Enhanced Coalescence-Induced Droplet-Jumping on Nanostructured

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Enhanced Coalescence-Induced Droplet-Jumping on Nanostructured Superhydrophobic Surfaces in the absence of Microstructures Peng Zhang, Yota Maeda, Fengyong Lv, Yasuyuki Takata, and Daniel Orejon ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.7b09681 • Publication Date (Web): 19 Sep 2017 Downloaded from http://pubs.acs.org on September 21, 2017

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ACS Applied Materials & Interfaces

Enhanced Coalescence-Induced DropletJumping on Nanostructured Superhydrophobic Surfaces in the absence of Microstructures Peng Zhang1†, Yota Maeda2, Fengyong Lv1, Yasuyuki Takata2,3, Daniel Orejon,2,3* 1

Institute of Refrigeration and Cryogenics, MOE Key Laboratory for Power Machinery and Engineering, Shanghai Jiao Tong University, Shanghai 200240, China 2

Department of Mechanical Engineering, Thermofluid Physics Laboratory, Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan

3

International Institute for Carbon-Neutral Energy Research (WPI-I2CNER), Kyushu University, 744 Motooka, Nishi-ku, Fukuoka 819-0395, Japan

†

[email protected]

* [email protected]

KEYWORDS:

dropwise

condensation,

coalescence-induced

droplet-jumping,

nanostructured superhydrophobic surfaces, microstructure density, angular deviation, surface engineering 1 ACS Paragon Plus Environment


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ABSTRACT Superhydrophobic surfaces are receiving increasing attention due to the enhanced condensation heat transfer, self-cleaning and anti-icing properties by easing droplet selfremoval. Despite the extensive research carried out in this topic, the presence or absence of microstructures on droplet adhesion during condensation has not been fully addressed yet. In this work we, therefore, study the condensation behavior on engineered superhydrophobic copper oxide surfaces with different structural finishes. More specifically, we investigate the coalescence-induced droplet-jumping performance on superhydrophobic surfaces with structures varying from the micro- to the nano-scale. The different structural roughness is possible due to the specific etching parameters adopted during the facile low-cost dual-scale fabrication process. A custom-built optical microscopy setup inside a temperature and relative humidity controlled environmental chamber was used for the experimental observations. By varying the structural roughness, from the micro- to the nano-scale, important differences on the number of droplets involved in the jumps, on the frequency of the jumps and on the size distribution of the jumping droplets were found. In the absence of microstructures, we report an enhancement of the droplet-jumping performance of small droplets with sizes in the same order of magnitude as the microstructures. Microstructures induce further droplet adhesion, act as a structural barrier for the coalescence between droplets growing on the same microstructure and causes the droplet angular deviation from the main surface normal. As a consequence, upon coalescence, there is a decrease in the net momentum in the out-of-plane direction and the jump does not ensue. We demonstrate that the absence of micro-structures has therefore a positive impact on the coalescence-induced droplet-jumping of micrometer droplets for anti-fogging, anti-icing and condensation heat transfer applications. 2 ACS Paragon Plus Environment

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INTRODUCTION The occurrence and morphology of the condensate during heterogeneous condensation is a direct consequence of the wettability and structure of the substrate, as well as of the nature of the fluid and of the surroundings1-10. The two main condensation mechanisms are filmwise condensation (FWC) and dropwise condensation (DWC) typically observed on a hydrophilic and on a hydrophobic or superhydrophobic surface (SHS), respectively. In the past decades, DWC has received increasing attention due to enhanced heat transfer performance when compared to FWC11-15. The greater performance reported in the case of DWC is attributed to the low adhesion between the condensate and the surface allowing for efficient and continuous shedding of the condensate and consequently offering new vacant surface area for droplet re-nucleation and growth15-17. In contrast, in the case of FWC, the condensate film covering the surface remarkably reduces the number of the condensation nucleation sites, and it also acts as an additional resistance lowering the heat transfer performance. More recently, a simultaneous DWC and FWC condensation mechanism with intermediate heat transfer performance between DWC and FWC was demonstrated by making use of microstructures on a completely hydrophilic configuration18. Aiming for continuous DWC, SHSs have been reported to provide with excellent selfcleaning19-21, anti-icing22-23 and condensation properties24-26. On SHSs droplets are found to shed off either by gravity or by a phenomenon termed coalescence-induced dropletjumping27-28. When two or more droplets coalesce, there is a decrease in the total liquid-vapor surface area, i.e. there is an excess in the total surface energy, which is then transformed into kinetic energy inducing the jump of the coalesced droplet29-31. Recent experimental and theoretical studies have focused on the physical mechanisms governing coalescence-induced droplet jumping and their potential applications32-37.

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Important research efforts have been devoted to address the effect of structure underneath a condensing droplet by taking a closer look into the size and the arrangement of the nanostructures, and to the thickness and nature of the hydrophobic coatings4, 9, 36, 38-44. Feng et al. reported an increase in the number of spontaneous droplet motion events by decreasing the spacing between chemically grown vertical nanoribbons

38

. Vertical and long nanoribbons

were found to have lower energy of adhesion between the condensate and the surface when compared to short and tilted ones. From the surface energy perspective, He et al. related the condensate work of adhesion to the droplet self-removal ability on hierarchically nano-porous aluminum surfaces39. Aiming for a more complete description DWC dynamics on SHSs, Li et al. developed a more detailed droplet growth model that takes into account the presence of irregular nanostructures underneath the condensate41. This model is based on a force balance at the edge of the nanostructures previously proposed by Enright et al.41, 45. From these works, viscous dissipation and adhesion of the condensate to the surface were reported to be the main factors hindering droplet jumping, which in turn dictate the minimum droplet size required for the jumping. By using thermally grown carbon nanotubes Cha et al. showed that contrary to previous works, viscous dissipation does not limit the minimum droplet departure size previously reported, and that droplet-surface adhesion does46. Using the ultra-low adhesion nanotubes, Cha et al. were able to decrease the minimum jumping droplets diameters to the order of hundreds of nanometers46. More recently, Mulroe et al. reported a systematic

study

of

condensation

and

coalescence-induced

droplet-jumping

on

nanostructured surfaces with remarkable controlled geometry44. In their work, they propose rational guidelines for the design of nanostructured surfaces that can enable the jump of droplets in the micrometer range. In addition to the aforementioned works, dual-scale roughness, i.e. micro- and nanoroughness, has also been reported to provide great water repellence properties and excellent dropwise condensation performance36,

