Directional Passive Transport of Micro-Droplets in Oil-Infused

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Surfaces, Interfaces, and Applications

Directional Passive Transport of Micro-Droplets in OilInfused Diverging Channels for Effective Condensate Removal Hongxia Li, Ablimit Aili, Mohamed H Alhosani, Qiaoyu Ge, and TieJun Zhang ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.8b00922 • Publication Date (Web): 24 May 2018 Downloaded from http://pubs.acs.org on May 25, 2018

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ACS Applied Materials & Interfaces

Directional Passive Transport of Micro-Droplets in Oil-Infused Diverging Channels for Effective Condensate Removal Hongxia Li‡, Ablimit Aili‡, Mohamed H. Alhosani, Qiaoyu Ge, TieJun Zhang* Department of Mechanical and Materials Engineering, Masdar Institute, Khalifa University of Science and Technology, P.O. Box 54224, Abu Dhabi, UAE. ‡These authors contributed equally to this work. *Correspondence and requests for materials should be addressed to T.Z. (email: [email protected])

KEYWORDS: Hierarchical structure, oil infusion, condensation, droplet, passive directional transport, micro-channel ABSTRACT Condensation widely exists in nature and industry, and its performance heavily relies on the efficiency of condensate removal. Recent advances in micro/nano-scale surface engineering enable condensing droplet removal from solid surfaces without extra energy cost, but it is still challenging to achieve passive transport of micro-droplets over long distance along horizontal surfaces. The mobility of these condensate droplets can be enhanced by lubricant oil infusion on flat surfaces and frequent coalescence, which lead to fast growth but random motion of droplets. In this work, we propose a novel design of diverging micro-channels with oil-infused surfaces to

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achieve controllable, long-distance, and directional transport of condensing droplets on horizontal surfaces. This idea is experimentally demonstrated with diverging copper and silicon microchannels with nano-engineered surfaces. Along these hierarchical surface structures, microdroplets condense on the top channel wall and submerge into micro-channels owing to the capillary pressure gradient in infusing oil. Confined by the micro-channel walls, the submerged droplets deform and maintain the back-front curvature difference, which enables the motion of droplets along the channel diverging direction. Subsequent droplet coalescences inside the channel further enhance this directional transport. Moreover, fast-moving deformed droplets transfer their momentum to downstream spherical droplets through the infusing oil. As a result, simultaneous passive transport of multiple droplets (20−400 μm) is achieved over long distance (beyond 7 mm). On these oil-infused surfaces, satellite micro-droplets can further nucleate and grow on an oilcloaked droplet, demonstrating enlarged surface area for condensation. Our findings on passive condensate removal offer great opportunities in condensation enhancement, self-cleaning and other applications requiring directional droplet transport along horizontal surfaces.

INTRODUCTION To date, a large number of liquid transport mechanisms existing in nature have been studied.1– 14

Various nature-inspired artificial methods have been developed and found applications in

condensation heat transfer,15–21 water harvesting,22–24 anti-icing and anti-contamination,25–27 and many other water-related fields.28–30 In droplet removal, reducing the friction or adhesion between solid surfaces and droplets is vital to activate the motion of droplets. Thus, superhydrophobicity31– 34

or oil-infusion35–47 can be utilized. Owing to the extremely low contact angle hysteresis (~1°)

on oil-infused surfaces, droplets can roll or slide off very easily.40–42,44,45 Moreover, oil infusion is the only way so far to achieve drop-wise condensation of low-surface-tension fluids. Experiments


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by Preston et al.

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have demonstrated great applications of oil-infused surface to water and

hydrocarbon gas condensation and their significant heat transfer enhancement. The rapid clearing off micro-sized condensate droplets can re-establish new nucleation sites, promoting dropwise condensation. For this reason, oil-infused surfaces are widely used for droplet removal. However, the motion of droplets can be random in any direction,47 unless a special surface design or an external force such as gravity assists as described in Table 1. Conventionally, droplet motion is caused by external forces. However, via the utilization of micro/nano-scale surface structuring, surface chemistry alteration, or the combination of both, droplets can also be passively transported without any extra energy cost. Depending on whether an external force is needed or not, the mechanisms for motion can be categorized into active transport and passive transport (Table 1). The most straightforward and well-known active transport is droplet removal by gravity26,49 or convective gas flow.50,51 Other types of active transport include droplet motion induced by electric or magnetic fields,52,53 acoustic or mechanical vibrations,54 etc. Of course, whether gravity-driven is an active transport or not can be argued because of the natural existence of the gravitational force. Each method mentioned above has some special requirements. For instance, in gravity-driven motion, the droplet size should be larger than the capillary length so that the gravity may play a role. Passive transport can be enabled by careful surface design. The droplet motion can be driven by intrinsic wettability gradient55–57 and surface curvature gradient. 3,5,9,20,21,23 The intrinsic wettability gradient can be achieved by varying the droplet surface tension or solid surface energy. To create droplet surface tension gradient, temperature gradient such as heating or cooling is applied to solid surface on which droplets sit (the thermocapillary effect).57 To generate solid surface energy gradient, heterogeneous chemical coatings can be used.55 On solid surfaces with wettability


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gradient, droplets are pulled towards higher-surface-energy or lower-contact-angle regions. Meanwhile, solid surface curvature gradient can deform and also drive a sitting droplet towards regions with smaller curvature.3,5,21,23,9,20 Moreover, asymmetries in surface structure density, dimension and orientation along the surface can have similar functions.12,63 In the above cases, droplets generally move parallel to the solid surfaces.

