Water Droplet Evaporation On Cu-based Hydrophobic Surfaces With Nanoand.pdf

International Journal of Heat and Mass Transfer 55 (2012) 2151–2159

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Water droplet evaporation on Cu-based hydrophobic surfaces with nanoand micro-structures Chi Young Lee a,b,⇑, Bong June Zhang b, Jiyeon Park b, Kwang J. Kim b a b

KAERI (Korea Atomic Energy Research Institute), 989-111 Daedeok-daero, Yuseong-gu, Daejeon 305-353, Republic of Korea Low Carbon Green Technology Laboratory, Department of Mechanical Engineering, University of Nevada-Reno, Reno, NV 89557, USA

a r t i c l e

i n f o

Article history: Received 28 January 2011 Received in revised form 30 November 2011 Accepted 30 November 2011 Available online 11 January 2012 Keywords: Droplet evaporation Surface structure (Super)hydrophobic surface

a b s t r a c t The characteristics of water droplet evaporation on three different hydrophobic surfaces, PCu (Plain Copper, h = 115°), MSCu (Micro-Structured Copper, h = 126°) and NSCuO (Nano-Structured Copper Oxide, h = 159°) with coating of the same SAM (Self-Assembled Monolayer) material, were experimentally investigated. For industrial heat transfer applications, copper material was used as the substrate, and the simple and cost-effective fabrication technique to prepare the superhydrophobic surface, NSCuO, was introduced. Based on the observations, the behavior of droplet evaporation was divided into three stages: Stage I (constant contact area stage), Stage II (constant contact angle stage) and Stage III (mixed stage). When studying the PCu surface, the Stages I, II, and III were observed, consistent with previous reports. For the MSCu surface, Stages I and III appeared without Stage II, and the pinning period of contact line was the longest among the test samples due to the formation of Wenzel state droplet. In the case of the superhydrophobic NSCuO surface, only Stage III occurred, and the contact line moved freely during the entire evaporation time because of the formation of Cassie state droplet. The total evaporation time of the NSCuO was the longest out of all the samples tested. At the last stage of evaporation, the edge of the droplet shrank at a much faster rate in all surfaces. On the other hand, the shrinking velocity of the droplet height drastically increased only on the NSCuO, which was considered as the unique behavior of superhydrophobic surface. In this experiment, it was found that the surface structure determines the motion of the contact line on the surface, which, in turn, strongly influences the characteristics of the droplet evaporation. Ó 2011 Elsevier Ltd. All rights reserved.

1. Introduction The natural evaporation of a droplet on various surfaces is a fundamental problem and has been studied intensively for a wide range of industrial and biological applications; e.g., inkjet printing, spray painting, DNA chip fabrication, and cell patterning. In general, the surface wettability is divided into two groups: the hydrophilic surface which is the surface with a water contact angle below 90°, and the hydrophobic surface when the contact angle is above 90°. The characteristics of droplet evaporation on a hydrophobic surface are more complicated than those on a hydrophilic surface. Picknett and Bexon [1] reported that droplet evaporation on the hydrophobic surface occurs in three distinct stages as shown in Fig. 1. The first stage is the ‘‘constant contact area stage,’’ also known as the pinned contact line stage (Stage I). As the droplet evaporates, the contact angle decreases, while the contact area radius remains constant. The second stage is the ‘‘constant contact ⇑ Corresponding author at: KAERI (Korea Atomic Energy Research Institute), 989111 Daedeok-daero, Yuseong-gu, Daejeon 305-353, Republic of Korea. Tel.: +82 42 868 4587; fax: +82 42 8630565. E-mail address: [email protected] (C.Y. Lee). 0017-9310/$ - see front matter Ó 2011 Elsevier Ltd. All rights reserved. doi:10.1016/j.ijheatmasstransfer.2011.12.019