47-51

. Rykaczewski et al. studied the effect of 4

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microstructure spacing on the dynamics of DWC on hierarchical truncated microcones SHSs. They found an optimal spacing that maximizes the occurrence of droplet departure40. More recently, the presence of microstructures on SHSs has been found to induce in-plane selfpropulsion of droplets

52-55

. The self-propulsion of droplets in a direction parallel to the

surface was proposed and supported by experimental observations to enhance droplet sweeping removal of the condensate52-53. On a similar hierarchical SHS, Chen et al. reported a 4 times increase in the cumulative droplet volume departure by either droplet shedding or droplet-jumping, when compared to the one-tier nanorough one48. On such hierarchical surfaces, the same authors found that the jumping speed was independent of the number of coalescing droplets42. This, however, is opposite to the findings of reported by Kim et al. on one-tier nano-structured SHSs, where greater jumping velocities were reported in the case of multidroplet jumping56. When comparing the droplet-jumping behavior on surfaces with different tiers and roughness clear differences upon the introduction of microstructures on a SHS configuration arise. In addition, to these works, Ölçeroğlu and McCarthy proposed the use of hierarchical SHSs with superhydrophilic tops to induce heterogeneous nucleation aiming for the fine control of the droplet jumping departure diameter36. They found a minimum pitch between the microstructures at which the droplet-jumping diameter was kept within tens of microns. The delay in surface flooding at high subcooling conditions was reported on such surfaces. Despite the extensive research carried out on SHSs, there is still a lack of understanding of the coupled effects of micro- and nano-structures on coalescence-induced droplet-jumping performance. Most recent works report the enhancement of the spontaneous droplet motion; however, these works do not differentiate between the potential reasons behind droplet shedding or droplet jumping performance38, 40, 48, 55. Chen et al. developed a theoretical model to account for the interactions between big droplets and microstructures, i.e. composite state, however the model over-predicted the jumping speeds obtained by depth-of-defocus image 5 ACS Paragon Plus Environment


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processing42. In addition, the model does not account for the lower number of jumping droplets with sizes in the same order of magnitude as the microstructures reported in our study. In the present work we found that the absence of microstructures has a positive impact on the droplet-jumping performance of small droplets. We propose that in the case of small droplets, besides the greater adhesion to the surface introduced by the microstructures, droplets growing at the side of the microstructures display an angular deviation from the normal to the main surface. Upon coalescence, energy released in the out-of-plane direction is not enough to overcome the adhesion and the droplets will remain on the substrate rather than jumping. In addition, the three-dimensionality of the microstructured bumps hinders the coalescence of small droplets sitting on opposite sides of the microstructures. As a consequence, in the presence of microstructures, the number of jumping events is decreased and the size distribution of the jumping droplets shifts towards greater diameters, which will have a strong impact on the heat transfer performance of small jumping droplets and on antiicing and anti-fogging applications15-16.


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RESULTS We study the droplet-jumping performance on surfaces with three different structural finish named SMN (high density and big size of microstructures), SmN (low density and small size of the microstructures) and SN (absence of microstructures). Scanning Electron Microscopy (SEM) and 3D Laser Scanning Microscopy of the three surfaces are presented in Figure 1 (See Experimental Procedure for more details on the fabrication and characterization procedure of the three surfaces).

Figure 1 – SEM with a tilt angle of 45° for (a) SMN, (b) SmN and (c) SN (scale bar is 30 µm). Insights of figures show enlarged image of the nanostructures at the microstructures tops (scale bar is 1 µm). 3D Laser Scanning Microscopy for (d) SMN, (e) SmN, and (f) SN of an area of 256 × 256 µm2. Color scale bar represent the height of the features between (purple) 0 µm to (red) 30 µm. Additional SEM images at different magnifications and 3D Laser Scanning Microscopy profiles for all three surfaces studied can be found in the accompanying Supporting Information (Figure SI.1 and Figure SI.2).

From SEM and 3D Laser Scanning Microscopy images presented in Figure 1, the presence of two-tier roughness on SMN (Figure 1a&d) and SmN (Figure 1b&e) when compared to the one-tier roughness on SN (Figure 1c&f) is evident. The presence of microstructures reported for SMN and for SmN are the consequence of the additional etching step during fabrication. Bigger and greater density of microstructures were grown by higher temperature and longer etching times in the case of SMN (Figure 1d) when compared to SmN (Figure 1e) (see 7 ACS Paragon Plus Environment


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Experimental Procedure and accompanying Supporting Information for more details on surface fabrication and surface characterization). When looking into the SEM images, SMN (Figure 1a) and SmN (Figure 1b) show clusters of flower/bump-like microstructures in the order of tens of microns. No such microstructures are observed in the case of SN (Figure 1c). The same procedure followed to grow the oxide nano-blades on all three samples showed no appreciable differences in the shape, the geometry or the size of the nano-structures (insights of Figure 1a,b & c)57-58. The etching and oxide growth procedure adopted here provides lowcost and facile scalability for the fabrication of two-tier superhydrophobic surfaces57-59. Furthermore, macroscopic contact angle measurements and experimental observations of condensation by optical microscopy carried out in different areas of the surface did not show appreciable differences on either the advancing contact angles or the droplet shape/morphology of the condensing droplets. The surface topography and the sample roughness were measured using a LEXT OLS4000 3D Laser Scanning Microscope from Olympus (Japan). The root mean square average surface roughness, SRMS, and the distance between the maximum peak height and the minimum depth valley, Sz, extracted by 3D Laser Scanning Microscopy are included in Table 1. The mean squared average surface roughness reported for SN was 400 nanometers (Table I), henceforth we refer to SN as the one-tier nano-rough sample. In addition, Table I includes the average advancing contact angle measured up to six times in an optical contact angle goniometer (OCA-20, Data Physics Instruments GmbH, Germany). The solid fraction was also calculated for each of the substrates using the Cassie-Baxter equation60-61:

f = (cosθa +1) / (cosθaflat +1) , where θa is the advancing contact angle of a droplet on the SHS and θaflat is the advancing contact angle on flat surface with the same the hydrophobic coating and equals 115° ± 3°. Table I includes surface roughness, maximum height of the microstructures, solid fraction, and advancing contact angles, for SMN, SmN and SN: 8 ACS Paragon Plus Environment

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Table I - Substrate characterization SMN

SmN

SN

2.79 1.06 0.40 SRMS (μm) 17.86 10.66 1.58 Sz (μm) 0.128 0.122 0.115 Solid faction, f 157° ± 3° 158° ± 3° 159° ± 3° Advancing Contact Angle, θa SRMS (µm): substrate roughness, Sz (µm): distance between the maximum peak height and the maximum valley depth, f: solid faction and θa: advancing contact angle.