Table 1. Active and passive liquid droplet transport mechanisms.

Active Transport

Passive Transport

Driving Mechanism

Description

Gravity

Gravity-driven drainage of condensing macro-droplets larger than the capillary length from non-horizontal solid surfaces 49

Gas flow

Removal of condensate droplets with steam flow in microchannels50,51

Magnetic field

Magnetic-field-induced motion of Ferro-droplets52

Electric filed

Electric-field-induced motion of conductive droplets on dielectric surfaces53

Vibration

Droplet motion driven by high frequency mechanical or acoustic vibration54

Liquid surface tension gradient

Droplet motion due to its own surface tension gradient induced by e.g. temperature gradient on solid surfaces (thermocapillary)57

Solid surface energy gradient

Droplet motion towards higher surface energy regions on solid surfaces55,56

Solid surface curvature gradient

Droplet motion towards regions with decreasing curvature on solid surfaces3,5,9,20,21,23

Asymmetric surface structures

Droplet motion due to asymmetry in structure density, dimension and orientation along the solid surface12,58–62

Self-transport

Self- transport or jumping or de-wetting transition of a single stretched droplet confined within structures65

Oil-infused surfaces

Random movement of droplets on lubricant infused surfaces, if not affected by gravity43–45,47


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Among the transport mechanisms discussed above, directional motion owning to solid surface energy or curvature gradient has attracted the most research attention.

3,5,9,20,21,23,55,56

Droplet

motion can be easily achieved by manipulating surface chemistry or surface structures. However, these structures mainly affect droplets with sizes comparable to the structure dimensions. Specifically, in order to effectively remove the micro-droplets, the sizes of surface structures have to be controlled at micro scale. As a result, these surfaces may gradually lose its functionality due to continuous droplet growth, therefore resulting in limited capability in long-distance transport (compared with droplet sizes).13,56,66 Another challenge for such surfaces is to collectively transport a large number of droplets in a relatively short time. In short, it remains challenging to achieve simultaneous and spontaneous directional transport of multiple micro-droplets over long distances on horizontal surfaces without the need of external forces.

Cooling Oil

Droplet

2

Solid

A

A 1

Optical Microscopy a. Cross-sectional view A-A

b. Bottom view

Figure 1. Schematic diagram of the two-step directional transport of condensate droplets in a diverging channel. (a) Cross-sectional view. (b) Bottom view. First, as droplets grow larger they submerge into the oil-infused channels due to capillary forces. Then, the difference between the front and back curvatures caused by channel confinement drives droplet motion in the channel diverging direction. Also, coalescence with other droplets sitting inside the channel accelerates the motion.


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In order to effectively remove condensate micro-droplets, we propose a novel long-distance passive transport approach, which utilizes diverging channels with oil-infused nanostructured surfaces. The idea is illustrated in Figure 1. As droplets condense and grow on the top of hierarchical channel walls, they are dragged, even against gravity, into the channel by the infusing and cloaking oil. The submerged droplets are mostly confined by the two channel walls and thus, move along the channel in the diverging direction. Most likely, droplet coalescence occurs inside the channel, which further accelerates the directional movement. This idea was jointly verified with two different diverging hierarchical channels, namely nanostructured copper channels and nanoparticle-coated silicon channels. In order to show the crucial role of infusing oil on facilitating the series motion of condensate droplets, we also tested un-infused surfaces. This transport mechanism is demonstrated by experiments and analytical modeling as well as numerical simulations.

FABRICATION OF HIERARCHICAL DIVERGING CHANNELS Scalable diverging copper hierarchical channels were prepared by winding copper wire tightly to a copper plate. The copper channel surfaces were chemically oxidized to obtain nanostructures.27,65 Firstly, a copper wire of 120 μm diameter was wrapped tightly around a piece of 10 mm × 20 mm × 0.2 mm copper plate to form bare copper channels. The sample was ultrasonically cleaned with acetone and rinsed with ethanol and DI water. It was then dipped into a dilute hydrochloric acid solution to remove the oxide layer on the surface and rinsed with DI water. Finally, the wet sample was immersed into an oxidizing solution, consisting of NaClO2, NaOH, Na3PO4∙12H2O and DI water (3.75: 5: 10: 100 wt. %), for at least 10 min at 95 ± 5°C to


