Wetting Transition of Condensed Droplets on Nanostructured

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Wetting Transition of Condensed Droplets on Nanostructured Superhydrophobic Surfaces: Coordination of Surface Properties and Condensing Conditions Rongfu Wen, Zhong Lan, Benli Peng, Wei Xu, Ronggui Yang, and Xuehu Ma ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b01812 • Publication Date (Web): 31 Mar 2017 Downloaded from http://pubs.acs.org on April 4, 2017

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ACS Applied Materials & Interfaces

Wetting Transition of Condensed Droplets on Nanostructured Superhydrophobic Surfaces: Coordination of Surface Properties and Condensing Conditions Rongfu Wen†,‡, Zhong Lan†, Benli Peng†, Wei Xu†, Ronggui Yang‡, Xuehu Ma†,*

†

State Key Laboratory of Fine Chemicals & Liaoning Key Laboratory of Clean Utilization of

Chemical Resources, Institute of Chemical Engineering, Dalian University of Technology, Dalian 116024, PR China ‡

Department of Mechanical Engineering, University of Colorado, Boulder, CO 80309-0427,

USA

/ 28 Environment ACS Paragon 1Plus


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Abstract Nanostructured superhydrophobic surfaces have been actively explored to promote favorable droplet dynamics for a wide range of technological applications. However, the tendency of condensed droplets to form as pinned states greatly limits their applicability in enhancing condensation heat transfer efficiency. Despite recent progresses, the understanding of physical mechanisms governing the wetting transition of condensed droplets is still lacking. In this work, a nanostructured superhydrophobic surface with tapered nanogaps is fabricated to demonstrate the coordination of surface wetting property, topography and the condensing condition on the wetting state and dynamic behavior of condensed droplets. Combining the environmental scanning electron microscopy and optical visualization methods, we systematically show the morphology of nucleated droplets in nanostructures and the droplet dynamic evolution throughout the growth stages, which provides the direct evidence of condensing conditioninduced droplet wetting transition. When the surface subcooling is smaller than 0.3 K, the droplets formed as the Cassie-Baxter state, followed by coalescence-induced droplet jumping. With the increase of surface subcooling up to 0.6 K, however, droplet formation occurs randomly inside nanogaps, resulting in the loss of superhydrophobicity. These new observations along with the new insights about the coordination of surface properties and condensing conditions on droplet wetting transition are useful for guiding the development of novel surfaces for improving droplet removal and phase-change heat transfer.

Keywords: nanostructured superhydrophobic surface, wetting transition, droplet dynamics, condensing condition, spatial confinement, synergistic coordination


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1. Introduction Condensation is a ubiquitous phenomenon in nature1,

2

and it plays an essential role in

various technological applications including water harvesting,3 power generation,4 environmental control,5 and thermal management.6, 7 It is known that the condensation modes (filmwise and dropwise) are highly dependent on surface chemistry and topography.8-10 Of particular interest is dropwise condensation on superhydrophobic surfaces where microscopic roughness together with hydrophobicity renders extremely low surface energy state and thus it exhibits non-wetting characteristics that droplets suspend on structured surfaces with vapor trapped underneath.11-13 When small water droplets merge on such superhydrophobic surfaces, the released surface energy during coalescence can potentially induce droplet jumping, which can efficiently remove droplets from the condensing surface and thus improve the heat transfer performance.14,

15

However, for drastic condensing conditions such as that in a pure water vapor or at high supersaturation,16-18 condensed droplets tend to form as immersed states rather than suspended modes, which greatly limits the applicability of such surfaces for enhancing condensation heat transfer. Despite that a considerable amount of work have focused on understanding the effect of surface structures on droplet wetting transition with a variety of explanations such as Laplace pressure instabilities,19-21 energy barriers,22, 23 and thermodynamic models,24 there is a lack of multiscale understanding on droplet wetting transition process that starts with the initial nucleation of nanoscale droplets. Fundamentally different from the wetting mechanisms of large droplets on superhydrophobic surfaces such as raindrops that are far larger than the characteristic scale of surface structures of lotus leaves, condensation on superhydrophobic surfaces can result in loss of non-wettability even on a hydrophobic coating.8, 25 Droplet transition from the mobile