Next, we present optical microscopy experimental observations recorded using a CCD camera equipped with a high-resolution zoom lens (Keyence VH-Z500R). The temperature and the relative humidity inside the chamber were set as 30 °C ± 2 °C and 90% ± 5%, respectively. Temperature of the Peltier stage was kept at 10 °C during the experimental observations providing supersaturation conditions of approximately S = 3.1 ± 0.2. Figure 2ad, Figure 2e-hand Figure 2i-l present snapshots taken by optical microscopy at different condensations times on sample SMN, SmN and SN:

Figure 2 – Optical microscopy snapshots during condensation on (top) SMN at (a) t = 0, (b) t = 216, (c) t = 218 and (d) t = 1800 seconds, (middle) SmN at (e) t=0, (f) t = 252, (g) t = 254 and (h) t = 1800 seconds, and (bottom) SN at (i) t = 0, (j) t = 254, (k) t = 256 and (l) t = 1800 seconds. With t=0 seconds as the first jump observed. Field view is 305 × 228 µm2 and scale bar is 100 µm. False color was applied to snapshot (b), (f) and (j) to readily identify the coalescing droplets being involved in the jumps. Dashed red circles in snapshot (c), (g) and (k) shows the new vacant area for droplet re-nucleation. 9 ACS Paragon Plus Environment


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As condensation developed, droplets grew bigger and began coalescing. After droplet coalescence, newly merged droplets either remained on the substrate or jumped away from the surface as a consequence of the excess in surface energy released upon coalescence27-28, 30

. We note here that in the case of hydrophobic smooth surfaces droplets only shed off by

gravity. Figures 2a, 2e and 2i represent the frame at which the first coalescence-induced droplet-jumping event took place. Figure 2b&c, Figure 2f&g and Figure 2j&k show representative droplet jumping events on SMN, SmN and SN, respectively. False color was applied to readily identify the droplets involved in the jump. Finally, Figures 2d, 2h and 2l show representative snapshots after 30 minutes on SMN, SmN and SN. From the experimental observations, differences on the droplet jumping performance were identified when comparing the different substrates studied. In the case of SN (Figure 2j), less number as well as smaller sizes of the coalescing droplets were required for the jump to ensue when compared to SMN (Figure 2b) and to SmN (Figure 2f). The complete condensation behavior on SMN, SmN and SN is included in Movie SI.1 (SMN), Movie SI.2 (SmN), and Movie SI.3 (SN). To address the droplet-jumping performance on the three different surfaces, the size distribution and the cumulative size distribution of all the coalescing-jumping droplets (premerged droplets) involved in the jumps as number of coalescing-jumping droplets versus droplet diameter, Di (µm), over a period of 30 minutes are represented in Figure 3a. The size of each of the coalescing-jumping droplets before the jump Di were manually measured using ImageJ62. In addition, the size distribution and the cumulative size distribution of the jumping-droplets (merged droplets) versus jumping droplet diameter, Dj (µm), are included in Figure 3b. Dj was calculated by adding the volume of each coalescing-jumping droplet, i,


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before the jump, Vi , of the N coalescing-jumping droplets involved in each of the jumps, j, 1/3

N   as D j =  6 π ∑ Vi  i =1  

. The volume of each coalescing-jumping droplet before the jump was

calculated as Vi = 1 Ri 2 (3 hi − Ri ) , where hi is the droplet height and hi = Ri − Ri cosθa , and 3

Ri is the coalescing-jumping droplet radius equaling Ri =Di /2. We note here that droplets coalescing with other droplets outside of the field of view were discarded from the experimental results.

Figure 3 – (a) Size distribution and cumulative size distribution in intervals of 1.2 µm as the number of coalescing-jumping droplets (pre-merged droplets) (pre-merged droplets) versus coalescing-jumping droplet diameter, Di (µm). (b) Size distribution and cumulative size distribution in intervals of 1.2 µm as the number of jumping droplets (merged droplet) versus jumping droplet diameter, Dj (µm), on (blue-squares) SMN, (green-triangles) SmN, and (red-circles) SN, over an area of 305 × 228 µm2 (1000× magnification) and for a period of 30 minutes. Gaussian fit is included for comparison.

From Figure 3a, clear differences in the size distribution and on the number of coalescingjumping droplets are evident when comparing the three samples. On one hand, when comparing the two-tier roughness samples, i.e. SMN versus SmN, greater number of droplets with Di smaller than 25 µm are able to coalesce and jump in the case of SmN when compared to SMN. Up to 40% more droplets with D i between 7 µm and 15 µm are removed from SmN by coalescence-induced droplet-jumping. There is an appreciable shift of the droplet size distribution towards smaller Di in the case of SmN. On the other hand, when comparing 11 ACS Paragon Plus Environment


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SmN to SN, the number of coalescing-jumping droplets with Di between 10 to 20 µm is 20% to 40% greater for SN. As we move towards bigger Di (between 25 µm and 35 µm), the number of droplets approach to each other. For Di greater than 35 µm, the number of coalescing-jumping droplets is greater for SMN. We emphasize here the greater number as well as the smaller nature size of the coalescing-jumping droplets on one-tier SN when compared to the two-tier SMN and SmN. When comparing the merged jumping droplets, Figure 3b shows similar trends to those previously reported for Figure 3a. SmN and SN show greater number of jumping droplets with Dj smaller than 25 µm when compared to SMN. When comparing Dj from 7 µm to 20 µm, up to 2 to 5-fold increase in the number of jumping events are reported for SmN when compared to SMN and up to 8-fold increase in the case of SN with respect to SMN. The total number of jumping events is greater with decreasing the size and density of the microstructures. Differences observed when comparing the cumulative number of coalescingjumping droplets (Figure 3a) and the number of jumping events (Figure 3b) are a direct consequence of the number of droplets involved in each of the jumping events. Presumably, due to a greater adhesion of the droplets in the presence of microstructures as it will be further discussed. To evaluate differences observed in the droplet-jumping performance on the different substrates, Figure 4 shows the percentage of the number of coalescing-jumping droplets involved in the jumping events every 4 minutes. For simplicity, we group into 2 to 4 (diagonal yellow pattern), 5 to 9 (diagonal checker blue pattern) and 10 or more (checker red pattern) droplets coalescing per jump on SMN (Figure 4a), SmN (Figure 4b) and SN (Figure 4c). In addition, the droplet nucleation density and the average droplet diameter versus time are also presented in Figure 4d.