angle stage’’ also known as the moving contact line stage. As opposed to Stage I, the contact area radius recedes in Stage II and the contact angle remains constant. The third stage is the ‘‘mixed stage’’ (Stage III), an unpinned contact line stage where both the contact angle and contact area radius decrease. Birdi and Vu [2] and Birdi et al. [3] investigated the evaporation behavior of water and n-octane droplets on smooth glass and Teflon surfaces. Both studies reported that the evaporation of a water droplet on a glass surface and n-octane on a Teflon surface were stationary processes each with a constant contact radius and linear evaporation rates. However, when the contact angle was over 90°, a constant contact angle with a decreasing contact radius and a non-linear evaporation rate was observed. None of these studies [1–3] considered the effect of the surface morphology on the behavior of droplet evaporation, and mentioned the behavior of droplet evaporation on a superhydrophobic surface. Recently, studies on superhydrophobic surfaces, which exhibit a water contact angle larger than 150° [4], have been extensively performed. A superhydrophobic surface is notable as it has the features of water repellency and low surface energy. These two attributes have vast potential in various industrial applications such as anti-sticking, self-cleaning, anti-fouling, anti-corrosion, friction

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Nomenclature A Bo F f g H h Dh P DP R r Dr s t Dt V

surface area [m2] Bond number [–] force per unit length [N/m] fractional flat geometrical area [–] gravitational acceleration constant [m/s2] Height of structure [m] droplet height [m] droplet height change [m] pressure [Pa] pressure difference [Pa] roughness factor [–] contact area radius [m] contact area radius change [m] spacing between structures [m] time [s] time difference [s] shrinking velocity [m/s]

Greek letters a a half of nano-structure cone angle [°] h contact angle [°] Dq density difference [kg/m3] r interfacial tension [N/m]

reduction, and heat transfer enhancement [5–9]. Additionally, researchers [10–14] have investigated the droplet evaporation on the (super)hydrophobic surfaces with structures. Shin et al. [10] examined the evaporation characteristics of a water droplet on hydrophilic, hydrophobic, and superhydrophobic surfaces. They used glass (h = 58.64°), OTS (octadecyltricholorosilane, h = 122.52°), and AKD (alkylketene dimmer, h = 160.59°) surfaces as test samples. On the hydrophilic surface, the contact angle, center-height and volume of droplet decreased linearly over the entire evaporation time. The long pinning time – which is defined as the total time that the contact area radius remains fixed during the evaporation – was distinct and predictable. As a droplet evaporated on the hydrophobic surface, typically three distinct stages (see Fig. 1) were observed, but there was no pinning period for an evaporating droplet on the superhydrophobic surface. This study concluded that as the hydrophobicity of a surface became stronger, the pinning time became shorter and the total evaporation time lasted longer. In a later study, Shin et al. [11] examined the evaporation of a sessile water droplet using non-patterned PDMS (polydimethylsiloxane) and submicron sized post array silicon surfaces, each with the same hydrophobic contact angle. On the non-patterned PDMS surface, the contact angle showed the three noted, distinct stages during evaporation (see Fig. 1). On the patterned silicon post array surface, however, the contact angle decreased linearly while the contact area remained constant until the droplet

Subscripts A apparent contact angle a advancing contact angle D dynamic contact angle E equilibrium (intrinsic) contact angle e total evaporation time f roughness factor g gas h height i initial l liquid lg liquid–gas p projected surface area r radius sg solid–gas sl solid–liquid t total (rough) surface area UY unbalanced Young force Superscript normalized

⁄

completely evaporated. Zhang et al. [12] investigated the droplet evaporation on superhydrophobic lotus leaf and on biomimetic polymer surfaces. Both hierarchically structured surfaces appeared to maintain almost a constant contact radius stage during the evaporation. Choi and Kim [13] studied on the evaporative process of sessile droplets on superhydrophobic surfaces of the sharp-tip post structures with three kinds of heights (i.e., 100, 300 and 500 nm) and a given constant pitch of 230 nm. A pure water and a protein solution were used for testing. They concluded that the superhydrophobicity of surface and the behavior of droplet evaporation are strongly influenced by the three-dimensional nano-structured morphology and the surface fouling such as protein adsorption. McHale et al. [14] reported the water droplet evaporation process on the superhydrophobic SU-8 patterned polymer surfaces. Based on the diffusion model of water vapor into the surrounding atmosphere, they performed the quantitative analysis of initial pinned contact line phase of evaporation, and estimated the diffusion coefficient and the concentration difference. Currently, for the fabrication of well-ordered nano-structure, the silicon substrate and MEMS technique are widely used [4,7,8,11,13,14], but they are expensive. For industrial applications, the fabrication technique of a nano-structure should be convenient and cost-effective, and should have the ability to be applied to large surface areas of a conventional metal substrate (e.g., copper). Our group has tried to apply the nano-structured surfaces we

Fig. 1. Typical droplet evaporation stages on smooth hydrophobic surface: (a) Constant contact area (Stage I), (b) constant contact angle (Stage II) and (c) mixed (Stage III) stages.