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jumping mode to pinned states with the increase of supersaturation was observed using optical microscopy,17,

26

and it was explained by the interaction between the structure scale and

nucleation density of droplets. However, the theoretical analysis of droplet nucleation density on nanostructured surfaces lacks experimental verification. Although the local energy criterion is widely used to assess the effect of surface structures on droplet wetting modes,27 it cannot predict the condensing condition-induced the wetting transition since it ignores the behavior of nucleated droplets within the structures (the initial stage of wetting transition). Droplet growth on superhydrophobic surfaces is a dynamic evolution process from droplet nucleation to shedding, which is highly dependent on the interaction of chemical property, surface topography and the condensing condition. Understanding the multiscale evolution of droplet growth from a few nanometers in the nucleation stage to hundreds of micrometers in the shedding stage is the key to the development of novel functionalized surfaces. Here, a nanostructured copper surface with tapered hydrophobic nanogaps is fabricated and tested to study droplet nucleation and wetting behaviors on superhydrophobic surfaces under different condensing conditions. To capture the intriguing phenomenon, both the environmental scanning electron microscopy (ESEM) and high-speed optical visualization techniques are used to record the wetting state and dynamic behavior of condensed droplets at various growth stages. Significantly different from the previous studies, the condensing condition-induced droplet wetting transition is demonstrated, highlighting the coordination of surface properties and condensing conditions on the wetting transition of condensed droplets on nanostructured superhydrophobic surfaces. 2. Results


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Chemical oxidation was employed to fabricate the dense tapered nanogaps on copper surface and the hydrophobic coating was formed on the nanostructures by chemical vapor deposition (see Methods for details). Figure 1a illustrates the morphology of the nanostructured superhydrophobic surface. A tapered nanogap is formed between two nanosheets with the wider opening on the top and the densely packed nanosheets compose the plexiform nanocluster on the entire surface. The scale of hydrophobic tapered nanogaps ranges from a few nanometers at the bottom to several hundred nanometers at the top. Figure 1b shows typical scanning electron microscope (SEM) images of sharp knifelike copper oxide nanosheets on the substrate. Largermagnification SEM images in Figure 1c-d show the characteristic height h of the copper nanosheet is ~1 µm and the separation between two adjacent nanosheets on the top surface, i.e., the width w of the formed tapered nanogaps is 200~300 nm. The average angle of opening of nanostructures is ~35°. The apparent contact angle and contact angle hysteresis are measured using the goniometer with a 4 µL water droplets to be θaCB = 167.2° ± 1.8° and ∆θ = 4° ± 0.8°, respectively (inset of Figure 1b). Goniometric measurements on the corresponding smooth hydrophobic copper surface show the apparent contact angle of θa = 110° ± 2.5° and contact angle hysteresis of ∆θ = 35° ± 5.8°, respectively. The effective solid fraction φeff corresponding to the surface area fraction is calculated by the apparent contact angle of a water droplet on the surface using the Cassie-Baxter equation,28 cosθaCB = φeff (cosθa + 1) - 1, which is calculated to be φeff = 0.038. Similar to the macroscopic measurement results (inset of Figure 1b), condensed droplets in the Cassie-Baxter state with diameters as small as tens of micrometers exhibit extreme water repellent property, as shown in Figure 1e. Condensing Condition-Induced Droplet Wetting Transition. Here the condensation condition is pure water vapor, i.e., with a humidity of 100%. The effect of surface subcooling