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form copper oxide nanostructures. The sample was again rinsed with DI water and dried with nitrogen flow. Meanwhile, diverging silicon hierarchical channels were fabricated through photolithography and deep reactive ion etching (DRIE). Carbon nanoparticles were deposited by placing the channeled silicon wafer on top of a candle flame for about 10 s.67,68 Paraffin wax was vaporized and subsequently a thick layer of candle soot nanoparticles was formed on the silicon wafer. Since those carbon nanoparticles were not mechanically robust, a SiO2 layer was then deposited through chemical vapor deposition (CVD). The sample was placed in a desiccator, together with a small amount (5 ml) of tetraethyl orthosilicate (TEOS) and the same amount of ammonia water solution. The desiccator was then pumped for 10 min to remove the air and kept for another 2 hours to coat the carbon nanoparticles with a thin SiO2 layer. Finally, carbon-silica hybrid nanoparticles were formed through calcination at 600˚C for 2 hours in an oven. Both the diverging copper and silicon channel surfaces become hydrophobic after silanecoating.65 Afterwards, the hydrophobic samples were completely immersed in oil (Krytox 1506) and slowly pulled out. The excess oil was carefully removed by lab tissue paper and by blowing nitrogen. The nanostructures played a key role in spreading and maintaining the oil film uniformly over the channels (discussed in section S2, SI). Figure 2 shows the scanning electron microscopy (SEM) images of the channels and their surface nanostructures prior to silane-coating and oil-infusion. The diverging angle of the silicon channels was more precisely controllable than that of the copper channels. Here, the angle of the fabricated silicon channels was 5˚ after considering the design principles (Section 2.1, SI) and the blockage risk of channel with small angle. The surface morphology of the oil-infused silicon channel is shown in Figure 2e. It is only a thin layer of oil that adheres to the top surface of the


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channel wall and channel base, because its particle-like surface roughness is still observed. However, more oil has accumulated at the corner of the channel wall and base to form an oil ridge as illustrated in the schematic diagram.

(a)

(b)

(e)

(c)

View A

(d)

200 µm

1 µm

200 µm

Oil Ridge

Channel Base

1 µm Channel Wall

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100 µm

Figure 2. SEM images of diverging copper and silicon channels prior to hydrophobic coating and oil infusion. (a) A diverging copper channel. (b) Copper oxide nanostructures grown on the copper channel. (c) A diverging silicon channel. The channel angle 2α is 5˚. (d) Calcined carbon-silica nanoparticles deposited on the silicon channel. (e) Surface morphology of the oil-infused silicon channel.

RESULTS AND DISCUSSION Water Condensation on Horizontal Flat Surfaces with/without Oil Infusion Infusing oil on a surface can increase the mobility of water droplets, bridge multiple droplets and facilitate their coalescence. To reveal the mechanism, we first conducted water condensation experiments on flat surfaces – hydrophobic nanostructured copper plate surfaces with and without infusing oil (see Section S3 in the Supplementary Information for the details of condensation


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experiments). Experimental conditions are: ambient temperature 23 ± 0.5 ˚C, sample surface temperature 5 ± 0.5 ˚C, relative humidity 50 ± 5%, and the corresponding supersaturation 1.53. Each condensation experiment was repeated three times for oil-infused and un-infused surfaces alternatively to eliminate the influence of fluctuation of operational conditions on the condensation performance (also in Section S3, SI). During the water condensation (Movie S1.0, SI), frequent coalescence and intense motion of condensate droplets were observed on the oil-infused surface. Figure 3a and b partly show droplet coalescence and motion on those surfaces during condensation. On the un-infused surface (Figure 3a), even though two droplets (circled in blue) were nearly in contact, their coalescence did not occur even until after 30 seconds. Even if there was coalescence (circled in red) at t = 59.50 s, the coalescence was not able to cause any motion in nearby droplets. On the contrary, as Figure 3b shows, coalescence of two neighboring droplets D1/D2 (t = 60.00 s) easily took place on the oil-infused surface even though there was a noticeable gap (~ 6 um) in between. Moreover, a nearby smaller droplet D4 (circled in yellow) was perturbed by the coalescence and moved toward the merged droplet D3, leading to another coalescence at t = 60.10 s. Consequently, the released surface energy upon coalescence was propagated in the form of kinetic energy to the blue-circled droplets (D5/D6) through the oil, thus causing chain-reaction coalescence over a short period of time. We counted the total number of coalescences over the duration of observation (Figure 3c). More frequent coalescences are found on the oil-infused surface compared to the un-infused surface. Consequently, the droplet size increased much more rapidly on the oil-infused surface as shown in Figure 3d. The growth rate was around 2 µm/s on the oil-infused surface, while it was only 0.2 µm/s on the un-infused surface. On the un-infused surface, the droplet growth was mainly from phase-change at the liquid-vapor interface of water. The abrupt increase in droplet size was caused by droplet coalescence. The droplets on the un-


