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Sliding of water droplets on micropillar-structured superhydrophobic surfaces
Journal Pre-proofs Full Length Article Sliding of Water Droplets on Micropillar-structured Superhydrophobic Surfaces Chun-Wei Yao, Sirui Tang, Divine Sebastian, Rafael Tadmor PII: DOI: Reference:
S0169-4332(19)33309-4 https://doi.org/10.1016/j.apsusc.2019.144493 APSUSC 144493
To appear in:
Applied Surface Science
Received Date: Revised Date: Accepted Date:
14 August 2019 19 October 2019 22 October 2019
Please cite this article as: C-W. Yao, S. Tang, D. Sebastian, R. Tadmor, Sliding of Water Droplets on Micropillar-structured Superhydrophobic Surfaces, Applied Surface Science (2019), doi: https://doi.org/10.1016/ j.apsusc.2019.144493
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© 2019 Published by Elsevier B.V.
Sliding of Water Droplets on Micropillar-structured Superhydrophobic Surfaces
Chun-Wei Yao a,*, Sirui Tangb, Divine Sebastiana, Rafael Tadmorb,c
a Dept.
of Mechanical Engineering, Lamar University, Beaumont, TX, 77710, USA
b Dan
F. Smith Department of Chemical Engineering, Lamar University, Beaumont, TX 77710, USA
c Dept
of Mechanical Engineering, Ben Gurion University of the Negev, Beer Sheva 8410501, Israel
* Correspondence: [email protected]; Tel.: +1-409-880-7008
Keywords: Sliding angle, Wetting properties, Micro textured surfaces
ABSTRACT Understanding the specific behavior of water droplet detachment from a micropillar-structured superhydrophobic surface is essential in a variety of potential applications. Herein, the sliding behavior of water droplets on three different micropillar-structured superhydrophobic surfaces was studied. From tilting plate experiments and retention force measurements, we probed the motion of water droplets with different volumes. The effects of droplet sizes and contact angle hysteresis on the roll-off angle were also investigated. Furthermore, three different models are proposed to estimate a roll-off angle. The lateral retention force-based model agrees well with the roll-off angle measurements, and the other two contact angle hysteresis-based models capture the trend in the variation of the roll-off angle.
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1. Introduction Superhydrophobic surfaces have been in the limelight of the scientific community over the last decade owing to the plethora of applications ranging from membrane distillation to anti-icing and selfcleaning [1–3]. Generally, superhydrophobic surfaces are designed using materials with low surface energy and specific surface morphology [4,5]. Micro-textured hydrophobic surfaces have been studied in an effort to understand the effects of micro-structures on hydrophobicity [6–12]. Such surfaces are characterized by their high contact angles, which result from the fractal micro- or nanostructure of the surface [5]. The behavior of a droplet sliding off a micro-structured surface remains a challenge in many applications; therefore, many studies to date have focused on the sliding behavior of water droplets on inclined micro-textured superhydrophobic surfaces under the influence of gravity. Recent studies have also modified the classical Cassie-Baxter relation and proposed theoretical models [13–19]. For example, Cunjing Lv et al. [16] proposed an energy-based model that is suitable for calculating the sliding angle of the droplet in terms of known physical properties such as area fraction, droplet volume, and Young’s contact angle. However, experimental results have shown some inconsistency with theoretical predictions. It has been widely accepted that the retention force of liquid droplets sliding on solid surfaces is critically related to the contact angle hysteresis and the roll-off angle [20–22]. Various efforts to study the lateral adhesion force have been included in recent studies [23–26]. The most prominent one among them is the tilted plate method, which can be employed to effectively investigate static lateral adhesion
2
forces [23,27,28]. In the tilted plate method, the inclination of the surface where the droplet rests is controlled, and the motion of the droplet is recorded by a high-speed camera; thus, the roll-off angle can be accurately measured [23]. The static lateral adhesion forces can be conveniently calculated by considering the gravitational force necessary for the initiation of the droplet’s motion. A limitation to this approach is that it cannot be employed for accurate measurement of static lateral adhesion forces for smaller droplets (a few microliters), as their gravitational forces are too small to overcome the adhesion; thus, this method is applicable only with considerably larger droplets. Nguyen Thanh-Vinh et al. [29] used a MEMS-based two-axis force sensor array and measured the lateral adhesion force when a water droplet moves on the array of micropillar during sliding. However, this method is also valid only with a large droplet. As for the other methods, D.W. Pilat et al. [30] directly measured the lateral adhesion force when they moved drops over micropillar surfaces using a capillary tube. This method provided information about lateral adhesion forces only for very small volumes of up to 2 μL. Even though the relation between the lateral adhesion force and rolling ability of a water droplet on micro-structured surfaces was investigated in some recent studies, the sliding mechanism of the droplet on the micropillar-structured superhydrophobic surfaces has not yet been fully understood. This research considers the effect of surface hydrophobicity on droplet roll-off angles with specific micropillar-structured superhydrophobic surfaces, and proposes a possible way to effectively measure the lateral retention force and estimate a more accurate roll-off angle by different models. Moreover,
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the effects of droplet size on contact angle hysteresis, roll-off angle, and moving velocity were investigated.