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(∆T = Tv – Tw, defined as the temperature difference between the vapor temperature and the surface temperature) on the droplet wetting state and dynamic behavior on the nanostructured superhydrophobic surface is investigated using ESEM (Figure 2, see details in Methods). At a small surface subcooling (∆T = 0.3 K), droplets appear in spherical shape in the Cassie-Baxter state and continuously grow in size with large apparent contact angle (Figure 2c). Once the droplet coalesces with the adjacent droplets, the released surface energy will overcome droplet adhesion, leading to self-propelling droplet removal.29 After droplet jumping occurs, the condensing surface is refreshed and exposed for the subsequent nucleation and growth of new droplets (Figure 2d). Such jumping condensation has distinct advantages including gravityindependent, rapid droplet removal at micrometric scale and intense disturbance near the liquidvapor interface, which have many applications including condensation heat transfer enhancement,17 frost prevention,30 and energy harvesting.31 As the surface subcooling increases up to 1.4 K, however, condensed droplets appear in the Wenzel state, where droplets grow with pinned contact lines (Figure 2e). As a result, coalesced droplets remain on the condensing surface without droplet jumping (Figure 2f). Further condensation may result in the flooding condensation, which indicates the failure of superhydrophobic surface. To further confirm the wetting states of condensed droplets formed under various condensing conditions as shown above, we characterized the evolution dynamics of the droplet interface by reversely evaporating the condensed droplets. We note that condensation and evaporation are not completely reversible processes due to the contact angle hysteresis in condensation and evaporation. However, as long as we can observe the movement of contact line by evaporating the droplets originally condensed at different surface subcooling, regardless of the contact angle hysteresis, we can confirm the wetting state (Wenzel or Cassie-Baxter) of those


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droplets originally formed. Despite that the droplets condensed at different surface subcooling (0.3 K and 0.9 K) were evaporated at the same surface superheat (0.2 K), dramatic difference in droplet evolution behaviors were observed (see Supporting Information S1). For the droplets originally condensed at ∆T = 0.3 K, the contact line remains circular throughout the evaporation process. The contact line continuously shrinks with the decreasing droplet size, which indicates that the droplets were formed as suspended state with no pinned contact line. However, for the droplets condensed at ∆T = 0.9 K, a discontinuity of contact line shrinkage occurs, which is due to the pinned contact line and indicates that the droplets were formed as the immersed droplets. This experiments further demonstrate that the droplets on a nanostructured superhydrophobic surface can either be in the mobile Cassie-Baxter state with the possible self-jumping or be in the pinned Wenzel state with the immersed contact line, depending on the condensing condition, i.e., surface subcooling. Droplet Dynamic Behaviors and Condensation Modes. To obtain a large field of view of droplet behaviors under various condensing conditions, we employ the high-speed optical visualization technique in a custom-built experimental apparatus (see details in Methods). For each surface subcooling, the condensation experiment was conducted continuously for 40 minutes, excluding the time needed to adjust condensation conditions. The droplet wetting state and condensation mode can be maintained throughout the experimental test at each surface subcooling. The droplet wetting states presented in this study are based on the steady-state condensation experiments. Four typical droplet wetting states and removal modes are found at various surface subcooling, as shown in Figure 3. Comparing Figures 3a-d (or e-h), a significant trend clearly observed is that the condensation mode transforms from jumping condensation to flooding condensation with the increase of surface subcooling, as evidenced by the transition of



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droplet size distribution from the densely distributed small droplets to the pinned large droplets as well as the reduction of surface renewal frequency. At the surface subcooling of 0.3 K, condensed droplets are in the suspended Cassie-Baxter state. These droplets undergo spontaneous jumping at high departure frequency (~22 min-1) and the maximum size of droplets are less than several tens of microns (Figure 3e, also see Supporting Information Video 1). Although the coalescence-induced droplet jumping is also observed at surface subcooling of 0.5 K, the average and maximum radius of droplets significantly increases due to the partial immersion of the droplets (Figure 3f, also see Supporting Information Video 2). With further increase of surface subcooling to 0.8 K, condensed droplets tend to form as the immersed state rather than the suspended state so that the merged droplets remain on the surface rather than jump away, which leads to a further increase of average droplet size as well as the gravityinduced droplet shedding (Figure 3g, also see Supporting Information Video 3). When surface subcooling is large enough (3.0 K), condensed droplets completely immerse into the nanogaps and the pinned contact line is observed (Figure 3h, also see Supporting Information Video 4). The above visualization study clearly shows the condensing condition-induced droplet wetting transition. To quantify and highlight the dramatic difference in droplet behaviors under various surface subcooling, we analyze the droplet size distribution on the condensing surface. More than 350 droplets are statistically counted at various surface subcooling. The smallest radius of droplets that are counted is 10 µm while the size of the largest droplets depends on the droplet departure sizes at various surface subcooling. Figure 4a shows that the droplets with radius smaller than 20 µm dominate at small surface subcooling (∆T = 0.3 K), contributing to over 85% of the droplets during the whole condensation process. As the surface subcooling increases to 1.0 K, the


