Unidirectional Fast Growth and Forced Jumping of Stretched Droplets

Research Article www.acsami.org

Unidirectional Fast Growth and Forced Jumping of Stretched Droplets on Nanostructured Microporous Surfaces Abulimiti Aili, Hongxia Li, Mohamed H. Alhosani, and TieJun Zhang* Department of Mechanical and Materials Engineering, Masdar Institute of Science and Technology, P.O. Box 54224, Abu Dhabi, United Arab Emirates S Supporting Information *

ABSTRACT: Superhydrophobic nanostructured surfaces have demonstrated outstanding capability in energy and water applications by promoting dropwise condensation, where fast droplet growth and efficient condensate removal are two key parameters. However, these parameters remain contradictory. Although efficient droplet removal is easily obtained through coalescence jumping on uniform superhydrophobic surfaces, simultaneously achieving fast droplet growth is still challenging. Also, on such surfaces droplets can grow to larger sizes without restriction if there is no coalescence. In this work, we show that superhydrophobic nanostructured microporous surfaces can manipulate the droplet growth and jumping. Microporous surface morphology effectively enhances the growth of droplets in pores owing to large solid−liquid contact area. At low supersaturations, the upward growth rate (1−1.5 μm/s) of these droplets in pores is observed to be around 15−25 times that of the droplets outside the pores. Meanwhile, their top curvature radius increases relatively slowly (∼0.25 μm/s) due to pore confinement, which results in a highly stretched droplet surface. We also observed forced jumping of stretched droplets in pores either through coalescence with spherical droplets outside pores or through self-pulling without coalescence. Both experimental observation and theoretical modeling reveal that excess surface free energy stored in the stretched droplet surface and micropore confinement are responsible for this pore-scale-forced jumping. These findings reveal the insightful physics of stretched droplet dynamics and offer guidelines for the design and fabrication of novel super-repellent surfaces with microporous morphology. KEYWORDS: stretched droplets, self-/coalescence jumping, nanostructures, microporous, superhydrophobic, condensation

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INTRODUCTION Droplet jumping is an interesting phenomenon that occurs by taking advantage of the excess surface free energy released upon coalescence of droplets on superhydrophobic nanostructured surfaces.1−3 It has received great attention in enhanced condensation heat transfer4−8 and many other applications, such as self-cleaning9 and anti-icing surfaces10 and water11,12 and energy harvesting.13 Previous studies thus have been mainly focused on designing extremely rough surfaces with micro- and nanostructures coated with ultra-low-surface-energy materials.14−17 This strategy gives significantly small contact area and solid fraction to droplets growing on the condensing surface, greatly minimizing the surface adhesion upon jumping. However, there exists a contradiction that a very small solid− liquid contact area is an obstacle to fast droplet growth and heat transfer while it is beneficial for droplet jumping.6,18 This contradiction comes from the following assumptions: (a) solid surface is always underneath the droplet and acts mainly as a heat conductor, and (b) condensate droplets are always spherical and release excess surface free energy only through coalescence. Several studies then have been done on hybrid surfaces to enhance droplet growth while ensuring that droplet jumping still takes place.19−21 However, these kinds of surfaces generally require sophisticated and expensive cleanroom © 2016 American Chemical Society

technologies for large-scale applications. Despite these intense efforts, simultaneously enhancing both growth and removal of condensate droplets on homogeneously superhydrophobic surfaces is still contradictory and challenging. On traditional superhydrophobic surfaces, spherical droplets can grow to any size until they coalesce and jump. While a wetting transition was observed on micropillar surfaces, where deformed droplets within the micropillars self-pull themselves to the top of the structures, no direct droplet jumping occurred.4,22 This is probably due to larger surface adhesion when droplets and surface nanostructures have similar dimensions. In this work, however, we report that droplet growth can be significantly enhanced owing to the increased solid−liquid contact area of nanostructured micromesh surfaces. Meanwhile, droplets in micromesh-confined pores are highly deformed and forced to jump at sizes determined by the pore opening. The pore confinement also favors the coalescence and unidirectional growth of droplets inside the pore. We used a facile and scalable method to fabricate a microporous superhydrophobic surface by covering a copper plate surface with a microporous copper Received: May 4, 2016 Accepted: August 3, 2016 Published: August 3, 2016 21776

DOI: 10.1021/acsami.6b05324 ACS Appl. Mater. Interfaces 2016, 8, 21776−21786

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ACS Applied Materials & Interfaces

Figure 1. Schematic diagram of the fabrication process of a copper-micromesh-covered microporous superhydrophobic surface. A copper plate surface was covered with a copper micromesh, followed by heat treatment in vacuum, chemical oxidation, and hydrophobic silane coating. water multiple times and dried with nitrogen flow to forcibly remove the remaining water. Silane coating was used to convert the nanostructured sample from hydrophilic into superhydrophobic.25,26 Before coating, the sample was plasma-cleaned for 30 min to remove any existing organic contaminants and to increase the surface temperature to ensure that the coating would be uniform. Then, it was quickly placed in a desiccator with a small amount (∼0.1 μL) of trichloro(1H,1H,2H,2Hperfluorooctyl)silane (Sigma-Aldrich Chemical Co.) that has an intrinsic contact angle of around 115°.25 The desiccator was pumped for 15 min to remove the air, and a valve was closed to isolate the chamber to deposit a thin layer of silane in vacuum for another 30 min. Note that insufficient deposition time led to a thick greenish contamination layer upon exposure to air. After deposition, the sample was cleaned with DI water and dried with nitrogen. It took a few minutes for the surface to become completely superhydrophobic in air, possibly due to the slow hydrolysis and dehydration reaction between silane chains. Figure 1 is the schematic diagram of the fabrication process described above. For comparison, a superhydrophobic copper plate surface without micromesh was also prepared using the same oxidization and silanization processes. Surface morphologies and geometries of copper oxide nanostructures were obtained by using scanning electron microscopy (SEM) (Quanta 250 and Nova NanoSEM, FEI). Static contact angles of the samples were measured with a goniometer (DM501, Kyowa Interface Science Co., Ltd.). ESEM Condensation Experiment. The microscale water condensation experiment was carried out by ESEM (Quanta 250, FEI) with a gaseous secondary electron detector (GSED).27,28 The sample was mounted on a 90° custom-designed copper stub (Figure S1, SI) using high-purity silver paint, and the stub was placed on a Peltier coiling stage. Once the chamber was completely evacuated, the stage temperature was set at 2 °C, and the vapor pressure was gradually increased to 700 Pa. When the temperature stabilized, the pressure was set to 750 Pa, and water droplet nucleation started. Images and videos were recorded at a working distance of about 5 mm and a constant beam energy of 10 keV. The cooling stage was tilted at angles ranging from 5° to 30° according to imaging and other special requirements. A smaller spot size of 2.0 (beam current of 0.13 nA) and 2.5 (0.22 nA) was generally used to achieve better imaging resolution and to avoid significant heating of the condensate surface and growing droplets on it. In a special case, a larger spot size of 3.0 (0.51 nA) was used to hinder the nucleation and growing of droplets outside the pores.