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Figure 4– Columns show the percentage of jumping events involving (diagonal pattern) 2-4 droplets, (diagonal checker board) 5-9 droplets, and (checker board) 10 or more droplets, in intervals of 4 minutes on (a) SMN, (b) SmN and (c) SN. (d) Droplet density (number of drops/m2) and average droplet diameter (µm) at time intervals of 4 minutes with t = 0 as the first jump. Over an area of 305 × 228 µm2 (1000× magnification) and for a period of 30 minutes. Error bars represent the standard deviation of the average droplet diameter. From Figure 4, the number of coalescing-jumping droplets required for the jump to ensue is greater in the case of SMN. On the other hand, on SmN (Figure 4b) and SN (Figure 4c) more than 80% of the jumps reported require 4 or less droplets, whereas on SMN (Figure 4a) this percentage falls below 60%. In addition, the number of jumps involving 10 or more coalescing-jumping droplets is limited to one or two events in the case of SmN and SN. When comparing the intermediate case, i.e. 5-9 droplets, SmN and SN also present considerably lower percentage of jumping events when compared to SMN. It is clear that SmN and SN require less number of coalescing-jumping droplets for the jump to ensue, which is a direct consequence of the absence of microstructures. When looking at Figure 4d, greater droplet density is reported for SMN when compared to SmN and SN for any of the representative times analyzed. The greater droplet density as well as the bigger size of the droplets reported in the case of SMN, i.e., greater surface coverage, 13 ACS Paragon Plus Environment


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suggests the greater probability for droplet coalescence in the presence of microstructures. For SMN and SmN, the monotonic reduction in the droplet density coupled with the increase in the average droplet diameter, reveals the lack of condensation shedding. On the other hand, in the case of one-tier nanorough sample SNSN, the average droplet diameter is kept between 15 to 20 µm with constant droplet density over the times analyzed. This latter supports the coalescence-induced droplet-jumping ability of SN.. In the presence of microstructures,. the total number of coalescing-jumping droplets required for the jump to ensue (Figure 3a) compared to the total number of jumps (Figure 3b)

reveals the need for multidroplet

coalescence56. The need for multidroplet coalescence in the case of SMN implies that greater excess of surface energy is required to overcome the adhesion between the condensate and the surface when compared to SmN and to SN. Table II summarizes the most relevant data extracted from both Figure 3 and Figure 4, which will be used to support our discussion.

Table II – Data summary SMN (SRMS = 2.79 μm)

SmN (SRMS = 1.06 μm)

SN (SRMS = 0.40 μm)

Jumping events/m2/s

( 2.0 ± 0.1 ) x 106

( 4.2 ± 0.1 ) x 106

( 5.3 ± 0.1 ) x 106

Average Number of Drops/Jump/m2

( 4.6 ± 2.9 ) x 106

( 2.9 ± 1.2 ) x 106

( 3.1 ± 1.2 ) x 106

Average Droplet Diameter (µm)

20.8 ± 10.9

18.9 ± 9.2

18.3 ± 7.1

Maximum Droplet Diameter (µm)

165.3 ± 10.9

140.6 ± 16.6

75.3 ± 7.1

Minimum Droplet Diameter (µm)

10.0 ± 2.0

8.8 ± 2.0

8.3 ± 2.0

Number of jumps/m2/second, average of number of droplets/jump/m2, average droplet diameter (µm), maximum and minimum droplet diameters (µm) for SMN, SmN and SN. From Table II, differences on the jumping frequency, the number of droplets per jump, the average and the maximum and minimum droplet diameters, are evident when comparing the three samples. The one-tier nanorough sample (SN) presents the highest droplet jumping frequency, which is 2.5-fold greater than that of the roughest sample (SMN). The average number of coalescing droplets was also found to increase in the presence of microstructures and when increasing the microstructure density. In addition, important differences are 14 ACS Paragon Plus Environment

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observed when comparing the average droplet diameter and the maximum and minimum droplet diameters. The average diameter of the coalescing droplets is 25% smaller in the case of SmN and SN when compared to SMN. Furthermore, on SN the maximum coalescing droplet diameter observed is half of the one reported on the two-tier rough samples SMN and SmN. From the experimental results presented from Figure 2 to Figure 4 and in Table II, it is clear that the presence of microstructures clearly influences the droplet jumping performance. Next we discuss the different coalescence mechanisms observed in our experiments. In addition, we provide an ener,gy analysis to support the enhanced droplet-jumping reported in the absence of micro-structures.



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DISCUSSION Upon coalescence, the following mechanisms already reported in literature were observed in our experiments: mobile coalescence (Figure 5a)40 and/or droplet sweeping (Figure 5b)5253

, which can bring the new merged droplet to a lower adhesion state (Figure 5c)63-65 or

induce the self-propulsion of droplets (Figure 5b)52-54, and/or the jump of the droplet (Figure 5d)27-28. On the other hand, due to the high adhesion between the condensate and the surface immobile coalescence was also observed

(Figure 5e)27,

40

. Furthermore, immobile

coalescence upon the coalescence between a droplet growing at side of a microstructure with a droplet growing at the bottom of the substrate was observed (Figure 5f). In addition to these latter mechanisms, the presence of a microstructure induces the droplet growth in opposite directions hindering the coalescence between droplets in the same order of size as the microstructures (Figure 5g).