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droplets with radius larger than 100 µm begin to appear while the percentage of droplets with a radius smaller than 20 µm significantly decreases. With further increase of surface subcooling (∆T = 3.0 K), condensed droplets grow in successive coalescence instead of jumping, leading to the increased proportion of large size droplets (>300 µm). Figure 4b shows the average and maximum radius of condensed droplets at different surface subcooling. As the surface subcooling increases from 0.3 to 3.0 K, the maximum radius of droplets increases from 40 µm to 750 µm and the average radius of droplets on the whole condensing surface increases nearly ten times from ~25 µm to ~220 µm. Corresponding to the droplet size change, droplet departure mode transitions from the coalescence-induced self-jumping to the gravity-induced droplet departure, due to the increase of surface subcooling. The condensing condition-induced droplet wetting transition has not been taken into account by any of existing models in literature,21, 27, 32, 33

which calls for a theoretical study that details the effect of condensing condition on the droplet

wetting transition on nanostructured superhydrophobic surfaces. 3. Discussion Physical Mechanism Governing the Wetting States of Condensed Droplets under Various Condensing Conditions. How does such wetting transition from the mobile CassieBaxter state to pinned Wenzel state occur spontaneously with the increase of surface subcooling? Here, the nucleation theory34 is used to explain the droplet formation in the tapered nanogaps. Condensation starts from the initial nucleation with the formation of nanoscale droplets like clusters. Those clusters that exceed a critical size that is determined by the interfacial and volumetric contributions to the Gibbs free energy will grow further and form the macroscopic liquid phase.34,

35

According to the nucleation theory, larger surface subcooling results in a

smaller energy barrier for droplet nucleation whereas fewer molecules are needed to reach the



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critical size (see Supporting Information S2). Specifically, the critical size36 can be expressed by re = 2Tsatσlv/(Hfgρl∆T). Here, Tsat, Hfg, ∆T, σlv and ρl are the saturation temperature at specified pressure, latent heat, surface subcooling, liquid-vapor surface energy, and liquid density, respectively. As shown in Figure 5a, the critical size varies from a few nanometers at large surface subcooling to more than one hundred nanometers at small surface subcooling. In the meantime, the nucleation site density37 is inversely proportional to the critical size Ns = 0.037/re. Due to the strong dependence of nucleation on the energy barrier, the distribution of nucleated droplets shows obvious difference with the increase of surface subcooling as illustrated in Figure 5b. With the increase of surface subcooling, more nucleated droplets occur but with smaller size. In order to describe the effect of spatial confinement on droplet nucleation on the nanostructured superhydrophobic surface as shown in Figure 1, the wetting states of initial droplet is analyzed by the energy minimization theory.23, 38 The clusters that are larger than the critical nucleation size can grow continuously. Due to the inability to overcome the energy barrier of nucleation, however, the clusters smaller than the critical size may re-evaporate and disappear.34 In a tapered nanostructure as shown in Figure 6a, the cluster will be suspended when it reaches the critical size. Assuming that a nucleated droplet is in equilibrium state (Figure 6b), the relationship between the suspended height H of droplets, intrinsic wetting property of nanosheets (intrinsic contact angle θY), the geometric angle between two nanosheets β, and critical radius re can be expressed by the simple geometric relation (H + re)·sin(β/2) = re·sin(θY π/2). We can further write the suspended height H relevant to droplet immersion as a function of critical size as:   π β  H = re sin  θ Y −  / sin − 1 2 2   