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infused surface were at the Cassie state after the wetting transition from the Wenzel state.18,32–34 And, due to the large contact angle hysteresis (Section S2, SI), the released surface energy from coalescence was unable to mobilize the coalesced droplet. On the contrary, intense motion of the condensate droplets on infused surface was observed. These water droplets were at the CassieBaxter state44 with a thin oil film cloaking the droplets. Because the oil film covered both droplets and the solid surface, the cloaked droplets became susceptible to their surroundings, including nearby droplets or momentum propagation from the coalescences of other droplets. In addition to causing frequent coalescence and resultant fast growth, oil infusion also changed the droplet nucleation behavior. On the oil-infused surface, the unique “droplet on droplet” phenomenon was observed under environmental scanning electron microscope (ESEM) (Figure 3e). The water vapor was observed to nucleate at the interface of oil and water vapor, rather than penetrating through the oil layer to form condensation. Most importantly, the new satellite droplets did not sit stably on the surface of their host droplet, and spontaneously slipped and accumulated in the oil ridge of the host droplet, as highlighted by the yellow circle in Figure 3e. This interesting spontaneous motion attracted great attention. The mechanism for such behavior of satellite droplets is explained with the schematic diagram shown in Figure 3f. According to Young’s equation, the capillary pressure inside the cloaking oil film is calculated as P   / R  P0 . The minimum pressure P1 can be found at the oil ridge overlapping point between the early-formed hosting Droplet 1 and 2, where the oil film curvature is negative but with the largest magnitude. The pressure P2 at the nucleate cite of Droplet 3 is positive and much higher than P1. Owing to the pressure gradient inside the oil film, the newly-formed satellite Droplet 3 is transported directionally into the oil ridge of the hosting Droplet 1 and 2. As a result, the satellite droplets, just like Droplet 3 or 4, accumulate within the oil ridge around the hosting droplets.


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On the flat surface, it was the early-formed hosting droplets (e.g. Droplet 1 and 2 in Figure 3f) that led to the capillary pressure difference inside the infusing oil film. It means that the position of hosting droplets determined the directional motion and the final location of satellite droplets. In the light of this finding and the desire to direct micro-droplet motion, we can fabricate the patterned surface to actively control the capillary pressure distribution. In the next section, we demonstrate how to achieve directional condensate transport by using the oil-infused diverging channel surfaces.


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(a)

t=59.55s

t=59.50s

(b)

t=59.60s

t=60.00s

t=60.05s

t=60.10s

D1

D3

D2

D4

50µm

50µm

t=96.15s

t=96.20s

t=60.15s

t=60.25s

t=60.20s

… … after 36.50s

D5 D6

(c) 1000

(d) 100 Un-infused Surface Oil-infused Surface

800

Oil-infused Surface

Un-infused Surface 80

Droplet Size (m)

Total Coalescence Number

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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600

400

Two Representive Droplets 60

40

[ Aili. A et al ] 20

200

0

0 0

30

60

90

120

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150

20

40

60

80

100

Time (s)

Time (s)

(e)

(f)

Water droplet Oil layer 3

4 1

2P0 > P1

Diffusion

Water droplet Oil layer

Water droplet

P2

4

30 μm

1

2

ROil 1 layer 3

4

P1

R2

1

2

Figure 3. Condensation of water on nanostructured and hydrophobic copper surface with and without oil infusion. (a) Optical microscopy images of water droplet coalescence on the un-infused surface. (b) Optical microscopy images of water droplet coalescence on the oil-infused surface. (c) Total number of coalescence on oil-infused surface and un-infused surface. The frequency of coalescence was higher on the oil-infused surface due to increased droplet mobility and chainreaction coalescence. (d) Droplet size vs. time during condensation. The faster droplet growth on


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the oil-infused surface was owing to frequent droplet coalescence. Droplets on the oil-infused surface were at the Cassie-Baxter state,44 while the droplets on the un-infused surface were at the Cassie state after the wetting transition from the Wenzel state.33 (e) ESEM image of water condensation on the oil-infused surface. Droplet nucleation (circled in red) on the cloaking oil film of the early-formed droplet is observed as well as accumulation of the satellite droplets (circled in yellow) in the oil ridge of the early-formed droplets were observed. (f) Illustration of the satellite droplet motion. Droplet 1 and 2 are early-formed hosting droplets, while Droplet 3 and 4 are the newly-formed droplets, or the satellite droplets. The capillary pressure gradient inside the oil film guides the motion of the newly-formed Droplet 3 and 4.