Figure 5 – Schematic and optical microscopy snapshots of coalescence at 1000x as: (a) mobile coalescence (b) droplet sweeping, (c) coalescence to a lower energy adhesion state, (d) droplet jumping and (e) immobile coalescence. Observations by optical microscopy at 2000x of small droplets growing and coalescing on the sides of microstructures as: (f) immobile coalescence and (g) no coalescence of droplet growing in opposite directions. Red arrows show the vector normal to the main surface or to the microstructure surface for each droplet. Red false color was applied to identify the droplets involved in the coalescence and blue false color for the new coalesced droplet. 16 ACS Paragon Plus Environment

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Time between frames is 2 seconds. Time between snapshots (c) and (d) is 30 seconds. In (f) time between frames is 25 seconds and dashed circles represent the size of the droplets after 25 seconds, suggesting that in the absence of the microstructure, coalescence should take place. Besides common droplet contact line pinning, we found that in the presence of microstructures, jumping of droplets with sizes smaller than 20 µm is lower when compared to the one-tier nanorough sample (Figure 3b). If the energy released is high enough to overcome the energy of adhesion but not sufficient to ensure the jump, the coalesced droplet will move and sit in a different location as in Mode A (Figure 5a)40. On the other hand, if the energy of adhesion is very high the new coalesced droplet will remain at the same position as in Mode E (Figure 5e)27, 40. In the case of droplets sitting between microstructures, typically, an additional coalescence event is required in order to bring the droplet into a lower energy of adhesion state before the jump takes place as in Mode C (Figure 5c). This additional coalescence event was also reported in the case of spontaneous navigation of condensing droplets on randomly structured textured surfaces and on clustered ribbed nanoneedle structures64-65. Last, if the energy released upon coalescence is great enough to overcome the energy of adhesion, droplet-jumping (Figure 5d) will occur as represented in Mode B and Mode D, respectively. The presence of microstructures prompts coalescing events in Mode A, Mode B, Mode C and Mode E rather than jumping (Mode D). In addition, when looking closer to the growth of droplets in the vicinity of the microstructures (2000x magnification), we present additional experimental observations supporting the reduction in jumping events of small droplets with smaller or with similar sizes as the microstructures. Droplets sitting at the sides of the microstructures grow and eventually coalesce with other droplets sitting at the bottom of the surface as in Mode F (Figure 5f). Upon coalescence, the energy released in the out-of-plane direction is not enough to overcome the energy of adhesion. Last, the three-dimensionality of the microstructures act as structural barriers for the coalescence of droplets growing on the sides of the same 17 ACS Paragon Plus Environment


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microstructures as in Mode G (Figure 5g). Droplets sitting on the microstructures, are only able to grow in a direction normal to the microstructure surface. As a consequence, these droplets are not able to coalesce with each other reducing the number of jumps of jumping droplets with similar size as the microstructures. Dashed circles in Figure 5g show that in the absence of the microstructure, droplets would have coalesced with each other. When looking into all coalescing events taking place our experimental observations, up to 20% more coalescing events are reported in the case of the two-tier roughness sample SMN when compared to SN (see Droplet Coalescence Statistics in Table SI.I within the accompanying Supporting Information). The greater number of coalescing events (Table SI.I) and the greater droplet density (Figure 4d) reported on SMN is attributed to the larger surface area available for nucleation, growth and coalescence induced by the microstructures, which is consistent with the literature48, 55. Despite the greater number of coalescing events on SMN, the average number of coalescing droplets was found to be 2.6 ± 1.1 and 2.3 ± 0.7 on SMN and SN, respectively. We must note here that the hereby reported multi-droplet coalescence reported in the presence of microstructures is a consequence of the additional excess of surface energy required for the jump to ensue and not to an enhancement of multidroplet coalescence events induced by the presence of microstructures. We also report here, up to 2 times greater number of self-propelled sweeping droplets and sweeping events in the presence of microstructures, which is consistent with the literature (see Table SI.I)52-53. However, such increase in the number of sweeping events does not account for the reduction in coalescence-induced droplet-jumping events. We also rule out droplet mismatch, as the reason for the differences on the droplet-jumping events reported when comparing the three samples. The maximum droplet mismatch ratio for two coalescing droplets before the jump was found to be similar in all cases: 1.74 for SMN, 2.01 for SmN and 1.73 for SN. Droplet coalescence analysis reported above evidences that the lower number of jumping events of small droplets in the case of SMN is a direct consequence of the greater number of 18 ACS Paragon Plus Environment

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immobile coalescing events taking place in Mode A and Mode F, while Mode G also reduces the number of coalescence events between droplets with sizes of tens of microns. Since we are unable to accurately quantify the different coalescence mechanisms proposed due to the limitations of our experimental setup, we will base our analysis on the evidences retrieved from the coalescing-jumping droplets before the jump37, 42, 66. Next, we calculate the rate energy of adhesion to excess of surface energy upon coalescence,

E

adh, j

/ ∆E

36 surf , j

for each of the jumping events. On a nanostructured

superhydrophobic surface without microstructures we calculate the energy of adhesion of all the droplets involved in each of the jumps from surface energy principles,

E adh , j

, as:

N

E adh − Cassie , j = π f γ lg sin 2 θ a (1 + cos θ aflat ) ∑ Ri 2

(1)

i =1

where γ lg is the solid-gas surface tension and i represents each of the N individual droplets involved in each of the j jumps. However, upon coalescence, the interface of the droplet will compress against the surface increasing work of adhesion42. To account for the increase in the liquid-solid area of the new merged droplet, we estimate the new area of contact as the sum N

of the area covered by all the droplets involved in the jump ( π ∑Ri ) rather than using the 2

i =1

N

2 2 solid-liquid interfacial area of the pre-merged droplets, ( π sin θa ∑ Ri ), which would i =1

actually underestimate the energy of adhesion. The excess of surface energy upon coalescence for each jump, ∆ E s u r f , j , is given by: N

N

i=1

i =1

∆Esurf , j = ∑Ecoalescing,i − Ejumping, j − ∑Eadh,i

(2)

with E coa lescing , i as the surface energy of each individual droplet before coalescing, E

ju m p in g , j

the final surface energy of the coalesced droplet, and E a d h , i is the energy of



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adhesion to the surface for each droplet. In Equation 2 we neglect viscous dissipation46. E

ju m p in g , j

can be obtained as:

Ejumping, j =π Dj2γlg On the other hand, Ecoalescing ,i =

E co a lescin g , i

2π rb ,i 2 1 + cos θ a

(3) is calculated as in the work of Chen et al.42, 67 as:

γ lg + π rb ,i 2 (1 − f )γ lg + π rb ,i 2 f γ s l + π rb ,i 2 ( rn − f )γ sg

(4)

where rb is the base radius as rb,i = Ri sinθa , and f is the solid fraction included in Table 1. γ sg

and γ sl are the solid-gas and liquid-gas surface tension and the solid-liquid surface

tension. By establishing a force balance at the triple contact line as proposed by Young, the flat solid-liquid surface tension can also be expressed as: γ sl = (γ sg −γ lg cosθa ) 68-69.