mesh, followed by heat treatment, oxidation, and hydrophobic silanization. Condensation experiments were carried out at low supersaturations (S ≈ 1.06) by environmental scanning electron microscopy (ESEM) at different working currents, which enabled us to better observe the dynamics of droplet growth and jumping. Micropores wrap the droplets, providing larger liquid−solid contact area and side confinement. As a result, droplets in pores grow mainly in the upward direction at a rate of 1−1.5 μm/s, which is about 15−25 times that (0.6− 0.7 μm/s) of the droplets outside micropores or on the surface without micropore. Meanwhile, the top curvature radius of these droplets growing in pores increases relatively slowly at a rate of around 0.25 μm/s, leading to a highly stretched droplet surface. Micropores then release these droplets at a range of micropore sizes, leading to coalescence jumping or even selfjumping without coalescence. Theoretical analysis and modeling results reveal that forced coalescence jumping of stretched droplets in pores is due to the released excess surface energy and abrupt pressure drop in the upper part of the droplets upon coalescence with spherical droplets outside the pores. On the other hand, self-jumping is due to the excess surface free energy stored in the stretched droplet surface and due to the local high-pressure point at the droplet base upon detaching from the base substrate. This work offers new insights into enhancement of droplet growth and removal on nanostructured superhydrophobic surfaces with microporous surface morphology. We believe these findings act as guidelines for designing novel super-repellent surfaces for enhanced condensation heat transfer and surface self-cleaning.

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EXPERIMENTAL SECTION

Superhydrophobic Microporous Surface Fabrication. The microporous surface was prepared sequentially through heat treatment, chemical oxidation, and silane coating of a copper plate covered with a copper micromesh. The thickness of the copper plate is 0.20 mm, and the average pore opening and wire diameter of the copper mesh is 34 μm. In this case, the condensation surface area of the meshcovered microporous surface is up to 5 times larger than that without mesh pores, as indicated in section S5 of the Supporting Information (SI). Prior to treatment, copper mesh and plate were ultrasonically cleaned in acetone for 10 min to remove the organic contaminants, triple rinsed with ethanol and deionized (DI) water, and cleaned with nitrogen gas. They were then immersed into hydrochloric acid solution to remove the oxide layer, which otherwise would impede the attachment of copper plate and copper mesh. After that, the mesh was placed on top of the plate, pressed by a strong binder, and put into a vacuum oven at 200 °C for 4 h, which led to welding of the copper plate and copper mesh. Chemical oxidation was used to obtain nanoscale roughness on surfaces of the base plate and attached mesh.23,24 The microporous surface prepared with the above procedures was again cleaned in hydrochloric acid and rinsed with DI water. The sample was then immersed into a hot oxidation bath containing a solution of NaClO2, NaOH, Na3PO4·12H2O (Sigma-Aldrich Chemical Co.), and DI water (3.75:5:10:100 wt %) for at least 10 min at 96 ± 6 °C to form an oxide layer of bladelike nanostructures. After that, it was cleaned with DI

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RESULTS Surface Morphology and Wettability. The top view of the microporous surface formed by a base substrate and a micromesh with a pore size of around 34 μm is given in Figure 2a, and the insets are the magnified top views of the pore wall (top) and pore base (bottom). Figure 2b is the magnified tilted view of the nanostructures covering the whole sample surface. The surface is coated with a hydrophobic silane. Due to high roughness, we would expect a larger apparent contact angle of macroscopic water droplets from the measurement of a goniometer than on the surface without micropores. Interestingly, the apparent contact angles of both surfaces turned out to be almost the same163° ± 2° on the microporous surface 21777


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≈ 4°, respectively. However, our contact angle of interest is that on the surface without micropores because it provides more reliable information when we deal with microscopic droplets in micropores during condensation experiments (Figure 2c,d). Dropwise Condensation. Microscopic water condensation experiments were carried by ESEM. As shown in Movie S1.1 (SI) and Figure 3, condensate droplets are three-dimensionally located inside and outside pores, and droplets in pores are deformed. It is clearly demonstrated that stretched droplets in micropores are growing at a significantly higher rate than droplets outside the micropores, even when there is no coalescence, which is discussed in detail in the following section. Another interesting phenomenon observed is that stretched droplets in pores always jump after growing to the same size as the hosting pores. By taking a snapshot of Movie S1.1 (SI) at the 12 s mark or viewing part d of the graphic that accompanies the abstract, we can see that several droplets have big tails (in a “V” shape) left inside the pore while they are squeezed by surrounding mesh wires before jumping. This is different from the coalescence jumping of spherical droplets on plain superhydrophobic surfaces widely reported in the literature, where the size of the jumping droplet varies from a few to a hundred micrometers or beyond.1,16,29 This observation has a special implication that droplet jumping can be forcibly induced and that the size of the droplets upon jumping can be predetermined by adding micropores with specific sizes to the condensing surface. Individual Droplet Growth and Jumping. As previously mentioned, droplets in micropores grow at a higher rate than the droplets outside the pores. In order to capture the detailed growth dynamics, we also filmed at a high magnification (Movie S1.2, SI), and time-lapse ESEM images are given in Figure 4a. Note that a small beam current of 0.13 nA was used to avoid overheating the droplets at high magnification.27,28 The visible height evolution, H* = Ht − H0, of two droplets (droplets 1 and 2), outside pores, and a droplet (droplet 3) emerging from

Figure 2. Surface morphology and wettability of the microporous surface. (a) SEM image of the microporous surface formed by a micromesh and a base plate. Insets are magnified views of pore walls (top) and the pore base (bottom). (b) Magnified view of the surface nanostructures covering both pore wall and base surfaces. (c) Tilted ESEM images of condensate droplets with high contact angles of around 164° on the microporous surface. Droplets are threedimensionally located inside and outside pores. (d) Magnified view of droplets inside and outside a pore. Condensation was conducted at T = 2 °C, P = 750 Pa, and 100% humidity, which corresponds to supersaturation S ≈ 1.06. ESEM images were captured at a beam current of 0.22 nA.

and 162° ± 2° on the surface without microporesalthough we admit that the Cassie−Baxter equation is still valid. The advancing contact angle and contact angle hysteresis of two surfaces are θ*a = 166° ± 2, Δθ* ≈ 5°, and θ*a = 164° ± 2, Δθ*

Figure 3. Pore-scale-forced jumping of stretched droplets. (a) Time-lapse tilted ESEM images at low magnification. (b) Time-lapse ESEM images taken from the top at high magnification. Stretched droplets leave the pores when they are at the size of the hosting pores, implying that micropores have a determining effect on the size of the droplets upon jumping. Images were taken at a beam current of 0.22 nA. Yellow circles represent the stretched droplets about to forcibly jump, and red circles in the same position as the yellow circles represent the pores without the previous stretched droplets. 21778


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droplets is increasing at a relatively lower rate of around 0.25 μm/s, and their radius upon jumping is all around 25 μm. This confirms the predetermined droplet size upon jumping previously mentioned. However, their observable time spans are different, with droplets 4 and 5 having a time span of around 13 s and droplet 6 having a time span of as long as 32 s. More interestingly, droplets 5 and 6 leave the surface without a significant coalescence effect, implying the possibility of selfjumping without coalescence. Note that the size mismatch between coalescing droplets leads to significantly decreased conversion of the excess surface energy to kinetic energy of the resulting jumping droplet, diminishing the probability of jumping.29 This further supports the possibility of self-jumping, since there are large droplets around the pores of interest. Moreover, it was also reported in ref 32 that the directional movement of a single droplet and its departure size were determined by the groove shape angle. In their work,32 the droplet was dispensed by a syringe needle rather than the condensate. In this study, we were able to capture the unidirectional growth of a pore-confined condensing droplet before self-jumping, as shown in part d of the abstract graphic. In fact, experimental characterization of self-jumping during the condensation process is challenging due to the difficulty of fully eliminating coalescence interference. Theoretical analysis of self-jumping will be shown in the subsequent droplet jumping section.