(a)

(b)

1 Nucleation t=43.95s

water vapor

2 Coalescence & Growth 3 Submergence t=44.00s

t=48.15s

1

50 µm

t=48.20s

2

2

channel

Focal Plane

t=48.25s

t=50.40s

2

wire

t=50.45s

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t=51.00s

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channel

oil

pressure gradient

(c) 150

(d) 1.0 Un-infused Oil-infused

Droplet coverage

Number of droplets

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Figure 4. The effect of infusing oil on droplet submergence into copper channels. (a) Schematic of the capillary pressure gradient in the infusing oil film. During condensation, the observing plane of the confocal microscope was focused at the top surface of the copper wire. (b) A typical lifecycle of a condensate droplet on the oil-infused wire: Droplet nucleation occurred on the fresh area created by submergence; frequent coalescence led to fast growth of the condensate droplet; droplet submerged into the channel owing to capillary pressure gradient. (c) and (d) Evolution of the number of droplets and droplet coverage on oil-infused and un-infused wire surfaces, respectively. The values for the oil-infused channel wall were much smaller due to frequent droplet submergence into the channel.

Step1: Droplet Submergence On the patterned surface, the curvature of the channel surface creates the desired pressure gradient inside the infusing oil film as shown in Figure 4a. The capillary pressure can be calculated according to the Young-Laplace equation P  P0   o / R , where P0 is the ambient pressure. The highest pressure P2 is at the top of the channel wall, while the lowest pressure P1 is inside the channel, where the oil film has a negative curvature. Guided by the pressure gradient, the droplet that forms at the top surface can submerge into the channel. In order to experimentally observe this phenomenon, water condensation experiments were conducted on channel surfaces with and without oil infusion, respectively. We take the copper channels as an example. The condensation processes on the un-infused surface and oil-infused surface are shown in Movie S1.1 and S1.2 (SI), where t = 0 s is the time when the droplets were large enough to be seen under the microscope. Compared with the condensate droplets on the un-infused channel surface, we observed that the droplets on the oil-infused surface continuously submerged into the channel from the top surface


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of the channel wall. From Movie S1.2 (SI), we can find the typical lifecycle of a water droplet starting from condensation, growth, and ending with submergence. Snapshots taken from the Movie S1.2 show such a full lifecycle as in Figure 4b. At t = 43.95 s, the nucleation site was established after the submergence of the red circled droplets. The droplets (circled in blue) start to nucleate on the surface at t = 44.00 s, and grow rapidly owing to the chain-coalescence effect. At t = 50.40 s, the droplet experienced the last coalescence and submerged into the channel. Note that a confocal microscope was used in our experiment (features of confocal microscope explained in Section S3, SI) and was focused at the top surface of channel wall as illustrated in Figure 4a. So once the droplet submerged into the channel (t = 50.45 s), it could not be observed anymore. At t = 51.00 s, another cycle of droplet nucleation (circled in purple) started on the refreshed areas. We counted the number of droplets and measured the droplet coverage throughout the condensation process from Movie S1.1 and S1.2 (SI), and the results are given in Figure 4c, d, respectively. Although the number of droplets on the un-infused channel wall (open circles) gradually decreased from around 130 to around 25 mainly due to coalescence, the droplet coverage (open diamonds), defined as the fraction of the area covered by droplets, just had a slight decrease initially and then remained above 60% due to lack of condensate removal. On the contrary, the number of droplets on the oil-infused channel wall (solid circles) was around 80 in the beginning and then shortly decreased to about 15. The large-view images showing the droplet coverage change during the condensation on the infused surface are given in Figure 4c. The droplet coverage remained as low as 10% throughout the condensation process owing to continuous droplet submergence. As shown in the video (Movie S1.2, SI), the rapid removal of the microdroplets soon after condensation has enabled new nucleation sites and promoted dropwise condensation. Note that in this experiment, the submergence was anti-gravity.


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Step 2: Directional Motion in Diverging Channels Capillary-driven and coalescence-enhanced directional motion We expected that once droplets submerged into the channel, they would move along the channel in the diverging direction. In Movie S1.3 (SI), we show the submergence and subsequent directional motion of droplets in the copper channel. Since condensation occurred along the whole channel wall, the submerged droplets downstream might cause a temporary pause or gentle backward motion of moving droplets. The directional motion of droplets from Movie S1.3 are partially given in Figure 5a. A droplet, confined and stretched by the two channel walls, was moving along the channel (highlighted by an oval). At t = 31.15 s, a droplet submerging from the channel wall (highlighted by a circle) met with the moving droplet inside the channel. Upon coalescence, the resulting droplet continued its directional motion. Similar phenomena of droplet submergence and directional motion were also observed on the diverging silicon channel surface, although the imaging of droplet submergence turned out to be challenging due to significant light scattering by the silica nanoparticles on the top of channel walls. Figure 5b shows directional motion of a droplet, marked as D1, inside a silicon channel. We can clearly observe the droplet shape at t = 0 s and, most importantly, the difference between its front and back curvatures. The curvature difference was the driving force that induced the directional motion. At t = 3.35 s, this droplet encountered and coalesced with another droplet awaiting inside the channel, gaining a sudden increase in size. Note that the blurred appearance of the merged droplet D2 at t = 3.40 s was the result of defocusing caused by the sudden increase in its size. In less than ∆t = 0.1 s, the droplet D2 coalesced with a second droplet, again gaining sudden increase in size (D3). The whole process is given in Movie S1.4 (SI).