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introduced for heat transfer applications such as the nucleate boiling heat transfer, and achieved some successful and meaningful results [15,16]. Meanwhile, in order to understand how the liquid droplet evaporation can be influenced by the surface material (chemical heterogeneity) and surface structure (roughness), both effects need to be separately examined. It is believed that a comparative study of droplet evaporation between the plain and various structured surfaces under the similar conditions (e.g., contact angle and surface material) is one effective way to understand the interaction of the surface structure on droplet evaporation. The objective of this study is to experimentally investigate the effect of a surface structure on the evaporation characteristics of a water droplet using plain, micro-, and nano-structured hydrophobic surfaces. Copper, a popular metal substrate in industrial heat transfer applications, is used as the test sample. For a superhydrophobic surface (Nano-Structured Copper Oxide: NSCuO), a convenient and cost-effective technique that creates a well-ordered nano-structure on a large surface area is introduced. In order to examine the effect of the surface structure on droplet evaporation, (i) the same hydrophobic SAM (Self-Assembled Monolayer) coating is applied on all the sample surfaces, removing the effect of a surface material (chemical heterogeneity) during evaporation; and (ii) the plain and structured surfaces with a similar contact angle are prepared. The characteristics of an evaporating droplet (i.e., contact angle, contact area radius, droplet height, shrinking velocities of droplet height and contact radius) are measured on each surface and are reported on utilizing the droplet imaging measurement technique. Based on the experimental results and the analysis of the surface structures, the relationship between the droplet evaporation and the surface structure is able to be reviewed and discussed in detail.

2. Experiment 2.1. Preparation of test samples The following three test specimens were prepared: PCu, indicating a Plain (non-structured) Copper surface; MSCu, a Micro-Structured Copper surface ground by power tool; and, NSCuO, NanoStructured Copper Oxide surface, whose fabrication procedure is described presently. For NSCuO, the initial surface treatment of the copper foil, obtained from Alfa Aesar (99.98%, thickness 500 lm), power tool grinding (Grit-120) is used. A specimen, then, is cleaned in acid (HCl:HNO3 = 1:1 by volume) to remove organic residues. The specimen is placed under ultra-sonication for 10 min and thoroughly rinsed with DI water several times. Next, the specimen is cleaned in acetone for 10 min under ultra-sonication. Subsequently, the specimen is immersed in NH4OH solution (0.05 M) for a day at 55 °C. The self-assembled copper oxide black coating is then homogeneously applied to the surface. Thorough DI water rinsing is carried out several times. The specimen is dried in the oven at 90 °C. In order to remove the chemical heterogeneity on the surface and achieve the hydrophobicity, all the samples are coated by SAM in a process of immersion in 1.1 mM dodecanethiol for 1 h. By developing these surfaces and coating the samples, only surface structures influence the behavior of droplet evaporation. The initial contact angles of all samples and the FESEM (Field Emission Scanning Electron Microscopy) images of the MSCu and NSCuO surfaces are shown in Figs. 2 and 3, respectively. The PCu and MSCu had the initial contact angles of 115° and 126°, respectively. Both are hydrophobic surfaces that have similar initial contact angles (the contact angle difference is approximately 11°). It should be noted that NSCuO has the well-ordered nano-structure (see Fig. 3(b)) and becomes a superhydrophobic surface with the initial contact angle of 159°.

2.2. Experimental set-up and details Using a syringe, a pre-measured de-ionized water sessile droplet was placed on test specimens. All droplets were of equal weight. Contact angles that changed due to natural evaporation were measured using a CAM-100 (KSV Instruments Ltd., Finland as shown in Fig. 4). The temperature and relative humidity of the environment were maintained at 23.5 °C and 18%. In order to determine if the shape of a sessile droplet on test surfaces has a spherical cap, the Bond number, which is a dimensionless number defined as the ratio of gravitational force to surface tension force, is calculated using Eq. (1).