Figure 4. Droplet growth inside and outside micropores. (a) Timelapse tilted ESEM images of two droplets (D1 and D2) growing outside pores and a droplet (D3) growing inside a pore. Images were captured at a low beam current of 0.13 nA in order to avoid a heating effect. (b) Height evolution of the three droplets shown in part a. Without coalescence, droplets 1 and 2 grow slowly at a rate of around 0.06−0.07 μm/s. Droplet 3 grows at a higher rate, especially at the last stage, where its growth rate is 1−1.5 μm/s. (c) Time-lapse images of three droplets, D4−D6, growing in pores. A larger beam current of 0.51 nA and a smaller tilt angle of 10°−20° was used to hinder droplet nucleation and growth outside pores. (d) Experimental results of droplet growth in part c. Droplet height grows at a significantly higher rate of 1−1.5 μm/s. Top curvature radius of these droplets, on the contrary, is increasing slowly at a rate of about 0.25 μm/s, resulting in a stretched droplet interface. Red circles represent droplets left the pores.

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DISCUSSION There are mainly two reasons for the faster growth of the droplets in micropores even when there is no coalescence, corresponding to smoothly increasing sections of the growth lines. The first reason is pore confinement, which forces the droplets to grow mainly in the upward direction. The second but most important reason is the larger liquid−solid contact area, which leads to a higher heat transfer rate and thus faster growth. Droplets in micropores are in contact with the solid surface not only at their base but also around the droplets, which is obviously different from the droplets growing outside the pores. Of course, the temperature at the top of the wires could be slightly higher, even though condensation started when the temperature stabilized. Although detailed heat transfer analysis is challenging for stretched droplets growing in pores, the results shown here can be used to design novel superhydrophobic surfaces for enhanced condensation heat transfer. The significantly higher growth rate of droplet height in the upward direction than in the top curvature radius leads to a stretched droplet surface, which stores more excess surface energy budget for forced droplet removal either through selfcoalescence or coalescence jumping. In the case of coalescence jumping, a sudden pressure drop in the upper part of the stretched droplet occurs upon coalescence with a spherical droplet outside the pore. As the lower part is still confined by the pore and remains under high pressure, a pressure gradient is generated through the droplet, which is the driving force that leads to departure from the pores. Since the droplets in pores need to grow to a specific size at which they can reach the droplets outside pores, coalescence jumping always occurs at sizes determined by the hosting pores. Forced self-jumping of stretched droplets is also similar to the above case. As the droplet becomes increasingly large, its upper part expands and the pressure inside decreases. Meanwhile, lower part of the droplet is confined by the pore

a pore was measured and is plotted in Figure 4b. An abrupt increase in the slope of the curves represents droplet growth induced by coalescence. When there is no coalescence corresponding to the smooth section of the curves, droplets grow at a relative lower rate (0.06−0.07 μm/s) outside the pores. Meanwhile, droplet 3 grows at a significantly higher rate in the upward direction, especially at the last stage of growth, where its growth rate (1−1.5 μm/s) is about 15 times that of the droplets outside the pores. This is indeed a common phenomenon according to Movie S1.1 (SI). Note that at the last stage (t = 35 s) droplet 3 takes away many other droplets outside pores, which is called sweeping behavior.29,30 We tried to minimize the coalescence interference and clearly characterize the growth process of droplets in micropores. Images were taken under the same conditions, except that a higher beam current of 0.51 nA and a lower tilt angle were used for imaging. A higher beam current imposed a significant heating effect on droplets growing outside pores,27,28 and a lower tilt angle enabled scanning and heating the surface mainly in the direction parallel to the surface, with the droplets growing inside pores being less affected by the beam. The top curvature radius (r) and visible height (H*) of three droplets [droplets 4−6 in Movie S1.3 (SI) and in Figure 4c] in pores were measured by using ImageJ with a curve fitting plugin,31 and the results are plotted in Figure 4d. As shown, droplet height is increasing at a rate of 1.0−1.5 μm/s, which is at least 15 times larger than the growth rate of droplets outside pores in Figure 4b or on the surface without micropores in Figure S2 (SI). On the contrary, the top curvature radius (r) of these 21779


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spherical droplets, the related growth mechanism of which can be found elsewhere.23,33,34 Therefore, our analysis starts at a droplet that is just big enough to touch the pore walls. Upon touching, it rapidly reaches an equilibrium, leading to two triple-phase points on each wall−droplet contact line (in crosssectional view). The top point is marked with position angle ϕ1, and the bottom point is marked with position angle ϕ2. The position angle above the line joining the centers of mesh wires is considered positive, while position angle below this centerline is considered negative. Then the subsequent quasistatic droplet growth process begins, and contact angles at the top and bottom triple-phase points are assumed to be the same and remain constant during the whole growth process due to low contact angle hysteresis. A relationship between radius r of the top curvature of the droplet and its corresponding position angle ϕ1 is then obtained as

walls and remains under high pressure. This pressure difference pulls the lower part upward, and at a specific size the droplet base detaches from the base substrate, leading to subsequent self-jumping of the stretched droplet without coalescence. A similar case is the dewetting transition on superhydrophobic surfaces.4,22 In terms of energy, excess surface free energy stored in the stretched droplet interface is the driving force for this surprising self-jumping. Theoretical Model of Droplet Growth in Micropores. In order to build a theoretical model to probe the growth physics of stretched droplets in micropores, we conducted a hydrodynamic analysis under the condition that droplet growth is a quasistatic process (see Figure 5a and section S3 of the SI). Before touching the pore walls, when the droplet is relatively smaller, its growth process is supposed to be the same as that of

r = f1 (ϕ1) =

L 2

− R cos ϕ1

cos(α − ϕ1)

(1)

where R is the mesh wire radius, L is the center-to-center distance of micropores, and α is the supplementary contact angle (thus, α = 180° − θ* ≈ 17° in this work). Figure 5b shows, for R = 34 μm and L = 4R, how the radius r of the top curvature changes as the top position angle ϕ1 increases in the upward direction along the pore wall. Interestingly, r does not increase monotonically. Initially the pore slot in contact with the droplet gradually shrinks, squeezing the growing droplet and thus decreasing r. As the top triple-phase point exceeds a specific position, the pore slot in contact with the droplet then gradually widens, relaxing the droplet and thus increasing r. This slowly increasing radius corresponds to the experimental results given in Figure 4d. Note that relaxation does not occur where the pore slot is the smallest when ϕ1 is equal to zero. Instead, it occurs where the top curvature has a minimum radius as ∂r =0 ∂ϕ1

(2)

which yields a characteristic position angle ϕc of the top curvature ⎛ L − 2R ⎞ ϕc ≈ arctan⎜ tan α⎟ ⎝ L ⎠