β < 2θ Y − π H ≤ 0, β ≥ 2θ Y − π H > 0,

/ 28Environment ACS Paragon10 Plus

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Assuming an intrinsic water wettability of hydrophobic nanosheet material to be θY = 110°, the suspended height H of nucleated droplets as a function of β and ∆T is plotted (Figure 6c). Considering the size scale of initially nucleated droplets, a few to tens of nanometers, the nanoscale contact angle is essentially equal to the intrinsic contact angle as measured on the smooth hydrophobic surface made of the same materials.39 For a larger angle of tapered nanogaps (β = 60°), the suspended height is negative, which indicates that the nucleated droplet completely immerses in nanogaps. On the contrary, for a smaller tapered angle (β = 20°), nucleated droplets tend to suspend on nanogaps at small surface subcooling. As the surface subcooling increases, however, the suspended height reduces, which suggests that the nucleation position is closer to the bottom of nanogaps. It can be seen that the effect of spatial confinement of tapered nanogaps on droplet nucleation becomes weaker as the critical nucleation size becomes smaller. At large surface subcooling the nucleated droplets tend to form at the bottom of nanogaps, which would maintain as the pinned state in the subsequent growth and result in flooding condensation. The effect of spatial confinement in nanostructures on droplet nucleation as described here provides a reasonable explanation for the droplet wetting transition and condensation modes on superhydrophobic surfaces at various condensing conditions, i.e., surface subcooling. Comparison with Experiments. To validate the proposed effect of spatial confinement on droplet formation on nanostructured superhydrophobic surface, Figure 7 shows the experimental observation of the droplet wetting states in nanogaps at different condensing conditions. The schematics in Figure 7a show the droplet formation and wetting state under different surface subcooling. At small surface subcooling, a droplet forms and suspends in the tapered nanogap. With the increase of subcooling, the critical nucleation size of initial droplet is much smaller than



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the structure scale of nanogaps, leading to the failure of spatial confinement effect. By merging with adjacent droplets in the nanogap, droplets will grow and fill the nanogap from the bottom to top. In Figure 7b, a droplet suspending in the nanogap is observed at the small surface subcooling of 0.2 K. This is consistent with the theoretical analysis above. According to the calculation, the critical size of initial droplet is ~166 nm, which is comparable with the opening scale of hydrophobic nanogaps (~200 nm). As a result, the droplet forms at a position close to the top of nanogaps. However, as the surface subcooling increases to 0.6 K the condensate immerses in the nanogap (Figure 7c). The visualization results in this study have furthered the experimental observation of droplet morphology to near the nucleation stage. We observed that small surface subcooling promotes the formation of suspended droplets due to the large nucleation size while large surface subcooling leads to the immersed droplets with the small nucleation size. Considering the limited scanning frequency and resolution of ESEM in condensation environment, we further use Surface Evolver to predict the morphology of nucleated droplets in nanogaps to explain the surface subcooling-induced wetting transition phenomena (see Supporting Information S3). From the perspective of wetting transition, it is clear that the wetting state of condensed droplets is determined by the coordination of the surface property and condensing condition, 4. Conclusions In summary, the effect of spatial confinement on droplet nucleation is proposed to demonstrate the synergistic coordination of surface properties (contact angle and topography) and the condensing condition on droplet wetting transition and dynamic behavior on nanostructured superhydrophobic surfaces. With both ESEM and optical visualization methods, we systematically show the dynamic evolution of condensed droplets at various growth stages


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and the evidence that initial droplet formation has deterministic effect on droplet wetting. These new insights about spatial confinement effect on droplet behaviors can be used to guide the optimization of structured surfaces for condensation heat transfer enhancement under a broad range of condensing conditions. Furthermore, this work provides new opportunities for wide applications such as use of spatial confinement effect to control the droplet wetting and dynamics to enhance self-cleaning performance, improve anti-icing, and increase thermal diode efficiency.



