with a wicking reservoir, as shown in Fig. 1. Here, the
wicking reservoir is covered with a plastic sheet on all the faces except the
interior faces parallel to the substrate edges, through which the condensate
is absorbed. Hence, evaporation occurs only through the faces that are
parallel to the substrate edges. The temperature of the humid air near the
interior faces of the wicking reservoir is much lower than the $T_{env}$ due
to sensible cooling. Hence, the evaporation loss during condensate collection
is negligible and the corresponding contribution to the heat transfer
coefficient is not accounted in Eq. 2.

The formation of a greater number of liquid bulges reduces the CHTC on pattern
P2 substrate by $\sim$15% and $\sim$10% compared to pattern P1 at the
experimental conditions A and B, respectively. The flooding of condensate was
not observed in patterns P3 and P4. The passive transport of condensate
through SHL wedge tracks on the patterns P2 and P4 avoided the flooding of
condensate on the substrate. Hence, the condensation performance on substrates
having patterns P3 and P4 was found to be better as compared to the substrates
with patterns P1 and P2. In experimental condition A, the CHTC of pattern P3
and P4 substrates was enhanced by $\sim$136% and $\sim$178% compared to
pattern P1. For the experimental condition B, the enhancement was $\sim$107%
and $\sim$138%, respectively, for the substrates with pattern P3 and P4.
Interestingly, the CHTC of pattern P4 was enhanced by $\sim$18% and $\sim$15%
compared to pattern P3 at environmental conditions A and B, respectively. The
main reasons for this enhancement were the increase in the number of SHL
tracks and the decrease in the area occupied by the single SHL track on
pattern P4 compared to pattern P3.

###  3.5 Design limitations and scalability of the condenser platform

This study explored the feasibility of a plate-type condenser that can operate
continuously in a humid air environment in microgravity. The current work
attempted to address challenges related to the removal of condensate from the
condenser substrate in a microgravity condition. The condensate is transported
from the interior area of the horizontally oriented substrate to the side
edges by passive transport in the wedge shaped pattern, and its removal is
aided by continuous wicking from the side edges by a wicking reservoir.
However, the proposed condenser platform may fail once the wicking reservoir
is saturated with the condensate collected from the substrate, which could
further result in surface flooding. When the condenser is run continuously for
a longer duration or under high condensation flux conditions, the wicking
reservoir can saturate with the condensate liquid. Hence, the surrounded
wicking reservoir can only act as an intermediate reservoir, and condensate
must be continuously extracted from the wicking reservoir by an external
system during long-term operation. This can be accomplished by making
micrometer-sized holes in the wicking reservoir, with one end closed and the
other end attached to a micrometer-sized capillary tube. When the wicking
reservoir is filled with the condensate absorbed from the substrate, the holes
in the reservoir began to fill. Thereafter, the condensate will be carried by
capillary action through the connected capillary tube. This capillary tube may
continuously suck the collected condensate from the wicking reservoir.
Furthermore, the condensate from this tube can be pumped using either a
suction pump [14] or a capillary ejection mechanism [52, 53] in microgravity
to a storage tank.

Figure 12: Steady-state simulation of the passive droplet transport in the two
superhydrophilic tracks of pattern P4 that have been sandwiched in series. (a)
Initial, and (b) final state from the simulation. The volume of the water drop
was 10 $\mu L$.

The proposed condenser platform had an active condenser area of 40 $\times$ 40
$mm^{2}$. During the scaling of the condenser area, the length of the
superhydrophilic tracks should also be increased. However, the passive
transport of the condensate may fail when the length of the wedge is higher,
which can cause surface flooding. Therefore, for a larger substrate, the
proposed patterned design must be modified to avoid the flooding issue. In
such cases, multiple superhydrophilic tracks in the pattern P4 can be
sandwiched in series to increase the overall length of the superhydrophilic
track, as shown in Fig. 12a. The steady-state simulation elucidated that the
passive transport of the droplet is possible even with two superhydrophilic
tracks that are connected in series (see Fig. 12b). The formation of a liquid
bulge was observed in the wider end of both wedges. The size of the liquid
bulges will increase when the droplets from the superhydrophobic region are
transported to the superhydrophilic track by drop-film coalescence. Further,
the wicking at the side edges will occur when the interface of the liquid
bulge close to the side edges exceeds the gap between the substrate and
wicking reservoir.