(3)

By inserting ϕc into eq 1, the minimum radius (rmin) can be found. Note that eq 3 is only valid for large contact angles. Otherwise, the exact expression should be obtained from eq S3.16 (SI). Figure 5b also shows that radius r of the top curvature becomes even smaller with decreasing pore size (i.e., pore size = L − 2R = 2R). This is because the smaller the pore is, the more confined the droplet is. Meanwhile, the Laplace pressure, which is inversely proportional to the radius of curvature (ΔP = 2σ/r), first increases and then decreases, as shown in Figure 5c. The maximum pressure, corresponding to the minimum radius (rmin), is given by

Figure 5. Theoretical model of droplet growth in a micropore. (a) Experimental droplet morphology in a pore (left) and its schematic (right). (b) Evolution of top curvature radius r with top potions angle ϕ1; r initially decreases due to the shrinking pore slot in contact with the droplet. Then it starts to increase as the pore slot in contact with the droplet widens. (c) Laplace pressure evolution. ΔP is at its maximum when the top curvature has minimum radius. (d) Evolution of the bottom position angle ϕ2. ϕ2 first decreases because the bottom curvature is forced to expand sideward as ΔP increases until its maximum. (e) Evolution of the droplet base diameter 2b*, in response to base curvature evolution. When 2b* becomes zero, the droplet is no longer bound to the base substrate and leaves the pore due to the suddenly created pressure at the droplet base. In all plots, a negative position angle means it is below the line joining the centers of the pore walls. Black, blue, and red curves are for the three cases of R = 10, 17, and 25 μm, respectively.

ΔPmax =

2σlv f1 (ϕc)

(4)

where σlv is the liquid−vapor surface tension. It is worth mentioning that ΔP max is the so-called breakthrough pressure.35,36 In addition, pressure evolution is more drastic for smaller pore sizes. Furthermore, if a sudden coalescence 21780


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angle ϕ2c of the bottom curvature upon self-jumping is then expressed as

with droplets outside pores takes place during growth, the pressure in the upper part of the droplet decreases drastically and causes a huge pressure difference from the bottom part. This pressure difference is the driving force that immediately pushes the droplet out of the pore, leading to departure from the surface, as shown in Figure 3. This phenomenon is called mixed coalescence jumping due to the involvement of stretched and spherical droplets, which is further discussed in the droplet jumping section. Varying the top curvature and pressure inside the droplet affects the position angle ϕ2 of the bottom curvature. Since the pressure inside the droplet tends to be uniform during a quasistatic process, the radii of the top and bottom curvatures also tend to be the same, while the hydrostatic pressure inside a microscopic droplet is negligible.37 Thereby, a relationship between radius r of the top curvature and position angle ϕ2 of the bottom curvature can be obtained as r = f2 (ϕ2) =

(

π 4

+

−α

)

[D + R(1 + sin ϕ2)] sin

(

cos ϕ2 sin

π 4

−

ϕ2 2

ϕ2 2

ϕ2c = f3−1 (b*=0)

Another characteristic angle (ϕ1c) of the top curvature upon self-jumping is expressed as ϕ1c = f1−1 [f2 (ϕ2c)]

H * = r[1 + sin(ϕ1 − α)] − R(1 − sin ϕ1)

(10)

where H* is the visible droplet height, i.e., the difference between the actual droplet height and the distance from the base substrate to the top surface of pores (H* = H − 2R − D, where H is the actual droplet height). H* is used because the beam scan direction was almost parallel to the condensing surface in experiments; thus, we were able to see the droplets only when they grew beyond the top surface of pores. Results of eqs 1 and 10, for R = 17 μm, are given in Figure 6, showing

(5)

Thus, (6)

where D is the average distance from the base substrate to the bottom surface of the mesh wires, which is added due to consideration of the wavelike surface profile of the copper mesh. Figure 5d shows, for D = R/2, that ϕ2 is negative within the plotted range of ϕ1, meaning it lies below the centerline of the pore throughout the whole growth process. ϕ2 first decreases (becomes more negative) due to the initial increase in pressure inside the droplet, implying that the bottom curvature is growing sideward and filling the pore corner with more water. Then, it starts to increase (becomes less negative) due to the decrease in the pressure when the top position angle ϕ1 exceeds ϕc, implying that the bottom curvature is receding from the pore corner. The overlapping curves of the bottom position angle ϕ2 for different values of wire radius R are due to R, L, and D having a linear relationship here, although the effect of L and D for a fixed value of R is also discussed in Figure S6 and S7 (SI). The diameter of the droplet base in contact with the solid surface is another variable that changes with position angles ϕ1 or ϕ2. The normalized base diameter 2b* is given by

Figure 6. Theoretical evolution of the visible height and radius of top curvature of a droplet growing in a micropore. This growth pattern is in agreement with the experimental results in Figure 4d, although the independent variable is the top position angle instead of time due to the complication of heat transfer analysis. Relatively faster increase in the droplet height than its top curvature radius leads to a stretched droplet surface that stores more excess surface free energy than spherical droplets of the same size.

2b* = f3 (ϕ2) ⎤ ⎡D R R cos ϕ2 + 2⎢ + (1 + sin ϕ2)⎥ ⎣ ⎦ L L L ⎛ 1 ⎞ ⎜⎜tan ϕ2 + ⎟⎟ cos ϕ2 ⎠ ⎝

(9)

which is the upper limit of ϕ1 in all plots in Figure 5. Selfjumping is further discussed in detail in the droplet jumping section. It is shown in Figure 4d that droplets in pores grow at a significantly higher rate in the upward direction than in their top curvature radius. Geometrical height evolution is obtained as

)

ϕ2 = f2−1 (r ) = f2−1 [f1 (ϕ1)]

(8)

=1−2

that H* increases by around 32 μm until the droplet is forced to leave the pore while radius r of the top curvature changes from around 18 μm to only around 25 μm. This theoretical growth pattern is in agreement with the experimental results given in Figure 4d, although the position angle instead of time is taken as the independent variable due to the complication of heat transfer analysis. Growth mainly in the upward direction leads to a stretched droplet surface body that stores more excess surface free energy than spherical droplets of the same size. Pore-Forced Droplet Jumping. If two spherical droplets coalesce on a superhydrophobic surface, the resulting droplet may jump by taking advantage of the excess surface free energy

(7)

where b* is the base radius normalized by the interpore distance L. As shown in Figure 5e, 2b* initially increases due to the sideward expansion of the bottom curvature with the increasing Laplace pressure in Figure 5c. Then it decreases as the pressure starts to decrease until the droplet base is no longer in touch with the solid surface. This offers an important boundary condition under which the droplet pulls itself from the pore and leaves the surface, which is termed as “selfjumping” as mentioned previously. A characteristic position 21781


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Figure 7. Schematics of three types of droplet jumping. (a) Conventional coalescence jumping of two spherical droplets. (b) Self-jumping of a single stretched droplet without coalescence. (c) Mixed coalescence jumping of a stretched and a spherical droplet. Flow momentum of the spherical coalescing droplets has initially symmetrical up and down components, until this symmetry is broken by the condensing surface. Contrarily, flow momentum of the self-jumping droplet is largely in the upward direction, implying it has higher conversion efficiency of the excess surface energy budget to kinetic energy. The energy conversion efficiency of the mixed coalescence jumping is expected to be between those of coalescence jumping and self-jumping.