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Inside the silicon channels, more details such as droplets’ outline were clearly captured. More importantly, the angle of the diverging silicon channels was precisely designed and controlled during fabrication. These advantages enabled us to quantitatively analyze directional droplet motion inside those channels, as the channel angle and droplet outline were the crucial factors to determine the capillary driving force. Figure 5c shows the displacement distance and velocity of the droplet, which is obtained from the first 10 s of Movie S1.4 (SI). The displacement was almost at a steady speed before or after coalescence. It was much faster whenever coalescence occurred. Coalescence enhanced the directional motion by abruptly increasing the difference of the back and front curvatures of the droplet, thus exerting an escalated driving force. However, the velocity immediately diminished right after a sudden jump, and it was due to the collision with other droplets, which is discussed later. The displacement distance of the droplet was more than 400 μm within a short observation period of only10 seconds while the droplet width was overall around 100 μm.


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t=30.70s

t=31.15s

channel

t=33.95s

t=31.25s

copper wire

….

….

100 µm

submergence and coalescence

t=0.00s

t=3.35s

t=3.40s

t=3.45s

t=3.50s

t=19.45s

channel

(b)

t=31.20s

D3

….

…. D1

D2

D2

D3

D1

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100 µm

2nd coalescence

400

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500

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Displacement Velocity

400

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10

Time (s)

Figure 5. Submergence and subsequent directional motion of droplets inside diverging (a) copper channel and (b) silicon channel, observed under optical microscope: In a, a droplet submerged into the channel and coalesced with a moving droplet; in b, droplets coalesced along with their directional motion inside the silicon channel. (c) Displacement distance and displacement velocity of the droplet in b. The motion became much faster when calescence occurred. (b)

(c) Experiment

26 24 22

2

20

nd

Capillary driving force (mN)

28 -6

(a)

Interfacial energy (x10 J)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

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Theory: D1 D2 D3

coalescence

st

1 coalescence

18 140

160

180

200

220

Displacement (m)

14 Theory: D1 D2 D3

12 10 2

8

nd

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Displacement (m)


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Figure 6. Total droplet-oil interfacial energy and capillary driving force during directional motion. (a) Experimental morphology and 2-D model of a droplet moving inside a diverging channel. The advancing and receding contact angles were nearly the same, θr = θa ≈ 155˚. The 2-D coordinate system originates where the channel starts or the channel width is zero. With the exact location and size of the droplet known, the total droplet-oil interfacial energy available for driving the motion can be calculated. (b) Theoretical and experimental evolution of total droplet-oil interfacial energy as a function of displacement. The experimental data were obtained from the three droplet morphologies, D1, D2 and D3, in Figure 5b and Movie S1.4 (SI). (c) Theoretical evolution of the capillary driving force as a function of displacement.

In order to further understand the underlying mechanism for directional droplet motion in oilinfused diverging channels, we developed a simplified 2-D model as illustrated in Figure 6a. For a submerged droplet moving inside a diverging channel, the advancing contact angle of the front curvature and the receding contact angle of the back curvature were nearly the same, implying almost zero contact angle hysteresis. That is, θr = θa ≈ 155˚ in this work. For a droplet with a given volume V, if the y-coordinate of the back curvature is y, the y-coordinate of the front curvature yꞌ can be expressed as tan  2 ) (   sin  cos  ) y 2  tan  y 2 sin  tan  2 ( ) (  ' sin  ' cos  ')  tan  sin  '

V ( y' 

(1)

where β and βꞌ are the half arc angles of the back and front curvatures, respectively. And the total energy stored on the droplet-oil interface is given by E  2 WO (  R   ' R '

(y' y) ), cos 

(2)


19


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where γwo is the water-oil interfacial tension, and γwo ≈ 49.0 mN/m;47 R1 and R2 are the radii of the droplet back and front curvatures, respectively. The open circles in Figure 6b show the evolution of total droplet-oil interfacial energy of the three droplets D1, D2, D3 observed from experiments. The dashed lines in Figure 6b show the theoretical prediction of total droplet-oil interfacial energy as a function of displacement, for three droplet sizes with the volume of D1, D2 and D3, respectively. With the increase of droplet displacement, the total droplet-oil interfacial energy slowly decreases. The released energy is converted to the kinetic energy of the moving droplet. During the condensation experiments, droplet coalescence resulted in a sudden increase in droplet size, and the surface energy evolution jumped to a new path, as shown in Figure 6b. Our analytical model predictions agree well with the experimental data. As the derivative of interfacial energy with respect to displacement, the capillary driving force can be obtained as Fd 