Bo ¼

Dqrgh

ð1Þ

rlg

Here, Dq is the density difference between air and water, g is the gravitational acceleration constant, r is the contact line radius, h is the droplet height, and rlg is the water surface tension [17]. The Bond numbers calculated in the present experiments are in a range of 0.011–0.38 for PCu, 0.024–0.36 for MSCu, and 0.005–0.33 for NSCuO. As all Bond numbers are much less than unity, the surface tension force dominates the gravitational force. During evaporation, the images of a droplet are recorded every 1 min on a computer system. From the recorded images of the water droplet on the surfaces (as shown in Fig. 5), the contact angle (h), droplet height (h) and contact area radius (r) are measured using an image processing technique. 3. Results and discussion 3.1. General trends of water droplet evaporation on PCu, MSCu, and NSCuO In Figs. 6 and 7, the images and contours of a droplet evaporated on PCu, MSCu, and NSCuO surfaces are shown, respectively. In Fig. 7, the numbers on contours indicate time in second. The changes in the contact angle, the contact area radius and the droplet height measured on PCu, MSCu, and NSCuO surfaces during the water droplet evaporation are shown in Fig. 8(a)–(c), respectively. Fig. 9(a)–(c) show the trends of normalized contact angle, contact area radius and droplet height with normalized evaporation time, respectively. The normalized parameters are defined in Eq. (2).

h ¼

hðtÞ ; hi

r ¼

rðtÞ ; ri



h ¼

hðtÞ ; hi

t ¼

t te

ð2Þ

where h, r, h and t are contact angle, contact area radius, droplet height and time, respectively. Subscripts of i and e indicate initial value and total evaporation, respectively. A superscript of ⁄ signifies a normalized value. The initial contact angle of PCu is 115°. As shown in Fig. 8, until 1250 s, the contact angle steadily decreases to approximately 75°. At this angle, the radius of the area between the water droplet and the surface is almost the same as the initial value of 1.44 mm with only a decrease in the droplet height. In this region, the change in contact angle is about 40°. Although the droplet height continues to decrease, the constant contact angle of approximately 75° is maintained for about 1000 s. In this region, the contact area radius does being to decrease. After 2250 s, the contact angle, the contact area radius, and the droplet height all decrease. The total evaporation time of PCu is 2541 s. The present experimental data of PCu is in agreement with the trend of previous research [1,10,11]: the behavior of droplet evaporation for 0–1250 s, 1250–2250 s and 2250–2541 s indicate the

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Fig. 2. Contact angle measurement of test specimens: (a) PCu, (b) MSCu and (c) NSCuO.

Fig. 3. FESEM image of test specimens: (a) MSCu and (b) NSCuO.

Fig. 4. CAM-100 contact angle measurement equipment.

Fig. 5. Recorded image of water droplet on surface.

constant contact area, constant contact angle, and mixed stages, respectively. Based on Fig. 9, approximately 50%, 40% and 10% in total evaporation time occur in Stage I, II, and III, respectively. In the MSCu study, the contact angle steadily decreases during the entire evaporation time without having a region of a constant contact angle (i.e., Stage II), as shown in Fig. 8(a). The contact area radius remains constant until 2000 s (see in Fig. 8(b)); this behavior corresponds to Stage I, and the change in contact angle is about 80°. Then, both the contact angle and the contact area radius decrease (i.e., Stage III). The droplet height decreases over the whole evaporation period. Total evaporation time is 2388 s. As shown in Fig. 9(a) and (b), the portions of Stage I and III are approximately

80% and 20% of the evaporation time. In other words, when the water droplet on MSCu evaporates, the contact line – a perimeter contacted between air, water droplet, and substrate – is pinned over 80% of the time. Although the initial contact angle of MSCu (126°) was similar to that of PCu (115°), the detailed behavior of droplet evaporation on both of MSCu and PCu surfaces differs greatly. (i) Stage II, the constant contact angle stage, where the contact area radius recedes and the contact angle remains constant, does not occur in MSCu. Birdi and co-workers [2,3] reported that the constant contact area stage for h < 90° and the con-

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Fig. 7. Contours of droplet evaporated on (a) PCu, (b) MSCu, and (c) NSCuO.