A sufficient wettability contrast between the hydrophilic and hydrophobic
regions is a primary requirement for the efficient transport of condensate
through the superhydrophilic wedge track and the transport of drop from the
hydrophobic region to the hydrophilic track [51, 54]. The absorption of
volatile organic compounds (VOCs) present in the atmosphere might raise the
contact angle of the superhydrophilic region in ambient conditions [55].
However, such possibilities are rare on the space station because atmospheric
air conditions are artificially created in the space station using purified
gases carried from Earth. Despite repeated condensation cycles, the
superhydrophobic characteristic of the fabricated self assembled mono-layer
coating did not change, indicating that the superhydrophobic coating was
chemically stable.

In practical applications, the proposed wicking reservoir made from layers of
filter papers is inadequate and can be interchanged with metallic wicking
materials that offer better durability. Further research is required to
develop a working prototype for microgravity conditions that can be operated
for long durations or under high heat flux conditions. In such cases, the
proposed condenser platform must be integrated with an external system that
can continuously transport the collected condensate from the wicking reservoir
to a storage tank. The proposed condensate removal mechanism, which utilises
patterns of wettability and wicking reservoirs, can also be adopted for high
heat flux condensation. This study explored the experiments of water vapour
condensation in the presence of air. Therefore, the exhibited technology is
applicable to the management of humidity within the space station. After
filtration and mineralization, the collected condensate from the platform can
also be used as drinking water for astronauts.

##  4 Conclusion

In this study, we proposed a proof-of-concept for a novel plate-type condenser
platform that facilitates the continuous removal of condensate from a
horizontal wettability-patterned surface via a wicking reservoir surrounding
the condensing area. This study examined the condensation dynamics and heat
transfer performance of four distinct patterns of wettability comprised of
laser-engraved superhydrophilic tracks of varying shapes on a superhydrophobic
surface. Using coalescence-driven capillary pumping, the condensate from the
superhydrophobic region migrated to the superhydrophilic tracks. The physics
of the passive transport of the condensate liquid on various patterns of
wettability is investigated using numerical modelling. The Laplace pressure
difference of the wedge-shaped superhydrophilic track directs the condensate
to the substrate’s side edges. Further, the accumulated condensate along the
side edges is absorbed by the wicking reservoir. Flooding of the condensate is
observed on the engineered wettability designs of P1 and P2. On the engineered
wettability designs P3 and P4, we observed the continuous removal of
condensate without flooding. Pattern P4 has demonstrated better condensation
heat transfer performance than pattern P3 by more than 15%. Thus, the optimal
surface with a patterned wettability can enhance the effective condensation
performance. The current research could pave the way for developing efficient
condenser surfaces for space applications.

## Acknowledgement

The authors thank Science and Engineering Research Board (SERB) of Government
of India [Project number: ECR/2018/001806] for funding the work. This research
is partly supported by Indian Institute of Technology Madras to the Micro Nano
Bio Fluidics Group under the funding for Institutions of Eminence scheme of
Ministry of Education, Government of India [Sanction. No: $11/9/2019-U.3(A)$].