E  (y' y)  2 WO (  R   ' R ' ). y y cos 

(3)

The capillary driving forces for the three droplets D1, D2 and D3 are plotted in Figure 6c. For a droplet with a constant volume, the capillary force decreases with increasing displacement as the droplet becomes more spherical. At a specific position, a larger droplet size corresponds to a larger driving force since the droplet is more squeezed. This is why a sharp increase in the displacement velocity was observed when coalescence occurred in the experiments. The detailed analytical model derivation of the above interfacial energy and capillary driving force can be found in Section S4.1 of the Supporting Information, where we have also evaluated the viscous dissipation inside both the infusing oil layer and the droplet, as well as the contact angle hysteresis for a single droplet (Section S4, SI). The capillary number Ca, which is a measure of viscous force and surface force, is found to be at the order of 10-5. In parallel with theoretical analysis, the process of capillary-driven and coalescence-enhanced droplet motion in a diverging


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channel was simulated by using the lattice Boltzmann method (Section S4.2, SI).69,70 The simulation results directly show the pressure gradient inside the stretched droplet with front-back curvature difference. The streamlines indicate the detailed droplet motion direction along the channel.

(a)

t=1.20s

t=1.50s

t=2.20s

t=4.00s

t=7.00 s

100 µm

1200

(b)

1000 800 600

t motion

Concurren

Relaxation

M om tra ent ns um fe r

Position (m)

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400 200

Spherical Stretched

0 0

1

2

3

4

5

6

7

Time (s)

Figure 7. Momentum transfer from a fast-moving stretched droplet to static spherical droplets. (a) Time-lapse optical microscope images of a fast-moving stretched droplet and static spherical droplets. The rapidly approaching stretched droplet induced the motion of downstream spherical droplets through momentum transfer. (b) Position of the stretched and spherical droplets relative to the initial position of the back curvature of the stretched droplet in a.


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Momentum transfer and simultaneous motion of multiple droplets As condensation occurred along the whole channel surface, small spherical droplets were observed before their coalescence. Owing to the cloaking oil film, there is a non-coalescence lifetime for those water droplets. When two droplets came into contact, the drainage of intermediate thin oil film started, and the time for film rupture varied with droplet size.39 The collision with the moving droplets can speed up the film rupture process. Before their coalescence, the small spherical droplets, which were too small to be confined by the channel, could not generate capillary driving force for directional motion. However, they were pushed forward by the upstream stretched droplet. Therefore, instead of the fast motion of single stretched droplet, simultaneous motion of multiple droplets was achieved, which can ensure high-efficacy droplet removal and avoid filling up of the channel. The momentum transfer process and the resultant simultaneous motion of multiple droplets are demonstrated with the experimental observation in the Movie S1.5 (SI) and Figure 7. As seen from Figure 7a (also see Movie S1.5, SI), at t =1.2 s a stretched droplet (highlighted in yellow oval) was moving rapidly towards stationary spherical droplets downstream (highlighted in yellow circle). At t = 2.2 s, the stretched droplet moved into the spherical droplets, and they continued to accelerate together for a short time period although the visibility of the stretched droplet somewhat decreased. The image of stretched droplet became fuzzy because the droplet was no longer in focus. As Figure 7b shows, the highlighted spherical droplet was initially static at a location 520 µm relative to the position of the stretched droplet, which was approaching at a speed of as high as 1000 μm/s seen from the initial slope of the blue diamond curve. At t = 1.3 s, the stretched droplet rushed into the spherical droplets with a decreased speed of around 500 μm/s. Activated by the stretched droplet, the spherical droplets started to move along the channel with a similar speed of about 500 μm/s, although they did not have any curvature gradient to induce


22

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motion. However, the stretched droplet and the spherical droplets immediately and simultaneously slowed down within 0.5 s. Interestingly, all the droplets not only slowed down but also receded slightly. After this relaxation, all the droplets again started to move concurrently with a constant but rather low velocity of about 30 μm/s. Eventually, the spherical droplets, which cannot generate capillary driving force intrinsically, traveled by a distance of 400 μm within less than 6 seconds due to the momentum transferred from the single stretched droplet. Consequently, the speed of the single stretched droplet was reduced from 1000 µm/s to 30 µm/s after the momentum transfer process. Compared with the rapid motion of a single droplet, simultaneous motion of multiple droplets can sweep the surface more efficiently.

Long distance transport with droplet size growth In this section, we demonstrate the capability of our diverging channels to transport condensate micro-droplets over long distances. Figure 8 shows the displacement distance of a growing droplet inside a channel. Initially, the droplet was located at the channel starting point. For about 12 minutes, this self-propelled droplet travelled with a distance of around 7 mm. Meanwhile, its width increased from about 25 μm initially to about 400 μm. To our knowledge, such passive horizontal travel distance exceeds the largest value for micro-sized droplets in open literature

9,13,66

.