Fig. 6. Images of droplet evaporated on (a) PCu, (b) MSCu, and (c) NSCuO.

stant contact angle stage for h > 90° can dominate during the process. Based on the present observations of MSCu, the contact angle is 126° (>90°), and Stage II does not appear. How-

ever, Stage II is observed on PCu, consistent with previous reports, implying that the surface structure is more important than the initial contact angle when determining the droplet evaporation process. (ii) Stage I of MSCu lasts longer than that of PCu. Shin et al. [10] reported that, as the hydrophobicity of the surfaces became stronger (as the contact angle became larger), the pinning time became shorter. In this experiment, the MSCu has a similar (or slightly larger) contact angle compared to PCu, but the MSCu stays at Stage I much longer. Our belief is that this difference is due to the effect of the surface structure on droplet evaporation.

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(a) 180

(a)

1.0

Normalized Contact Angle

Contact Angle (deg.)

150

1.2

120

90

60

NSCuO MSCu PCu

30

0 0

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NSCuO MSCu PCu 0.2

Time (sec)

(b)

1.5

Normalized Contact Area Radius

Contact Area Radius (mm)

NSCuO MSCu PCu

1.0

0.5

1000

1500

2000

2500

1.2

3000

0.8

1.0

1.2

0.8

0.6

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3500

NSCuO MSCu PCu 0.2

0.4

0.6

Normalized Time

(c) 1.2

3.0

NSCuO MSCu PCu

2.0

1.5

1.0

0.5

0.0 0

500

1000

1500

2000

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NSCuO MSCu PCu

1.0

Normalized Droplet Height

2.5

Droplet Height (mm)

1.0

1.0

Time (sec)

(c)

0.8

1.2

0.0 0.0

0.0 500

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0

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Time (sec)

0.8

0.6

0.4

0.2

0.0 0.0

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Normalized Time

Fig. 8. Changes in (a) contact angle, (b) contact area radius and (c) droplet height.

Fig. 9. Normalized time vs. (a) normalized contact angle, (b) normalized contact area radius and (c) normalized droplet height.

The droplet evaporation behaviors of the superhydrophobic NSCuO are vastly different from those of the PCu and MSCu. The contact angle of the NSCuO gradually reduces due to evaporation with a decreasing contact area radius and droplet height until 3250 s. Then, the contact angle, the contact area radius, and the droplet height all decrease dramatically. The droplet completely evaporates at 3450 s, which is the longest period of evaporation time among the samples tested in the present study. The slow evaporation is because the droplet maintains its spherical shape

during the entire evaporation period. The spherical shape of the water droplet can prevent the thin liquid film near the edge of droplet from being formed, which leads to a suppression of the evaporation [10]. In the evaporation process of NSCuO, only Stage III is observed and can be further divided into two sub-stages: Slow and Fast. Until 3250 s (about 95% of total evaporation time), the contact angle and contact area radius slowly and steadily decrease (referred to as Slow Stage III), then, both the angle and the radius drastically shrink (Fast Stage III). The contact line on NSCuO is

C.Y. Lee et al. / International Journal of Heat and Mass Transfer 55 (2012) 2151–2159

Radius Shrinking Velocity (mm/s)

(a)

surface structures. In the following section, this will be discussed in detail.

0.012

NSCuO MSCu PCu

0.010

3.2. Effect of surface structure on water droplet evaporation

0.008 0.006 0.004 0.002 0.000 -0.002 0.0

0.2

0.4

0.6

0.8

1.0

1.2

In PCu, the Stages I, II, and III are observed, and the contact line is pinned during 50% of the total evaporation time. In MSCu, the Stages I and III occur, and the contact line is pinned during 80% of the total evaporation time. In NSCuO, only Stage III appears, and the contact line moves freely during the whole evaporation time. Observing the results, it can be determined that the behavior of droplet evaporation is closely related to the motion of the contact line, which, in turn, is influenced by the surface structure. When a droplet is placed on the surface, the equilibrium contact angle is determined by Young’s equation, Eq. (4), which is derived from the force balance acting on the contact line, as shown in Fig. 11.