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METHODS Fabrication of Nanostructured Superhydrophobic Surfaces. The preparation of nanostructured copper oxide surfaces was carried out by combining chemical oxidation with chemical vapor deposition (CVD) as described elsewhere.40 High-purity copper was used for nanostructured surface preparation. The copper block was polished and cleaned for 10 min in an ultrasonic bath. The sample was further rinsed with ethanol and deionized (DI) water. The copper block was then dipped into a 1.0 M hydrochloric acid solution, rinsed with DI water, and dried with the nitrogen gas. The cleaned copper substrate was then immersed into a alkaline solution composed of NaOH, Na3PO4·12H2O, NaClO2 and DI water (5 : 10 : 3.75 : 100 wt. %) at the temperature of 96 ℃ for 20 min. After sufficiently rinsed with DI water and dried with a clean nitrogen gas, the sample was placed in a desiccator. After drawing the vacuum to be less than 2 kPa which promote the volatilization of (1H, 1H, 2H, 2H-perfluorooctyl) silane, a fluorinated silane was deposited from a chemical vapor on the nanostructures for 10 min. The sample was then rinsed with DI water and dried with nitrogen gas. The surface morphology of the nanostructured superhydrophobic surface was characterized using SEM (FEI Quanta 450 SEM). Contact angle goniometer (OCAH200) was used to measure the surface wettability by dispensing a 4 µL water droplet, adding volume to the droplets and sucking the volume of water back. Condensation Experiments in ESEM. Initial nucleation and droplet behavior were imaged using an ESEM (FEI Quanta 200FEG ESEM). The temperature of the sample platform was controlled with a Peltier cooler. In order to reduce the thermal resistance between the cooler and the condensing surface, copper was selected as the sample platform instead of the original sample platform made of stainless steel (see Supporting Information S4). A triangular ridge with


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a tilt angle of 60° was designed on the upper surface of the sample platform. The nanostructured surfaces were directly fabricated on the copper platform. To remove non-condensable gas, the chamber was evacuated to less than 10-4 Pa before the start of condensation experiments. The pressure in the chamber was controlled by the vacuum pumping system. Condensation was achieved by keeping the substrate temperature constant while varying the chamber pressure according to the experimental needs, i.e., controlling the surface subcooling, which results in more uniform droplet growth and coalescence.41 A secondary electron detector was employed for imaging of droplet dynamics. To minimize the parasitic heating effect of electron beams and to ensure the image quality, different combinations of electron beam energies (10 - 20 keV) and image capture frequencies were used for capturing condensed droplets with different sizes. 42 Optical Imaging Procedure. Condensation experiments were carried out using a custommade chamber where the condensing condition can be precisely controlled and adjusted in a board range (see Supporting Information S4). A cylindrical high purity copper block, 13 mm in diameter and 22 mm in length, was thermally insulated. The condensing surface was oriented vertically and DI water was used to produce the vapor. The pressure of the chamber was measured by a pressure sensor with the accuracy of 0.1 kPa and a McLeod gauge with the accuracy of 0.1 Pa at low pressure. The temperature distribution in the copper block was measured by T-type thermocouples embedded to obtain the wall temperature Tw. The uncertainty of the temperature measurement was ± 0.1 K. All the thermocouples in condensation experiments were calibrated with a standard platinum resistance thermometer. The large-field of view on the droplet dynamic behavior was captured by a high-speed camera (PHOTRON, FASTCAM APX-RS). The test water was degassed by repeatedly heating the water and