## References

  * [1] Xiaoya Li, Jian Song, Guopeng Yu, Youcai Liang, Hua Tian, Gequn Shu, and Christos N Markides.  Organic rankine cycle systems for engine waste-heat recovery: Heat exchanger design in space-constrained applications.  Energy Conversion and Management, 199:111968, 2019.
  * [2] Luis Pérez-Lombard, José Ortiz, Juan F Coronel, and Ismael R Maestre.  A review of hvac systems requirements in building energy regulations.  Energy and Buildings, 43(2-3):255–268, 2011.
  * [3] Dimitrios Nioras, Kosmas Ellinas, Vassilios Constantoudis, and Evangelos Gogolides.  How different are fog collection and dew water harvesting on surfaces with different wetting behaviors?  ACS Applied Materials & Interfaces, 13(40):48322–48332, 2021.
  * [4] Haya Nassrullah, Shaheen Fatima Anis, Raed Hashaikeh, and Nidal Hilal.  Energy for desalination: A state-of-the-art review.  Desalination, 491:114569, 2020.
  * [5] Ying-Nan Song, Mao-Qin Lei, Dong-Lin Han, Yu-Chuan Huang, Shuai-Peng Wang, Jian-Yang Shi, Yue Li, Ling Xu, Jun Lei, and Zhong-Ming Li.  Multifunctional membrane for thermal management applications.  ACS Applied Materials & Interfaces, 13(16):19301–19311, 2021.
  * [6] E Schmidt, W Schurig, and W Sellschopp.  Condensation of water vapour in film-and drop form.  Technische Mechanik und Thermodynamik, 1:53–63, 1930.
  * [7] H Tanaka.  Further developments of dropwise condensation theory.  Journal of Heat Transfer, 101:603–611, 1979.
  * [8] Daniel Attinger, Christophe Frankiewicz, Amy R Betz, Thomas M Schutzius, Ranjan Ganguly, Arindam Das, Chang-Jin Kim, and Constantine M Megaridis.  Surface engineering for phase change heat transfer: A review.  MRS Energy & Sustainability, 1, 2014.
  * [9] H Jeremy Cho, Daniel J Preston, Yangying Zhu, and Evelyn N Wang.  Nanoengineered materials for liquid–vapour phase-change heat transfer.  Nature Reviews Materials, 2(2):1–17, 2016.
  * [10] Ngoc Giang Tran and Doo-Man Chun.  Ultrafast and eco-friendly fabrication process for robust, repairable superhydrophobic metallic surfaces with tunable water adhesion.  ACS Applied Materials & Interfaces, 2022.
  * [11] Kyle L Wilke, Dion S Antao, Samuel Cruz, Ryuichi Iwata, Yajing Zhao, Arny Leroy, Daniel J Preston, and Evelyn N Wang.  Polymer infused porous surfaces for robust, thermally conductive, self-healing coatings for dropwise condensation.  ACS Nano, 14(11):14878–14886, 2020.
  * [12] Daniele Mangini, Mauro Mameli, Davide Fioriti, Sauro Filippeschi, L Araneo, and Marco Marengo.  Hybrid pulsating heat pipe for space applications with non-uniform heating patterns: ground and microgravity experiments.  Applied Thermal Engineering, 126:1029–1043, 2017.
  * [13] Arya Chatterjee, Peter C Wayner Jr, Joel L Plawsky, David F Chao, Ronald J Sicker, Tibor Lorik, Louis Chestney, John Eustace, Raymond Margie, and John Zoldak.  The constrained vapor bubble fin heat pipe in microgravity.  Industrial & Engineering Chemistry Research, 50(15):8917–8926, 2011.
  * [14] Mohammad M Hasan, Lutful I Khan, Vedha Nayagam, and Ramaswamy Balasubramaniam.  Conceptual design of a condensing heat exchanger for space systems using porous media.  In 35th International Conference on Environmental Systems (ICES), pages E–15464, 2006.
  * [15] Gerhard Hauser, Ludwig Eicher, Joachim Lucas, Johannes Witt, and Tanguy Morel.  Condensing heat exchanger, July 16 2002.  US Patent 6,418,743.
  * [16] Christopher M Thomas and Yonghui Ma.  Condensing heat exchanger with hydrophilic antimicrobial coating, July 1 2014.  US Patent 8,763,682.
  * [17] Sam Lowrey, Kirill Misiiuk, Richard Blaikie, and Andrew Sommers.  Survey of micro/nanofabricated chemical, topographical, and compound passive wetting gradient surfaces.  Langmuir, 38(2):605–619, 2021.
  * [18] Haoyu Dai, Zhichao Dong, and Lei Jiang.  Directional liquid dynamics of interfaces with superwettability.  Science Advances, 6(37):eabb5528, 2020.