To account for the reduction in droplet surface energy due to the additional energy of adhesion exerted by the presence of microstructures, Chen et al. defined two different droplet-surface interactions depending on the size of the condensing droplets42. For big droplets sitting between the microstructures, a composite state where droplets are in contact with the nanostructures at the sides of the microstructure was defined. On the other hand, small droplets only interact with the nanostructures as in a Cassie-Baxter state42. As a consequence, the energy of adhesion and the surface energy of the coalescing droplet before the jump will differ depending on the presence or absence of microstructures. More details on the energy analysis in the presence of microstructures can be found in the Energy Analysis included within the accompanying Supporting Information. Then the percentage of excess of surface energy required to overcome the energy of adhesion for the jump to ensue on the three different surfaces can be calculated. Depending on the number of coalescing-jumping droplets involved in the jump, we averaged the percentage of excess of surface energy,


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Eadh, j / ∆Esurf , j , which is represented in Figure 6 (accompanying Supporting Information Figure SI.3).

Figure 6 – Average of the percentage of excess of surface energy required to overcome the adhesion, Eadh, j / ∆Esurf , j , versus the number of coalescing-jumping droplets, N, for (blue-squares) SMN, (green-triangles) SmN, and (red-circles) SN, over a period of 30 minutes. Power fitting is included for comparison. Error bars represent the standard deviation.

The ratio Eadh, j / ∆Esurf , j is inversely proportional to the number of coalescing-jumping droplets. This is consistent with results reported by other authors where greater number of droplets provide higher excess of surface energy42, 56. In addition, Figure 6 clearly indicates the greater excess of surface energy required to overcome the energy of adhesion in the presence of microstructures for any number of coalescing-jumping droplets. When comparing SMN and SN, up to 2-fold greater E adh , j / ∆ E surf , j are reported in the presence of microstructures. For lower density and smaller sizes of the microstructures as in SmN, the ratio Eadh, j / ∆Esurf , j is only 20% to 40% greater than that of SN. It is then evident that the absence of microstructures exerts lower droplet adhesion to the substrate leading to the greater excess in the surface energy released upon coalescence as supported by the low 21 ACS Paragon Plus Environment


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Eadh, j / ∆Esurf , j values reported. The low number (Figure 4c) and the small size (Figure 3a) of the coalescing-jumping droplets departing from the surface in the case of SN are then supported by the low energy required to overcome the adhesion. The enhancement of coalescenceinduced droplet-jumping performance of micrometer droplets in the absence of microstructures is then demonstrated for the first time by experimental observations and by our energy analysis. Eadh, j / ∆Esurf , j values reported for SMN (Figure 6) are of the same order of magnitude of those reported by Ölçeroğlu and McCarthy36. Although the energy analysis presented above does indeed support the greater excess of surface energy required for the jump to ensue in the presence of microstructures, it does not, however, provide a plausible explanation for the low number of jumping droplets with sizes smaller than the microstructures. The above analysis assumes that small droplets rest in the Cassie state, i.e. low energy adhesion state, and droplets should eventually jump after a coalescence event. To give a further insight on the droplet coalescence and on the droplet jumping mechanisms in the presence of microstructures, we look into the possible interactions between small droplets and the structured surface in Mode F (Figure 5f). In the case of droplets sitting on the side of a microstructure, these droplets will display a normal vector to the microstructure side, which presents to some extent, an angular deviation from the main surface normal as represented in Figure5. Then upon coalescence of droplets sitting on the microstructures, there is a decreased net momentum in the out-of-plane direction and as a consequence the jump does not ensue. Size mismatch, asymmetric droplet adhesion, as well as, the tangential motion of the coalescing droplets are some of the mechanisms proposed that can induce the reduction of the net momentum of the jumping droplet from the out-of-plane direction27, 30, 37, 40. We here propose that the droplet angular deviation from the main surface normal imposed by the microstructures also suppress the net momentum in the out-of-plane direction as well as inducing in-plane momentum and droplet sweeping52-53. 22 ACS Paragon Plus Environment

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Next, we attempt to estimate the influence of the microstructures on the droplet-jumping performance. Droplets growing on microstructures display a normal vector which has an angular deviation from the main surface normal, α . Since this vector is not parallel to the main surface normal, it seems reasonable to assume that these droplets will not fully contribute to the jump in the out-of-plane direction. For the accurate prediction of the droplet jumping performance, the microstructure surface orientation must therefore be taken into account. This latter, may also explain the over-predicted theoretical jumping velocities reported in the work of Chen et al.42. For simplicity we consider that all droplets rest in Cassie state and that all droplets are of the same size. This latter assumption is rather reasonable since calculations of droplet mismatch ratio between two coalescing droplets showed average values close to 1 (0.94 ± 0.17 for SMN, 0.99 ± 0.157 and 1.017 ± 0.167). Two different coalescing scenarios are then presented. In the first scenario, only one (i = 1) of the N coalescing droplets sits on the side of a microstructure, whereas in the second scenario, two or more droplets (i > 1) sit on inclined microstructures as in Figure 7a and Figure 7b, respectively.