released upon coalescence.2,38,39 We call this “conventional coalescence jumping” (Figure 7a) in order to differentiate the jumping involving stretched droplets in our work. The definition given above does not explicitly state two important reasons behind droplet jumping: (a) the release of the excess surface free energy is the result of a decrease in the total surface area of the droplets after coalescence, and (b) the resulting droplet jumps in the direction normal to the condensing surface, which breaks the symmetry of two momentum components in the upper and lower half of the resulting droplet.1,38,39 Because of the second reason, together with the incomplete release of the excess surface free energy upon jumping, the conversion efficiency of the excess surface free energy to the surface kinetic energy is generally low. Another counteracting factor during coalescence and jumping is surface adhesion, which plays a more or less significant role depending on the solid surface energy, solid fraction of the liquid−solid interface, and droplet size.6,40 In addition to this conventional coalescence jumping, droplet jumping can be further extended to self-jumping of a single stretched droplet (Figure 7b) and mixed coalescence jumping of stretched and spherical droplets (Figure 7c), as mentioned in previous sections. Self-Jumping of a Single Stretched Droplet. Experimental results in Figure 4c and the base diameter evolution in Figure 5e show that self-jumping of stretched droplets in micropores is possible due to the detachment of the droplet base at a specific droplet size determined by pore opening. Specifically, the reason for self-jumping is that droplets in micropores possess the characteristics needed for jumping as (a) they are stretched, thus storing more surface free energy than spherical droplets of the same size. Note that the effective solid fraction of the liquid−solid contact area is significantly small: fs ≈ 0.085 obtained from modified Young’s equation cos θ* = fs cos θ + fs − 1.41 (b) If they grow without coalescence jumping to the characteristic angle ϕ1c (eq 9), their base is no longer bound to the base substrate, which releases the droplets and leads to local high pressure at the lowest point of the droplet base. Since the droplet can expand only outside the pore, the pressure difference further results in unbalanced flow momentum. Moreover, this momentum is directed by the pore wall confinement mainly in the vertical direction, thus resulting in self-jumping (Figure 7b). Using the boundary conditions obtained from eqs 8 and 9, the volume of a stretched droplet upon self-jumping can be obtained through geometrical analysis (Figure 8a) as

Vtotal ≈

1 3 πrc [2 + 3 sin(ϕ1c − α) + sin 3(ϕ1c − α)] 3 ⎞3 ⎛ L ⎞3 ⎤ 1 ⎡⎛ L + π ⎢⎜ − R cos ϕ1c⎟ − ⎜ − R cos ϕ2c⎟ ⎥ ⎠ ⎝2 ⎠⎦ 3 ⎣⎝ 2 cot

ϕ1c + ϕ2c 2

−

ϕ − ϕ2c 4 3⎛ πR ⎜2 − 3 cos 1c 3 2 ⎝

+ cos3

ϕ1c − ϕ2c ⎞ ⎟ 2 ⎠

+ πrc 3

∫0

π /2 + ϕ2c − 2α

[sin(δ + α) − r sin α]2

sin(δ + α) dδ

(11)

Similarly, the total liquid−vapor interface area of this droplet is given by Stotal ≈ 2πrc 2[1 + sin(ϕ1c − α)] +

⎡ π⎢ ⎣

2

( L2 − R cos ϕ1c) sin

−

2⎤

( L2 − R cos ϕ2c) ⎦⎥

ϕ1c + ϕ2c 2

⎛ ϕ − ϕ2c ⎞ − 8fs πR2⎜1 − cos 1c ⎟ 2 ⎝ ⎠ + 2πrc 2

∫0

π /2 + ϕ2c − 2α

[sin(δ + α) − r sin α]

sin(δ + α) dδ

(12)

where fs is the effective solid fraction. Then, the radius of the self-jumping droplet (assuming it is spherical) and excess surface energy budget available for self-jumping can be easily calculated respectively as rj =

⎛ 3Vtotal ⎞1/3 ⎜ ⎟ ⎝ π ⎠

ΔEs ≈ (Stotal − 4πrj3)σw

(13)

Figure 8b shows that the top curvature radius of the droplet slightly increases after jumping, implying that the stretched body of the droplet becomes spherical. Also, a larger pore size produces a larger self-jumping droplet. The three dots in the figure are the experimentally measured top curvature radii of the three droplets upon jumping in Figure 4d. Figure 8c gives the surface energy before and after self-jumping, the difference 21782


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An inaccurate viscous dissipation equation has been used in many previous studies to predict the jumping velocity, which either over- or under-estimated the viscous dissipation.44−46 Instead, the portion of the excess surface free energy budget converted to the kinetic energy of the jumping droplet can be expressed as29

E k = ηsjΔEs(sj)

where η is the conversion efficiency, and sj represents selfjumping. It is important to point out, as shown in Figure 7a, that the flow momentum of two coalescing spherical droplets has initially symmetrical up and down components until this symmetry is broken by the condensing surface. On the contrary, the flow momentum of a self-jumping stretched droplet is largely in the upward direction (Figure 7b), indicating that it has a higher energy conversion efficiency than conventional coalescence jumping of two spherical droplets. According to ref 39, the energy conversion efficiency of conventional coalescence jumping for Oh ≈ 0.04, corresponding to r ≈ 25 μm under the conditions of this work, is only about 6%. Although an accurate simulation of the internal fluid dynamics of the self-jumping process is needed to estimate the energy conversion efficiency, the self-jumping velocity for a conversion efficiency of 6% and 10% is plotted against the top curvature radius upon jumping in Figure 8d. It shows a velocity of about 0.4 m/s for r ≈ 25 μm at η = 6%, and the jumping velocity decreases as the droplet size increases. Although larger jumping droplets (corresponding to larger pores) release more excess surface free energy, EC, defined as the excess surface free energy budget released per unit area and time, should be used to evaluate how much energy at most can be contributed by this microporous structure to the overall droplet removal process. If the droplet growth rate in the upward direction is assumed to be linear, EC can be expressed as

Figure 8. Self-jumping of a stretched droplet in a pore. (a) Experimental droplet morphology right before self-jumping (left) and schematic of this droplet (right). (b) Pore size (≈2R) effect on droplet size upon self-jumping. Black, red, and blue square dots are the respective experimentally measured curvature radii of the three droplets upon jumping in Figure 4d. (c) Droplet size effect on the excess surface free energy budget. A relatively small amount of excess surface energy budget (red curve) is available for self-jumping. Blue and green curves are the surface free energy before and after selfjumping. (d) Droplet size and conversion efficiency effect on selfjumping velocity. The energy conversion efficiency of self-jumping is supposed to be higher than that (≤6%) of conventional coalescence jumping; 10% is a qualitative value, while a quantitate value needs to be determined through numerical simulations and more detailed jumping experiments. (e) Pore size effect on excess surface energy contribution (EC) per unit area and time for the microporous structure.