  * [19] Tibin M Thomas, Imdad Uddin Chowdhury, K Dhivyaraja, Pallab Sinha Mahapatra, Arvind Pattamatta, and Manish K Tiwari.  Droplet dynamics on a wettability patterned surface during spray impact.  Processes, 9(3):555, 2021.
  * [20] Pallab Sinha Mahapatra, Ranjan Ganguly, Aritra Ghosh, Souvick Chatterjee, Sam Lowrey, Andrew D Sommers, and Constantine M Megaridis.  Patterning wettability for open-surface fluidic manipulation: Fundamentals and applications.  Chemical Reviews, 122(22):16752–16801, 2022.
  * [21] Imdad Uddin Chowdhury, Pallab Sinha Mahapatra, and Ashis Kumar Sen.  Self-driven droplet transport: Effect of wettability gradient and confinement.  Physics of Fluids, 31(4):042111, 2019.
  * [22] Uddalok Sen, Souvick Chatterjee, Ranjan Ganguly, Richard Dodge, Lisha Yu, and Constantine M Megaridis.  Scaling laws in directional spreading of droplets on wettability-confined diverging tracks.  Langmuir, 34(5):1899–1907, 2018.
  * [23] Jiaqian Li, Xiaofeng Zhou, Jing Li, Lufeng Che, Jun Yao, Glen McHale, Manoj K Chaudhury, and Zuankai Wang.  Topological liquid diode.  Science Advances, 3(10):eaao3530, 2017.
  * [24] Qiangqiang Sun, Dehui Wang, Yanan Li, Jiahui Zhang, Shuji Ye, Jiaxi Cui, Longquan Chen, Zuankai Wang, Hans-Jürgen Butt, Doris Vollmer, and Xu Deng.  Surface charge printing for programmed droplet transport.  Nature Materials, 18(9):936–941, 2019.
  * [25] Christos Stamatopoulos, Athanasios Milionis, Norbert Ackerl, Matteo Donati, Paul Leudet de la Vallee, Philipp Rudolf von Rohr, and Dimos Poulikakos.  Droplet self-propulsion on superhydrophobic microtracks.  ACS Nano, 14(10):12895–12904, 2020.
  * [26] Chenglin Zhang, Dehui Wang, Jinlong Yang, Wenluan Zhang, Qiangqiang Sun, Fanfei Yu, Yue Fan, Yong Li, Longquan Chen, and Xu Deng.  Charge density gradient propelled ultrafast sweeping removal of dropwise condensates.  The Journal of Physical Chemistry B, 125(7):1936–1943, 2021.
  * [27] Jonathan B Boreyko and Chuan-Hua Chen.  Self-propelled dropwise condensate on superhydrophobic surfaces.  Physical Review Letters, 103(18):184501, 2009.
  * [28] Abulimiti Aili, Hongxia Li, Mohamed H Alhosani, and TieJun Zhang.  Unidirectional fast growth and forced jumping of stretched droplets on nanostructured microporous surfaces.  ACS Applied Materials & Interfaces, 8(33):21776–21786, 2016.
  * [29] Daniel J Preston, Kyle L Wilke, Zhengmao Lu, Samuel S Cruz, Yajing Zhao, Laura L Becerra, and Evelyn N Wang.  Gravitationally driven wicking for enhanced condensation heat transfer.  Langmuir, 34(15):4658–4664, 2018.
  * [30] Yaqi Cheng, Mingmei Wang, Jing Sun, Minjie Liu, Bingang Du, Yuanbo Liu, Yuankai Jin, Rongfu Wen, Zhong Lan, Xiaofeng Zhou, et al.  Rapid and persistent suction condensation on hydrophilic surfaces for high-efficiency water collection.  Nano Letters, 21(17):7411–7418, 2021.
  * [31] Vaibhav Bahadur and Suresh V Garimella.  Electrowetting-based control of static droplet states on rough surfaces.  Langmuir, 23(9):4918–4924, 2007.
  * [32] Susan Daniel, Manoj K Chaudhury, and John C Chen.  Fast drop movements resulting from the phase change on a gradient surface.  Science, 291(5504):633–636, 2001.
  * [33] Ashley M Macner, Susan Daniel, and Paul H Steen.  Condensation on surface energy gradient shifts drop size distribution toward small drops.  Langmuir, 30(7):1788–1798, 2014.
  * [34] Vipul Sharma, Daniel Orejon, Yasuyuki Takata, Venkata Krishnan, and Sivasankaran Harish.  Gladiolus dalenii based bioinspired structured surface via soft lithography and its application in water vapor condensation and fog harvesting.  ACS Sustainable Chemistry & Engineering, 6(5):6981–6993, 2018\.
  * [35] Songnan Zhang, Jianying Huang, Zhong Chen, and Yuekun Lai.  Bioinspired special wettability surfaces: from fundamental research to water harvesting applications.  Small, 13(3):1602992, 2017.