Figure 7 – 2-Dimensional schematic representation of the coalescing scenarios proposed for coalescence between N droplets where (a) one droplet sits on the microstructure (i = 1), and (b) i droplets sit on the microstructures. Red arrows represent the droplet vector normal to the microstructure and normal to the main surface. Dotted arrow represents the tangential component. Black dashed arrow represents the main surface normal, α is the angular deviation equaling the microstructure inclination. In the presence of microstructures, the surface energy released in the out-of-plane direction of droplets sitting on the microstructures must scale with the microstructure inclination55. Then, it is reasonable to introduce sin α in

E coalescing − Cassie , j

as: 23

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2  Ecoalescing −Cassie, j ,α = π sin 2 θa  +1− 1 + cos θa 

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  N f  γ lg + f (γ s g − γ lg cos θaflat ) + (SRMS ,SN − f )γ sg  ∑ (sin αi ) Ri 2   i =1

(5)

We then estimate the percentage of excess of surface energy required to overcome the adhesion to the surface function of the angular deviation, Eadh−Cassie, j / ∆Esurf , j ,α , where ∆Esurf , j,α is calculated using E coalescing − Cassie , j ,α (Equation 5). Then,

E adh − Cassie , j / ∆ E surf , j ,α

can be plotted

versus the number of coalescing droplets and for the different angular deviations from the main surface normal. Figure 8a includes results for the cases where only one droplet (i = 1) presents angular deviation and Figure 8b the case where 3 droplets (i = 3) present angular deviation.

Figure 8 – Percentage of the excess of energy required to overcome the droplet adhesion, E a d h − C a s sie , j / ∆ E su rf , j ,α , function of the angular deviation from the main surface normal, α, versus number of coalescing droplets, N, for (a) i = 1, and (b) i = 3. E a d h , j / ∆ E s u r f , j values reported on Figure 6 for SMN and SN are included for comparison. Figure 8a and Figure 8b show the expected increase in E a d h − C a s s ie , j / ∆ E s u r f , j ,α as the angular deviation increases. When comparing experimental results on SMN to the ones estimated by introducing the angular deviation, in the case of i = 1 and N = 2, droplet jumping should ensue for a microstructure surface inclination below α < 60° , whereas if the surface inclination is greater than that, droplet jumping will not take place. For α ≥ 60° the excess of surface energy in the out-of-plane direction decreases notably, hence the high 24 ACS Paragon Plus Environment

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E a d h − C a s sie , j / ∆ E s u r f , j ,α

values reported. From SEM and 3D Laser Scanning Microscopy

(Figure 1, Figure SI.1 and Figure SI.2), the microstructures sides present in most cases inclination angles greater than 60°. The microstructure inclination and the barrier for coalescence imposed by the microstructures (Figure 5h) supports the low number of jumping droplets with sizes in the same order of magnitude as the microstructures in the case of SMN when compared to SN. For greater number of coalescing droplets, N > 4, Eadh−Cassie, j / ∆Esurf , j,α does not change considerably and the jump should ensue, hence the greater number of jumping events reported between more than 4 droplets in the case of SMN (Figure 4a). The case of three droplets sitting on the sides of microstructures before coalescing, i = 3, is represented in Figure 8b. For any microstructure inclination angle, the percentage of surface energy required to overcome the energy of adhesion is greater in the case of i = 3, when compared to i = 1. The need for multidroplet coalescence for the jump to ensue is evident, which is consistent with results reported in the case of high microstructure density SMN (Figure 4a). Experimental results on SN and estimated values for low inclination angles

α ≤ 20° agree fairly well. Although, the introduction of hierarchical microstructures was found to be beneficial in increasing the cumulative departure volume (by both droplet-jumping and shedding by gravity)48 and delaying surface flooding36, we found, nonetheless, that microstructures have actually a negative impact on the jumping performance of small droplets with sizes in the same order as the microstructures. The absence of microstructures on a nanostructured superhydrophobic surface allows for greater droplet-jumping frequency, less number of coalescing droplets as well as smaller droplet diameters for the jump to ensue. Microstructures induce further droplet adhesion. Moreover, ur revised energy analysis demonstrates that angular deviation from the surface normal introduced by the microstructures must be taken into account in order to fully characterize droplet coalescence 25 ACS Paragon Plus Environment


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and droplet-jumping phenomena on superhydrophobic substrates. Last, the threedimensionality of the microstructures hinders the coalescence and hence the droplet-jumping of droplets with sizes in the same order of magnitude as the microstructures All the latter will have a strong impact on the heat transfer performance. Since the heat transfer resistance through a single droplet on a hydrophobic and/or on a superhydrophobic surface was found to increase with the droplet size9, 15-16, the better heat transfer performance expected by solely coalescence-induced droplet-jumping of micrometer droplets on the one-tier roughness sample, SN, is then expected. Next we estimate the latent heat of condensation supplied to the surface by solely jumping droplets per unit of area. The latent heat supplied per unit of area, q’’ (kJ/m2) is calculated from the volume of the coalescing-jumping droplets involved in each jumping event as:

q '' =

ρ h fg Aview

n

∑V

(6)

i

i =1

where hfg is the latent heat of condensation, ρ is the density of water and Aview is the area field of view. Then, the cumulative latent heat per unit of area supplied to the surface by solely coalescing-jumping droplets is plotted in Figure 9.

Figure 9 – Cumulative latent heat removed from the surface by jumping droplets with seizes smaller than 50 μm (kJ/m2) versus time (seconds) for (red) SN, (green) SmN and 26 ACS Paragon Plus Environment

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(blue) SMN. Maximum and minimum values representing the cumulative latent heat were calculated for ± 5% of the droplet diameters. Up to 20% greater amount of heat is supplied by solely coalescence-induced dropletjumping of small droplets with diameters below 50 µm in the case of SN when compared to SMN and SmN. The enhanced heat transfer reported in the absence of microstructures is owed to the greater droplet-jumping performance when compared to two-tier rough substrates. The greater heat transfer reported in the absence of micro-structures is then demonstrated. The slightly greater heat transfer performance in the case of SMN when compared to SmN is presumably due to the greater surface area provided by the microstructures.



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CONCLUSIONS We studied the coalescence-induced droplet-jumping performance during condensation on superhydrophobic substrates with varying structural finish from the micro- to the nano-scale. Clear differences on the size distribution as well as on the number of coalescing droplets were found depending on the presence or absence of microstructures below the condensate. In the presence of microstructures, the jumping of micrometer droplets was found to decrease notably. A surface energy analysis based on experimental results demonstrates that the absence of microstructures actually lowers the energy of adhesion to excess of surface energy required for the jump to ensue. However, this energy analysis does not account for the lower number of small jumping-droplets reported in the presence of microstructures. We propose that droplets growing at the microstructures sides will display a normal vector with an angular deviation from the main surface normal. The revisited surface energy analysis account for the angular deviation induced by the microstructures, which anticipates that two coalescing droplets will not jump if one of the droplets sits on a microstructure with an inclination angle greater than 60°. The latter supports the lower number of jumping events reported in the presence of microstructures. In addition, we highlight the importance to take into account the orientation of the microstructures to accurately predict the droplet jumping velocity and trajectory. While the presence of microstructures on superhydrophobic surfaces has been found beneficial on condensate removal, we conclude that the absence of microstructures provides a great enhancement on the coalescence-induced droplet-jumping and on the heat transfer performance of micrometer droplets. The findings presented here will have an impact for the design of engineered superhydrophobic surfaces for self-cleaning, anti-icing and heat transfer applications.