EC =

Ḣ ΔEs(sj) HjL2

(16)

where Ḣ is the upward growth rate of droplets in pores, and it is taken as Ḣ ≈ 1 μm/s (see Figure 4d) for different pore sizes, which is not strictly correct, and Hj is the actual droplet height upon jumping (Hj = Hj* + 2R + D). Figure 8e shows that EC decreases as the pore size increases due to the inverse-quadratic decline in the number of pores per unit area and because droplets in larger pores need relatively more time to grow to the height upon self-jumping. An extreme case is that EC approaches zero if the pore size is very large, which is identical to the surface without micropores. In addition, the gravity effect can be significant for large droplets, causing self-jumping failure in large pores. This reveals an important finding that a surface with smaller pores contributes more energy to the overall droplet removal process. However, it needs to be taken into serious consideration that the apparent contact angle of smaller droplets has a higher discrepancy, generally less than the macroscopic contact angle measured by using a goniometer. This means that surface adhesion is relatively significant for smaller droplets, resulting in a decreased excess surface energy budget being available for jumping. This may be the reason that only a wetting transition is observed in ref 22. Therefore, nanoand submicron scale pores may contribute less or no excess surface free energy, which needs further study to be determined.

of which is the excess surface free energy budget. As shown, the excess surface free energy is significantly smaller than the surface free energy before and after jumping. Also, total and excess surface energy increases with increasing droplet size upon jumping. Not all the excess surface free energy budget can be converted into kinetic energy due to surface adhesion, viscous dissipation, and most importantly surface interaction.38,39,42 The work of adhesion (Ew) can be neglected because43 Ew ∝ fs (1 + cos θ )

(15)

(14)

where the effective solid fraction fs is only 0.085, and 1 + cos θ ≈ 0.57. 21783


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ACS Applied Materials & Interfaces Mixed Coalescence Jumping. Previous sections show that self-jumping is possible on the microporous surface if coalescence interference is illuminated by intentionally hindering the growth and nucleation of droplets outside pores. However, in condensation experiments, where there is less artificial interference, the most dominant jumping phenomenon is coalescence jumping of a stretched droplet growing in a pore with one or more spherical droplets growing outside this pore, which is called mixed coalescence jumping (Figure 7c). While mixed coalescence jumping is rather complicated, a simple comparison among the three types of jumping is given in Figure 9, assuming that coalescing droplets

which is a discretized form of the traditional Boltzmann transport equation (BTE) fa (x+eaΔt ,t +Δt ) = fa (x ,t ) −

Δt [f (x ,t ) − f aeq (x ,t )] τ a (17)

We can incorporate different equations of state (EOS) into the Shan−Chen LBM model as required. In our model, the Redlich−Kwong50 EOS is chosen p=

ρRT − 1 − bρ

aρ 2 T (1 + bρ)

(18)

An in-house MATLAB code was developed to solve the above problem. The detailed LBM model description is provided in our previous work,51 and nonslip boundary conditions are used here. Figure 10a shows flow streamlines and pressure evolution (illustrated with color change) during the self-jumping of a

Figure 9. Comparison of self-jumping, conventional coalescence jumping, and mixed coalescence jumping. (a) Excess surface energy budget of the three jumping models. Self-jumping has the least excess surface energy budget, while mixed jumping has the most. (b) Jumping velocity. Accordingly, mixed jumping has the highest jumping velocity. In all cases, the energy conversion efficiency is taken as 6%, although self-jumping and mixed jumping are supposed to have higher energy conversion efficiencies than conventional coalescence jumping.

Figure 10. Numerical modeling of self-jumping and mixed jumping. (a) Self-jumping of a stretched droplet growing in a pore. The initial stage is when the droplet base is detaching from the base substrate in order to balance the decreasing pressure in the top part of the droplet as it grows larger. The color change in the droplet represents pressure propagation (yellow represents high pressure, and blue represents low pressure). Upon detaching from the base substrate, the droplet base has a high curvature and thus high pressure (deep yellow). This pressure consequently leads to upward flow momentum, resulting in self-jumping of the droplet. (b) Mixed coalescence jumping of a stretched droplet with a spherical droplet. The flow momentum not only comes from coalescence but also from the detachment of the stretched droplet from the base substrate as in the case of self-jumping. The combined momentums lead the droplet to jump in the perpendicular direction.

have the same volume as the self-jumping droplet. As shown in Figure 9, mixed coalescence jumping has the most excess surface energy budget and highest jumping velocity due to the energy contribution given in Figure 8e and the excess surface free energy released during coalescence. In addition, Figure S3 (SI) shows the comparison of the droplet removal performance of the microporous surface and the surface without micropores under e-beam exposure for about 3 min. Larger droplets on the microporous surface are continuously removed by droplet jumping even after prolonged beam exposure due to their sufficient excess surface free energy budget. However, larger droplets on the surface without micropores only grow in size due to a lack of efficient droplet jumping. This further confirms the contribution of the excess surface free energy budget from the stretched droplets in micropores. Note that the energy conversion efficiency of only 6% is used in related calculations, although, as mentioned, self-jumping and mixed jumping is believed to have higher conversion efficiency than conventional coalescence jumping. Simulation. In order to further reveal the jumping mechanism, we modeled the movement of a self-jumping and mixed jumping droplet by using a lattice Boltzmann method (LBM). LBM was already applied to study the conventional coalesced jumping droplet evolution and its high accuracy was verified.47 We choose the Shan−Chen type of model48 after comparing it with the free energy model and the Rothman− Keller model.49 In the Shan−Chen model, the distribution function satisfies the following lattice Boltzmann equation,

stretched droplet. As discussed previously, upon leaving the base substrate, the lowest point at the droplet base has a high curvature and thus high pressure (deep yellow region). This pressure-driven force leads to the upward motion of the lower part of the droplet. Due to pore confinement, pressure and flow momentum propagates mainly in the upward direction. This leads to higher conversion of the small amount of surface energy to the kinetic energy of the self-jumping droplet. In the case of forced coalescence jumping of a stretched droplet with a spherical droplet, as shown in Figure 10b, the flow momentum required for jumping comes from two sources. One is the coalescence process, similar to conventional coalescence jumping, and the other is the upward motion of the stretched droplet upon detaching from the base substrate, which is similar to self-jumping. Since these two contributions 21784


Research Article


Reference Number 02/MI/MIT/CP/11/07633/GEN/G/00. The authors appreciate the technical support from Mr. Mike Tiner, Dr. Mustapha Jouiad, and Cyril Aubry at the Masdar Institute Microscopy Room, as well as the discussion with Prof. Evelyn Wang (MIT) and Dr. Aikifa Raza (Masdar Institute).

are not exactly in the same direction, the resulting droplet jumps at an angle away from the perpendicular direction to the condensing surface. An important point not discussed yet is the pore shape. In this work, micropores with curved walls are unique and easily achievable as we used commercially available copper micromesh. However, other pore shapes, such as circular and square pores with straight walls, may also affect the droplet growth and jumping processes, and they are also expected to yield similar fast growth and forced jumping of droplets. We believe that this can be a novel, interesting, and promising research area. Additionally, the proposed microporous structure can also be coupled with the electric field enhanced condensation heat trasfer3,52,53 to enhance further condensation heat transfer.