  * [36] Kyoo-Chul Park, Philseok Kim, Alison Grinthal, Neil He, David Fox, James C Weaver, and Joanna Aizenberg.  Condensation on slippery asymmetric bumps.  Nature, 531(7592):78–82, 2016.
  * [37] Youmin Hou, Miao Yu, Xuemei Chen, Zuankai Wang, and Shuhuai Yao.  Recurrent filmwise and dropwise condensation on a beetle mimetic surface.  ACS Nano, 9(1):71–81, 2015.
  * [38] Jianxing Sun and Patricia B Weisensee.  Microdroplet self-propulsion during dropwise condensation on lubricant-infused surfaces.  Soft Matter, 15(24):4808–4817, 2019.
  * [39] Aritra Ghosh, Sara Beaini, Bong June Zhang, Ranjan Ganguly, and Constantine M Megaridis.  Enhancing dropwise condensation through bioinspired wettability patterning.  Langmuir, 30(43):13103–13115, 2014.
  * [40] Pallab Sinha Mahapatra, Aritra Ghosh, Ranjan Ganguly, and Constantine M Megaridis.  Key design and operating parameters for enhancing dropwise condensation through wettability patterning.  International Journal of Heat and Mass Transfer, 92:877–883, 2016\.
  * [41] Dimitrios Nioras, Kosmas Ellinas, and Evangelos Gogolides.  Atmospheric water harvesting on micro-nanotextured biphilic surfaces.  ACS Applied Nano Materials, 2022.
  * [42] Yu Tang, Xiaolong Yang, Yimin Li, and Di Zhu.  Design of hybrid superwetting surfaces with self-driven droplet transport feature for enhanced condensation.  Advanced Materials Interfaces, 8(13):2100284, 2021.
  * [43] Theodore P Koukoravas, George Damoulakis, and Constantine M Megaridis.  Experimental investigation of a vapor chamber featuring wettability-patterned surfaces.  Applied Thermal Engineering, 178:115522, 2020.
  * [44] Melanie M Derby, Abhra Chatterjee, Yoav Peles, and Michael K Jensen.  Flow condensation heat transfer enhancement in a mini-channel with hydrophobic and hydrophilic patterns.  International Journal of Heat and Mass Transfer, 68:151–160, 2014\.
  * [45] W Vedder and DA Vermilyea.  Aluminum+water reaction.  Transactions of the Faraday Society, 65:561–584, 1969.
  * [46] Tibin M Thomas and Pallab Sinha Mahapatra.  Condensation of humid air on superhydrophobic surfaces: Effect of nanocoatings on a hierarchical interface.  Langmuir, 37(44):12767–12780, 2021.
  * [47] Lichao Gao and Thomas J McCarthy.  Wetting 101°.  Langmuir, 25(24):14105–14115, 2009.
  * [48] Qingfeng Yang and Anzhong Gu.  Dropwise condensation on sam and electroless composite coating surfaces.  Journal of Chemical Engineering of Japan, 39(8):826–830, 2006.
  * [49] Rongfu Wen, Shanshan Xu, Dongliang Zhao, Yung-Cheng Lee, Xuehu Ma, and Ronggui Yang.  Hierarchical superhydrophobic surfaces with micropatterned nanowire arrays for high-efficiency jumping droplet condensation.  ACS Applied Materials & Interfaces, 9(51):44911–44921, 2017.
  * [50] Hiroyuki Matsui, Yuki Noda, and Tatsuo Hasegawa.  Hybrid energy-minimization simulation of equilibrium droplet shapes on hydrophilic/hydrophobic patterned surfaces.  Langmuir, 28(44):15450–15453, 2012.
  * [51] Aritra Ghosh, Ranjan Ganguly, Thomas M Schutzius, and Constantine M Megaridis.  Wettability patterning for high-rate, pumpless fluid transport on open, non-planar microfluidic platforms.  Lab on a Chip, 14(9):1538–1550, 2014.
  * [52] Andrew Wollman and Mark Weislogel.  New investigations in capillary fluidics using a drop tower.  Experiments in Fluids, 54(4):1–13, 2013.
  * [53] Hadi Mehrabian and James J Feng.  Auto-ejection of liquid drops from capillary tubes.  Journal of Fluid Mechanics, 752:670–692, 2014.
  * [54] Xiao Yan, Feipeng Chen, Chongyan Zhao, Xiong Wang, Longnan Li, Siavash Khodakarami, Kazi Fazle Rabbi, Jiaqi Li, Muhammad Jahidul Hoque, Feng Chen, et al.  Microscale confinement and wetting contrast enable enhanced and tunable condensation.  ACS Nano, 16(6):9510–9522, 2022.
  * [55] Jingcheng Ma, Soumyadip Sett, Hyeongyun Cha, Xiao Yan, and Nenad Miljkovic.  Recent developments, challenges, and pathways to stable dropwise condensation: a perspective.  Applied Physics Letters, 116(26):260501, 2020.