Throughout the displacement, the droplet experienced multiple coalescences, which was the main cause of size increase. The increase in size ensured that the droplet remained confined and stretched by the channel walls, thus maintaining its capillary driving force. Note that the droplet was driving not only itself but also many other spherical droplets downstream and clearing the path for upstream droplets. Such simultaneous motion leads to high-efficient removal of the condensate droplets immediately after their formation, which is widely accepted as the key to


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enhancing dropwise condensation heat transfer. With the proposed design, the channeled surfaces with oil infusion are able to simultaneously transport multiple droplets as small as 10 µm. This approach, without the need of gravity and surface inclination, allows higher flexibility in designing surfaces for heat transfer enhancement applications. When the droplets were approaching the outlet of the channels, they gradually lost their repulsion and became sluggish. In the meantime, they kept coalescing with upcoming droplets and continued their motion, though at much lower velocity, thus the droplet accumulation was avoided at the channel outlet as shown in Figure S6. We have also observed that when the droplet size was much larger than the channel wall height (~100µm), it even merged with other droplets across the channel wall (Figure S6b, SI). Therefore, it may be beneficial to gradually increase the channel wall height and width to keep the droplets better confined and achieve a longer travel distance, which will be further studied in future work. While a water droplet slides off from the surface, it causes the loss of lubricant oil. In fact, oil drainage via cloaking, as well as the shear-induced oil drainage, is a major concern in the application of oil-infused surfaces. The cloaking-induced drainage rate can be estimated by evaluating the cloaking oil film thickness. For the cloaking oil with surface tension around 17 mN/m, the film thickness is around 20 nm on a 1 mm water droplet.45 Therefore, the drainage via cloaking is negligible compared with the shear drainage from the droplet slippage. In order to minimize the shear drainage, the copper and silicon channel surfaces have been etched or deposited with nanostructures, respectively, as shown in Figure 2. We are currently performing systematic characterization of oil drainage, oil-condensate separation and oil recirculation as a function of the surface structure dimensions, intrinsic wettability, and infusing oil type. And, by rewetting the surface with lubricant oil, the dropwise condensation performance can be recovered.48


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8

Displacement (mm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


t=0min 25 µm

6 t=12min

4 100 µm

2 100 µm

0 0

2

4

6

8

10

12

Time (min) Figure 8. Long distance directional transport of a stretched droplet inside an oil-infused diverging channel. Over a period of around 12 minutes, the droplet was displaced by a distance of around 7 mm. Meanwhile, its width increased from less than 25 μm to only around 400 μm.

CONCLUSION We achieved long distance directional transport of condensate micro-droplets on horizontally oriented diverging microchannels with an angle of 5 degrees. The microchannel surfaces are nanostructured, hydrophobic-coated, and oil infused. The oil, which cloaks both the solid surface and the droplets, leads to the submergence of droplets, even against gravity, into the oil-infused channels. The diverging channels deform the droplets and induce curvature gradient. The capillary driving force from the curvature gradient consequently drives the droplets to move along the channel diverging direction. The motion is significantly enhanced upon droplet coalescence, which causes an abrupt increase in droplet size and thus in the capillary driving force. Moreover, the momentum transfer from fast-moving stretched droplets to static spherical droplets, leads to simultaneous motion of multiple droplets. As a result of droplet submergence, deformation and


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coalescence, spontaneous displacement of micro-droplets (20−400 μm) is achieved over a distance of as long as 7 mm. This high-efficiency passive transport of multiple micro-droplets over long distances can have broad implications for the energy-water nexus applications.

ACKNOWLEDGEMENT This work was supported by the Abu Dhabi National Oil Company R&D Department Energy Efficiency and Environment Program. The authors would like to thank Dr. Weilin Yang from Jiangnan University China for initial support on LBM simulation.

NOTE The authors declare no competing financial interest.

SUPPORTING INFORMATION Videos showing droplet pinning, submergence, directional motion, and momentum transfer; information on surface characterization; condensation experiments; details of theoretical modeling as well as numerical simulation; Movie S1.0. Intense but random motion of water droplet on the oil-infused flat surface. Movie S1.1. Droplet pinning on un-infused copper channel walls. Movie S1.2. Spontaneous droplet submergence into copper channels. Movie S1.3. Directional motion of a submerged droplet in a diverging copper channel. Movie S1.4. Directional motion of submerged droplets in diverging silicon channels. Movie S1.5. Momentum transfer from a fast-moving stretched droplet to downstream spherical droplets.


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TOC Figure

8

1 μm

Displacement (mm)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60

Page 36 of 36

t=0min 25 µm

6 t=12min

4 100 µm

2 100 µm

0

100 μm

0

2

4

6

8

10

12

Time (min)


36

Directional Passive Transport of Micro-Droplets in Oil-Infused

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