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removing the accumulated non-condensable gas in the chamber. The pressure and temperature of steam were monitored throughout the condensation experiments. Supporting Information Verification of wetting states of droplets formed at various condensing conditions; detailed theoretical analysis on the effect of condensing condition on droplet nucleation; modeling of the Surface Evolver simulation; experimental setup in ESEM and optical imaging; four videos showing the wetting transition of condensed droplets at different condensing conditions. Corresponding Author Corresponding E-mail: [email protected] Author Contributions Xuehu Ma and Rongfu Wen conceived and designed the research. Xuehu Ma and Zhong Lan supervised the research. Rongfu Wen, Benli Peng, and Wei Xu carried out the surface fabrication and condensation experiments. Rongfu Wen carried out the ESEM observation and Surface Evolver simulation. Rongfu Wen, Zhong Lan, Benli Peng, and Wei Xu analyzed the data. Rongfu Wen, Xuehu Ma, and Ronggui Yang wrote the manuscript. All authors approved the manuscript. Conflict of Interest The authors declare no competing financial interest. Acknowledgement We gratefully acknowledge financial support from the National Natural Science Foundation of China under Grants No. 51236002 and No. 51476018.


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Figure 1. Surface topography and wettability of a nanostructured superhydrophobic surface. (a) Diagrams illustrating the surface topography: w ≈ 200-300 nm, h ≈ 1 µm. (b) SEM image of the nanostructured superhydrophobic surface. The inset shows the surface wettability with the corresponding goniometer image of a 4 µL water droplet on the surface. Large-magnification SEM images of tapered nanostructures from both (c) cross-section and (d) top view. (e) ESEM image of condensed droplets on the surface. Conditions: Pv = 622 Pa and Tw = 273.15 K.



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Figure 2.

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Droplet wetting states and dynamic behaviors at different surface subcooling.

Schematic drawings of the growth and coalescence of droplets in the Cassie-Baxter state (a) and Wenzel state (b). (c, e) Dynamic growth of a condensed droplet. Conditions: (c) Pv = 622 Pa, Tw = 273.15 K and (e) Pv = 675 Pa, Tw = 273.15 K. (d) Coalescence-induced droplet jumping and (f) coalesced droplets pinning on the surface without jumping. Conditions: (d) Pv = 623 Pa, Tw = 273.15 K and (f) Pv = 675 Pa, Tw = 273.15 K. The dashed red and blue circles indicate droplets before and after coalescence, respectively.


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Figure 3. Dependence of droplet dynamic behaviors and condensation modes on the surface subcooling. (a-d) Schematic illustrating droplet growth under various condensing condition. Time-lapse images of condensation at the surface subcooling of: (e) 0.3 K, (f) 0.5 K, (g) 0.8 K, and (h) 3.0 K. The red and yellow dashed circles in (e-g) indicate the droplets before and after coalescence, respectively. The white arrows in (e-f) show the track of droplet jumping. The red and yellow dashed lines in (h) indicate the pinned contact line of falling droplet and the irregular shape of small droplets, respectively.



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Figure 4. Droplet size distribution on the nanostructured superhydrophobic surface. (a) Effect of surface subcooling on the distribution of microdroplets. (b) The average and maximum droplet radius on the condensing surface under different surface subcooling.


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Figure 5.

Effect of condensing condition on droplet nucleation. (a) Nucleation size and

nucleation site density as a function of surface subcooling. (b) Schematics of droplet nucleation at various surface subcooling.



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Figure 6.

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Spatial confinement effect of tapered nanogaps on droplet nucleation assuming

intrinsic contact angle of nanosheet material to be θY = 110°. (a) Schematic of droplet nucleation in nanogap. (b) Illustration of relationship between geometric parameters with the intrinsic contact angle of a cluster (droplet) reaching the critical nucleation size. (c) The suspended height H as a function of surface subcooling and nanogap angles.


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Figure 7. Droplet wetting states in the tapered nanogaps. (a) Schematic illustrating droplet nucleation in nanogaps as a function of surface subcooling. The angle of opening of nanostructure is ~35°. (b) Suspending droplet in the nanogap. Conditions: Pv = 620 Pa and Tw = 273.15 K, ∆T = 0.2 K; (c) Immersing droplet in the nanogap. Conditions: Pv = 640 Pa and Tw = 273.15 K, ∆T = 0.6 K.



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Table of Contents Graphic


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Wetting Transition of Condensed Droplets on Nanostructured

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