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EXPERIMENTAL PROCEDURE Fabrication and characterization of SHSs Copper plates with dimensions of 10 × 10 mm2 and 500 µm in thickness were cleaned and dried prior to etching and oxidation. The cleaning procedure consisted of the ultrasonication of the copper plates in acetone, ethanol and distilled water. Then the plates were immersed in a 10 wt. % hydrochloric acid – water (HCl-H2O) solution to remove the oxide layer on the copper surface. Thereafter, the copper plates were ultrasonicated again with distilled water and dried using nitrogen gas. After cleaning, in order to create samples with different roughness, the copper plates were subjected to different fabrication procedures. All chemical substances used, unless stated otherwise, were purchased from Sinopharm Chemical Reagent Co., Ltd. (China). Three samples named SMN, SmN and SN were fabricated following different procedures. SMN and SmN samples exhibiting a two-tier roughness, i.e. micro- and nano-scale roughness, were etched with a mixture solution of 0.48 wt% hydrogen peroxide and 1.89 mol/L hydrochloric acid to form the microstructures59. In the case of SMN, the plates were immersed in the solution at 60 °C for 1 hour, whereas in the case of SmN, temperature of the solution was kept at 17 °C for 20 minutes. Thereafter, in order to confer these substrates with the nano-scale roughness, samples were oxidized using an aqueous solution of 2.5 mol/L of sodium hydroxide (NaOH-H2O) and 0.1 mol/L ammonium persulfate ((NH)4S2O8-H2O) at 70 °C for 30 minutes, which gives enough time for the formation of the nano-structures on the surface of the copper plate57-58. On the other hand, the one-tier nanorough sample (SN) was directly immersed in the same NaOH-H2O and ((NH)4S2O8-H2O) solution described above at 70 °C for 30 minutes. As a consequence of the additional etching step, SMN and SmN present different microstructural roughness, whereas SN present only nano-structures.



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After oxidation, the resulting black cupric oxide surfaces were cleaned with a large amount of distilled water. Then, surfaces were baked at 180 °C for 1 hour to completely dehydrate the sample. Thereafter, in order to render the cupric oxide surface superhydrophobic, baked surfaces were immersed into a solution of 1 wt% 1H,1H,2H,2H-perfluorooctyltriethoxysilane (POTS)-ethanol for 12 hours at room temperature. A monolayer of fluoroalkylsilane is then self-assembled on the copper oxide surface70-73. POTS with the purity of 97% was purchased from Alfa Aesar. Further details regarding the fabrication procedure can be found in Ref. 70 and 71. Finally, the substrates were baked again in an oven at 120 °C for 1 hour to obtain the SHSs. After the fabrication process, sample roughness was measured using a LEXT OLS4000 3D Laser Measuring Microscope from Olympus. Moreover, Scanning Electron Microscopy (SEM) was carried out in a FIB-ESEM 3D Versa from Gisborne Oregon (USA).

Experimental observations by optical microscopy An environmental chamber PK-3KT from ESPRC Corp. was used to control the ambient temperature and the relative humidity. A custom-built Peltier stage connected to a chiller and to a PID temperature controller was implemented within the environmental chamber. In order to ensure uniform cooling, SHS were attached to a copper block of the same size as the SHS (10.0 × 10.0 mm2) inserted in a PTFE insulator block. PTFE and copper block were in direct contact with the Peltier stage. Additional measurements with an external thermocouple showed differences less than ±1 °C when comparing the temperature displayed by the PID temperature controller and that of the SHSs. Optical microscopy observations were recorded using a CCD camera equipped with a high-resolution zoom lens Keyence VH-Z500R adjusted to a field of view of 305 × 228 µm2 (1000× magnification). The temperature and the relative humidity inside the chamber were set as 30 °C ± 2 °C and 90% ± 5%, respectively. The temperature of the Peltier stage was set as 35 C ̊ for at least 20 minutes to avoid any condensation. Then the environmental chamber was turned off to avoid vibrations, recording with a CCD camera was initiated, and temperature of the Peltier stage was lowered to 10 °C. 30 ACS Paragon Plus Environment

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The supersaturation conditions were approximately S = 3.1. Droplet nucleation started a few minutes after the chamber was turned off. Condensation experiments were imaged for ca. one hour at 2.5 fps.



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Acknowledgments Y.T. and D.O acknowledge the support of the International Institute for Carbon-Neutral Energy Research (WPI-I2CNER) sponsored by the Japanese Ministry of Education, Culture, Sports, Science and Technology (MEXT). D.O. gratefully acknowledges the support received by the Japanese Society for the Promotion of Science (JSPS) KAKENHI (Grant number JP16K18029). P.Z. and F.Y.L. acknowledge the support of the National Natural Science Foundation of China (Contract No. 51376128). The authors gratefully thank Dr. Nenad Miljkovic of University of Illinois for reading the manuscript and for his useful comments and insights. The authors also acknowledge the helpful comments and insights from the reviewers.

Authors Contributions P.Z and D.O. conceived the idea. Y.T. and D.O. guided the work. F.Y.L. fabricated and functionalized the samples. Y.M. and D.O. performed the optical microscopy experiments. D.O. analyzed the data and wrote the paper. All the authors commented on the paper.

Supporting Information Movies showing the condensation behavior over 30 minutes on SMN, SmN and SN, additional Figures for surface characterization of SMN, SmN and SN and the complete energy analysis are available free of charge via http://pubs.acs.org.

Corresponding authors †

[email protected]

* [email protected] 32 ACS Paragon Plus Environment

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Enhanced Coalescence-Induced Droplet-Jumping on Nanostructured

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