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(1) Nam, Y.; Kim, H.; Shin, S. Energy and Hydrodynamic Analyses of Coalescence-Induced Jumping Droplets. Appl. Phys. Lett. 2013, 103, 161601. (2) Yanagisawa, K.; Sakai, M.; Isobe, T.; Matsushita, S.; Nakajima, A. Investigation of Droplet Jumping on Superhydrophobic Coatings during Dew Condensation by the Observation from Two Directions. Appl. Surf. Sci. 2014, 315, 212−221. (3) Miljkovic, N.; Preston, D. J.; Enright, R.; Wang, E. N. Electrostatic Charging of Jumping Droplets. Nat. Commun. 2013, 4, 2517. (4) Zhu, J.; Luo, Y.; Tian, J.; Li, J.; Gao, X. Clustered RibbedNanoneedle Structured Copper Surfaces with High-Efficiency Dropwise Condensation Heat Transfer Performance. ACS Appl. Mater. Interfaces 2015, 7, 10660−10665. (5) Miljkovic, N.; Wang, E. N. Condensation Heat Transfer on Superhydrophobic Surfaces. MRS Bull. 2013, 38, 397−406. (6) Enright, R.; Miljkovic, N.; Al-Obeidi, A.; Thompson, C. V.; Wang, E. N. Condensation on Superhydrophobic Surfaces: The Role of Local Energy Barriers and Structure Length Scale. Langmuir 2012, 28, 14424−14432. (7) Zhao, Y.; Luo, Y.; Li, J.; Yin, F.; Zhu, J.; Gao, X. Condensate Microdrop Self-Propelling Aluminum Surfaces Based on Controllable Fabrication of Alumina Rod-Capped Nanopores. ACS Appl. Mater. Interfaces 2015, 7, 11079−11082. (8) Kim, H.; Nam, Y. Condensation Behaviors and Resulting Heat Transfer Performance of Nano-Engineered Copper Surfaces. Int. J. Heat Mass Transfer 2016, 93, 286−292. (9) Wisdom, K. M.; Watson, J. a; Qu, X.; Liu, F.; Watson, G. S.; Chen, C.-H. Self-Cleaning of Superhydrophobic Surfaces by SelfPropelled Jumping Condensate. Proc. Natl. Acad. Sci. U. S. A. 2013, 110, 7992−7997. (10) Kim, A.; Lee, C.; Kim, H.; Kim, J. Simple Approach to Superhydrophobic Nanostructured Al for Practical Antifrosting Application Based on Enhanced Self-Propelled Jumping Droplets. ACS Appl. Mater. Interfaces 2015, 7, 7206−7213. (11) Seo, D.; Lee, C.; Nam, Y. Influence of Geometric Patterns of Microstructured Superhydrophobic Surfaces on Water-Harvesting Performance via Dewing. Langmuir 2014, 30, 15468−15476. (12) Zamuruyev, K. O.; Bardaweel, H. K.; Carron, C. J.; Kenyon, N. J.; Brand, O.; Delplanque, J. P.; Davis, C. E. Continuous Droplet Removal upon Dropwise Condensation of Humid Air on a Hydrophobic Micropatterned Surface. Langmuir 2014, 30, 10133− 10142. (13) Miljkovic, N.; Preston, D. J.; Enright, R.; Wang, E. N. JumpingDroplet Electrostatic Energy Harvesting. Appl. Phys. Lett. 2014, 105, 013111. (14) Celia, E.; Darmanin, T.; Taffin de Givenchy, E.; Amigoni, S.; Guittard, F. Recent Advances in Designing Superhydrophobic Surfaces. J. Colloid Interface Sci. 2013, 402, 1−18. (15) Darmanin, T.; Guittard, F. Recent Advances in the Potential Applications of Bioinspired Superhydrophobic Materials. J. Mater. Chem. A 2014, 2, 16319−16359. (16) Miljkovic, N.; Enright, R.; Nam, Y.; Lopez, K.; Dou, N.; Sack, J.; Wang, E. N. Jumping-Droplet-Enhanced Condensation on Scalable Superhydrophobic Nanostructured Surfaces. Nano Lett. 2013, 13, 179−187. (17) She, Z.; Li, Q.; Wang, Z.; Li, L.; Chen, F.; Zhou, J. Novel Method for Controllable Fabrication of a Superhydrophobic CuO Surface on AZ91D Magnesium Alloy. ACS Appl. Mater. Interfaces 2012, 4, 4348−4356.

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CONCLUSION We simultaneously achieved fast growth and pore-forced jumping of stretched water droplets on a homogeneously superhydrophobic nanostructured micromesh surface. At low saturations (S ≈ 1.06), droplets in micropores show a significantly high growth rate of 1−1.5 μm/s in the upward direction, about 15−25 times that of droplets growing outside pores or on the surface without micropores. Meanwhile, the top curvature radius of these droplets in micropores increases relatively slowly at a rate of around 0.25 μm/s due to pore confinement, leading to a highly stretched droplet surface. In a predictable manner, stretched droplets in pores are forced to jump at pore scale through coalescence with spherical droplets outside pores. The growth pattern of stretched droplets is revealed, and a new jumping mechanism termed as self-jumping (without coalescence) of a single stretched droplet growing in a pore is proposed. It is shown that excess surface free energy stored in the stretched droplet surface is partially responsible for this surprising self-jumping. It also plays an enhancing role in pore-scale-driven coalescence jumping. We believe our findings provide novel insights into enhanced growth and jumping of condensing droplets on microporous superhydrophobic surfaces, which are greatly valuable to various energy and water applications.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acsami.6b05324. Captions describing Movies S1.1−S1.3 and additional information on the theoretical analysis of the growth and jumping of stretched droplets in micropores (PDF) Three videos (Movies S1.1−S1.3) showing microscale droplet growth and jumping during ESEM condensation on the mesh-covered microporous superhydrophobic surface (ZIP)

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REFERENCES

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was supported by the Cooperative Agreement between the Masdar Institute of Science and Technology, UAE, and the Massachusetts Institute of Technology (MIT), USA, 21785