Normalized Time

(b) Height Shrinking Velocity (mm/s)

coshE ¼ 0.012 0.010 0.008 0.006

rlg

F UY ¼ rlg ðcoshD  coshE Þ 0.004 0.002 0.000 -0.002 0.2

0.4

0.6

0.8

1.0

1.2

Normalized Time Fig. 10. Normalized time vs. shrinking velocities of (a) radius and (b) height of droplet.

not pinned over the entire evaporation time. This trend may be considered as a unique behavior of the superhydrophobic surface. In Fig. 10, the shrinking velocities of contact area radius (Vr) and height (Vh) of droplet on PCu, MSCu and NSCuO are shown. Vr and Vh are defined as Eq. (3)

Vr ¼

ðrsg  rsl Þ

Dr ; Dt

Vh ¼

Dh Dt

ð4Þ

Here, rsg, rsl and rlg are interfacial tensions of solid–gas, solid–liquid, and liquid–gas, respectively. At the initial moment of wetting, the droplet appears to be at or near the equilibrium contact angle. As the droplet begins to evaporate, the droplet height and contact angle decrease. Therefore, it is no longer the initial equilibrium condition and the unbalanced Young force can be expressed as below.

NSCuO MSCu PCu

0.0

2157

ð3Þ

The shrinking radius velocities of all the samples are drastically increased at the last stage of droplet evaporation as shown in Fig. 10(a). Based on the measurements, the edge of droplets shrink very fast for the last 10% period of the total evaporation time. However, the trend of the shrinking droplet height velocity seems to vary from that of the shrinking radius velocity. At the last evaporation stage, the shrinking velocity of the droplet height in NSCuO rises more sharply than that of PCu and MSCu, as shown in Fig. 10(b). This difference is due to the droplet on NSCuO maintaining a spherical shape during the entire evaporation time. This spherical formation is owing to the low surface energy and the free moving contact line on the superhydrophobic surface, which is different from that on PCu and MSCu (see Figs. 6 and 7). This peculiar behavior of water droplet evaporation on the superhydrophobic surface is unique. Based on the present observations, the evaporation characteristics of a water droplet on a surface are significantly influenced by

ð5Þ

where, hD is the dynamic contact angle by evaporation. According to Eq. (5), the contact line tends to recede, and the unbalanced Young force makes the contact line pinned or de-pinned. An opposing frictional force between the liquid and the solid surface, which leads to the pinning of the contact line, is induced by the surface roughness, and chemical heterogeneities of the solid surface. Whether the contact line is pinning or de-pinning is determined by the competition between the unbalanced Young force and frictional forces. When the unbalanced Young force overcomes the frictional force, the contact line can be de-pinned [18]. In general, when a water droplet resides on a rough surface, (i) the liquid can completely wet the cavities of rough surface or (ii) the liquid cannot penetrate into the cavities. If the droplet wets the surface structure (without an air-pocket inside the cavity), its apparent contact angle is given by Wenzel’s model [19]. Wenzel [19] proposed the relationship between the apparent (hA) and the intrinsic (hE) contact angles through the modification of Young’s equation to utilize a roughness factor (Rf) that is defined as a ratio of projection and total surface areas, as follows.

 cos hA ¼

At Ap



rsg  rsl ¼ Rf cos hE rlg

Fig. 11. Force balance at contact line during the evaporation [18].

ð6Þ

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where, At and Ap are the total surface and projection areas, respectively, and, therefore, the value of Rf is greater than unity. Wenzel’s equation in Eq. (6) implies that the free energy of the liquid–solid interface on the rough surface is Rf times larger than that on the perfectly smooth surface. The Wenzel’s model of Eq. (6) predicts that, if the intrinsic contact angle is larger than 90°, the apparent contact angle increases with an increase in the roughness factor. If the intrinsic contact angle is less than 90°, the roughness factor leads to a decrease in the apparent contact angle. On the other hand, the droplet can sit on the peaks of the surface roughness (with an air-pocket inside the cavity). In this case, a liquid–solid–gas interface is formed, and Wenzel’s model [19] can be modified by considering the fractional areas of wetted and non-wetted surfaces. The apparent contact angle is given by Cassie and Baxter’s model [20].

cos hA ¼ Rf  flg ðRf cos hE þ 1Þ

ð7Þ

Here, flg is the fractional flat geometrical area of the liquid–gas interface under the droplet. Two different droplet states, Wenzel and Cassie, can be determined by the surface structures and may be related to the detailed behavior of the droplet evaporation. Therefore, it is worthwhile to evaluate the droplet state formed on the each structured surface we used. Choi et al. [8] proposed the criteria of structure spacing (s) and height (H) for liquid meniscus to withstand the pressure of liquid using a simple geometrical calculation and the Laplace–Young equation, as follows:

pffiffiffi j cosðha  aÞj s < 2 2rlg DP

ð8Þ

1  sinðha  aÞ s H > pffiffiffi 2j cosðha  aÞj

ð9Þ

The idealized surface structure in Fig. 12 is different from that in the present surface structure, but Eqs. (8) and (9) may be a good indicator when evaluating the spacing and height of structure for Cassie drop. In order to estimate the drop states on the present structured surfaces, the spacing and height of the structure were calculated at the following condition [8]: rsl = 0.0727 N/m, ha  a = 120° and DP (=Pl  Pg) = 1 atm. It is figured that the spacing between the structures is less than 1.0 lm, and the height of structures is larger than 0.2 lm. Based on Fig. 3(b), the NSCuO structure is satisfied with the s < 1.0 lm and H > 0.2 lm proposed by Eqs. (8) and (9). However, the MSCu structure does not seem to meet the criteria. The structure spacing in y-direction is above about tens of lm, and the interface curvature of x-direction in Fig. 3(a) between liquid and gas is

Fig. 12. Gas–liquid interface on an idealized structured hydrophobic surface.

likely too large to be maintained. In this case, the liquid may touch the bottom surface of the cavity, and the surface structures may then be flooded. From these findings, we conclude that Cassie and Wenzel state droplets are formed on the NSCuO and MSCu, respectively. Two different states of a droplet on the structured surface, the Wenzel and the Cassie, can affect the behavior of the evaporation. The stages of droplet evaporation are closely related to whether the contact line is pinned or not. The motion of the contact line depends on the droplet states on the structured surface and the different frictional forces of both drop states. In the droplet of Cassie state on a superhydrophobic nano-structured surface, a slip of liquid can occur due to the air trapped between the nano-structures [8]. In this case, the frictional force becomes smaller due to the small shear stress and the small contact area on the surface when compared to the droplet in Wenzel state. Moreover, in the Wenzel droplet state, the surface structure may play a role as the defect and severely prevents the contact line from moving. Consequently, Cassie state droplet on the nano-structured surface appears to have a smaller contact angle hysteresis and a weaker pinning of the contact line. In the NSCuO, which exhibits only Stage III, the contact line is observed to move freely, and the shrinking velocity of droplet height drastically increases at the last stage of evaporation due to the formation of Cassie droplet state. The MSCuO has the longest period of Stage I, where the contact line is pinned in test samples due to the formation of the Wenzel droplet state. In summary, the surface morphology has a great influence on the behavior of droplet evaporation. The surface structure determines the state of the droplet placed on the surface, and this affects the motion of the contact line. The behavior of the contact line (i.e., whether it is pinned or de-pinned) results in a change of the details in droplet evaporation, for example, a change of the contact angle, contact area radius, droplet height, shrinking velocities of droplet radius and height.

4. Conclusion In the present experimental study, the characteristics of droplet evaporation on three kinds of hydrophobic surfaces were investigated utilizing PCu, MSCu and NSCuO surfaces, all coated by the same hydrophobic SAM material. In the PCu experiment, Stages I, II, and III were observed, which was consistent with previous reports. In the MSCu experiment, Stages I and III were observed without Stage II – in spite of a similar contact angle to the PCu experiment. The pinning period of the contact line was longest (80% of total evaporation time) in the MSCu test sample. This was due to the Wenzel state droplet that was formed on the MSCu surface which prevents the contact line from moving due to the large frictional force. In the NSCuO experiment, only Stage III occurred. During the total evaporation time, the contact line was able to move freely due to the sliding effect of the contact line caused by the formation of the Cassie state droplet. The total evaporation of NSCuO lasted the longest out of the three tested surfaces. While the shrinking velocity of the contact area radius drastically increased for all surfaces at the last evaporation stage, the droplet height shrunk sharply for only the NSCuO surface, which was considered as one of the unique evaporation behaviors of the superhydrophobic surface. These findings are presumed to be caused by the droplet on such a surface maintaining its spherical shape. In this study, the superhydrophobic surface can be fabricated utilizing simple and cost-effective techniques to create well-controlled nano-structures on a large surface area. It is found that the surface structure is a more important factor than the initial

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