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ACS Applied Materials & Interfaces (18) Miljkovic, N.; Enright, R.; Wang, E. N. Effect of Droplet Morphology on Growth Dynamics and Heat Transfer during Condensation on Superhydrophobic Nanostructured Surfaces. ACS Nano 2012, 6, 1776−1785. (19) Cheng, J.; Vandadi, A.; Chen, C.-L. Condensation Heat Transfer on Two-Tier Superhydrophobic Surfaces. Appl. Phys. Lett. 2012, 101, 131909. (20) Hou, Y.; Yu, M.; Chen, X.; Wang, Z.; Yao, S. Recurrent Filmwise and Dropwise Condensation on a Beetle Mimetic Surface. ACS Nano 2015, 9, 71−81. (21) Chen, X.; Wu, J.; Ma, R.; Hua, M.; Koratkar, N.; Yao, S.; Wang, Z. Nanograssed Micropyramidal Architectures for Continuous Dropwise Condensation. Adv. Funct. Mater. 2011, 21, 4617−4623. (22) Lv, C.; Hao, P.; Zhang, X.; He, F. Dewetting Transitions of Dropwise Condensation on Nanotexture-Enhanced Superhydrophobic Surfaces. ACS Nano 2015, 9, 12311−12319. (23) Enright, R.; Miljkovic, N.; Dou, N.; Nam, Y.; Wang, E. N. Condensation on Superhydrophobic Copper Oxide Nanostructures. J. Heat Transfer 2013, 135, 091304. (24) Xiao, R.; Miljkovic, N.; Enright, R.; Wang, E. N. Immersion Condensation on Oil-Infused Heterogeneous Surfaces for Enhanced Heat Transfer. Sci. Rep. 2013, 3, 1988. (25) Li, G.; Alhosani, M. H.; Yuan, S.; Liu, H.; Al Ghaferi, A.; Zhang, T. Microscopic Droplet Formation and Energy Transport Analysis of Condensation on Scalable Superhydrophobic Nanostructured Copper Oxide Surfaces. Langmuir 2014, 30, 14498−14511. (26) Jeong, H. E.; Kwak, M. K.; Park, C. I.; Suh, K. Y. Wettability of Nanoengineered Dual-Roughness Surfaces Fabricated by UV-Assisted Capillary Force Lithography. J. Colloid Interface Sci. 2009, 339, 202− 207. (27) Barkay, Z. Wettability Study Using Transmitted Electrons in Environmental Scanning Electron Microscope. Appl. Phys. Lett. 2010, 96, 183109. (28) Rykaczewski, K.; Scott, J. H. J.; Fedorov, A. G. Electron Beam Heating Effects during Environmental Scanning Electron Microscopy Imaging of Water Condensation on Superhydrophobic Surfaces. Appl. Phys. Lett. 2011, 98, 093106. (29) Kim, M. K.; Cha, H.; Birbarah, P.; Chavan, S.; Zhong, C.; Xu, Y.; Miljkovic, N. Enhanced Jumping-Droplet Departure. Langmuir 2015, 31, 13452−13466. (30) Qu, X.; Boreyko, J. B.; Liu, F.; Agapov, R. L.; Lavrik, N. V.; Retterer, S. T.; Feng, J. J.; Collier, C. P.; Chen, C. H. Self-Propelled Sweeping Removal of Dropwise Condensate. Appl. Phys. Lett. 2015, 106, 221601. (31) Schneider, C. a; Rasband, W. S.; Eliceiri, K. W. NIH Image to ImageJ: 25 Years of Image Analysis. Nat. Methods 2012, 9, 671−675. (32) Xu, W.; Lan, Z.; Peng, B.; Wen, R.; Chen, Y.; Ma, X. Directional Movement of Droplets in Grooves: Suspended or Immersed. Sci. Rep. 2016, 6, 18836. (33) Kim, S.; Kim, K. J. Dropwise Condensation Modeling Suitable for Superhydrophobic Surfaces. J. Heat Transfer 2011, 133, 081502. (34) Miljkovic, N.; Enright, R.; Wang, E. N. Modeling and Optimization of Superhydrophobic Condensation. J. Heat Transfer 2013, 135, 111004. (35) Hensel, R.; Finn, A.; Helbig, R.; Killge, S.; Braun, H. G.; Werner, C. In Situ Experiments to Reveal the Role of Surface Feature Sidewalls in the Cassie-Wenzel Transition. Langmuir 2014, 30, 15162−15170. (36) Liu, T. L.; Kim, C.-J. C. Turning a Surface Superrepellent Even to Completely Wetting Liquids. Science 2014, 346, 1096−1100. (37) Sarkar, A.; Kietzig, A.-M. Design of a Robust Superhydrophobic Surface: Thermodynamic and Kinetic Analysis. Soft Matter 2015, 11, 1998−2007. (38) Liu, F.; Ghigliotti, G.; Feng, J. J.; Chen, C.-H. Self-Propelled Jumping upon Drop Coalescence on Leidenfrost Surfaces. J. Fluid Mech. 2014, 752, 22−38. (39) Enright, R.; Miljkovic, N.; Sprittles, J.; Nolan, K.; Mitchell, R.; Wang, E. N. How Coalescing Droplets Jump. ACS Nano 2014, 8, 10352−10362.

(40) Lo, C.-W.; Wang, C.-C.; Lu, M.-C. Scale Effect on Dropwise Condensation on Superhydrophobic Surfaces. ACS Appl. Mater. Interfaces 2014, 6, 14353−14359. (41) Cassie, A. B. D.; Baxter, S. Wettability of Porous Surfaces. Trans. Faraday Soc. 1944, 40, 546−551. (42) Liu, F.; Ghigliotti, G.; Feng, J. J.; Chen, C.-H. Numerical Simulations of Self-Propelled Jumping upon Drop Coalescence on Non-Wetting Surfaces. J. Fluid Mech. 2014, 752, 39−65. (43) Xiu, Y.; Zhu, L.; Hess, D. W.; Wong, C. P. Relationship between Work of Adhesion and Contact Angle Hysteresis on Superhydrophobic Surfaces. J. Phys. Chem. C 2008, 112, 11403−11407. (44) Liu, T. Q.; Sun, W.; Sun, X. Y.; Ai, H. R. Mechanism Study of Condensed Drops Jumping on Super-Hydrophobic Surfaces. Colloids Surf., A 2012, 414, 366−374. (45) Lv, C.; Hao, P.; Yao, Z.; Song, Y.; Zhang, X.; He, F. Condensation and Jumping Relay of Droplets on Lotus Leaf. Appl. Phys. Lett. 2013, 103, 021601. (46) Wang, F. C.; Yang, F.; Zhao, Y. P. Size Effect on the Coalescence-Induced Self-Propelled Droplet. Appl. Phys. Lett. 2011, 98, 053112. (47) Peng, B. L.; Wang, S. F.; Lan, Z.; Xu, W.; Wen, R. F.; Ma, X. H. Analysis of Droplet Jumping Phenomenon with Lattice Boltzmann Simulation of Droplet Coalescence. Appl. Phys. Lett. 2013, 102, 151601. (48) Shan, X.; Chen, H. Lattice Boltzmann Model for Simulating Flows with Multiple Phases and Components. Phys. Rev. E: Stat. Phys., Plasmas, Fluids, Relat. Interdiscip. Top. 1993, 47, 1815−1819. (49) Huang, H.; Wang, L.; Lu, X. Y. Evaluation of Three Lattice Boltzmann Models for Multiphase Flows in Porous Media. Comput. Math. with Appl. 2011, 61, 3606−3617. (50) Yuan, P.; Schaefer, L. Equations of State in a Lattice Boltzmann Model. Phys. Fluids 2006, 18, 042101. (51) Li, H.; Yang, W.; Huang, H.; Chevalier, S.; Sassi, M.; Zhang, T.; Zahaf, K.; Al-Farisi, O. Pore-Scale Lattice Boltzmann Simulation of Oil-Water Flow in Carbonate Rock with Variable Wettability. In Abu Dhabi International Petroleum Exhibition and Conference; Society of Petroleum Engineers, 2015; DOI: 10.2118/177548-MS. (52) Miljkovic, N.; Preston, D. J.; Enright, R.; Wang, E. N. ElectricField-Enhanced Condensation on Superhydrophobic Nanostructured Surfaces. ACS Nano 2013, 7, 11043−11054. (53) Birbarah, P.; Li, Z.; Pauls, A.; Miljkovic, N. A Comprehensive Model of Electric-Field-Enhanced Jumping-Droplet Condensation on Superhydrophobic Surfaces. Langmuir 2015, 31, 7885−7896.

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Unidirectional Fast Growth and Forced Jumping of Stretched Droplets

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