2. Experimental 2.1. Surface fabrication Micropillar array surfaces were fabricated using a photolithography process. The substrates used were single-side polished silicon wafers. The desired pattern consisting of an array of 25 m x 25 m micropillars was developed by using plasma and chemical resistant positive photoresist (SPR-220) with an adhesion promoter (AP8000). A total of three designs were exposed on the photoresist with a mask aligner, with edge-to-edge spacings of 25 m, 37.5 m and 50 m, respectively. The wafer then underwent an anisotropic dry etch process for 50 min to etch around the photoresist squares and towers was made at least 75 m in height. The wafer was then submerged in photoresist stripper AZ 400T for 24 hr to remove the photoresist. The substrate underwent an anisotropic dry etch process (Plasmatherm ICP-DRIE) to etch around the photoresist squares. The substrate then was left in the ICP-DRIE, and C4F8 plasma was run for 1 min to deposit a thin layer of Teflon-like hydrophobic material ((C2F4)n) on the whole surface. The combination of micro-pillar structures and the chemical coating makes surfaces superhydrophobic. The desired samples consisting of a micropillar array of 25 m x 25 m were made as shown in Fig. 1. At least 75 m height of micropillars was measured using optical profilometry (see Fig. 2).
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Energy-Dispersive X-Ray Spectrouscopy (EDX) data indicates that the surfaces include a Carbon and Fluorine signature, suggesting the deposition of ((C2F4)n) on the surface as shown in Fig. 3.
Fig. 1. SEM images of the micro textured surfaces with a micropillar array with spacing values of (a) 25 m (b) 37.5 m, and (c) 50 m. All micropillar-structured surfaces exhibit a hydrophobic property when water droplets (10 L) are gently placed on them as shown in inserted pictures.
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Fig. 2. (a) 3D Profilometer image of the micropillar surface with 37.5 m spacing and (b) the pillar height measurements.
Fig. 3. EDX spectrum analysis of the micropillar array surface. (𝑎)2
The area fraction of the solid-liquid interfaces (f) could be defined as 𝑓 = (𝑎 + 𝑏)2, where 𝑎 is the micropillar width, 𝑏 is the pillar spacing. The values of 𝑓 for the spacings of 25 μm, 37.5 μm and 50 μm surfaces are 0.25, 0.16 and 0.11, respectively.
2.2. Experiment setup Contact angle measurements were performed using a contact angle analyzer with tilting table (DSA25E, Krüss) for each spacing design. Advancing, receding, static, and roll-off angles were determined using droplet volumes in the range from 8 to 12 μL at room temperature (23℃). These angle values were obtained by averaging five measurements per sample. Advancing and receding contact angles were measured right before the droplet started to move and roll off the surface by tilting the 6
contact angle analyzer at a rate of 0.5°/s. The inclined angle of the tilting system was recorded as the roll-off angle of each droplet. Lateral retention force measurements were performed using a customized Centrifugal Adhesion Balance apparatus (see Fig. 4) [24,31], which can measure the lateral retention force directly. There is a shaft that can rotate with the help of a motor, and a centrifugal arm is attached to the shaft. When the shaft rotates, the centrifugal arm rotates in the horizontal plane. At the end of the centrifugal arm, there is a chamber in which a camera is mounted to monitor the motion of the drop. Sequential images were taken at the rate of 15 frames per second. The samples (surface and liquid drop) were placed in the goniometer inside the chamber.
Fig. 4. Images of the Centrifugal Adhesion Balance. a) Structure of CAB, b) details of the goniometer inside the chamber. (1) Camera (lens), (2) mirror (45 ° tilted), (3) sample stage, (4) light source, (5) satellite drops, and (6) central drop. Reprinted with permission from [31]. Copyright (2019) American Chemical Society.
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In this study, we defined the forces which are parallel to the surface as the lateral force 𝐹𝑙𝑎𝑡 as shown in Fig. 5 [24,31]. Namely, the lateral force 𝐹𝑙𝑎𝑡 is the centrifugal force which starts from zero and increases with set angular acceleration, and can be calculated as 𝐹𝑙𝑎𝑡 = 𝑚𝜔2𝐿
(1)
where 𝑚 is the mass of the liquid drop, 𝜔 is the angular velocity of the rotation of the centrifugal arm, and 𝐿 is the distance from the central axis of the system to the center of the drop.
Fig. 5. Schematic illustration of a drop resting on the horizontal, rotating plate of the apparatus. During the rotation, the drop experiences a centrifugal force in the lateral direction which is parallel to the surface and a gravitational force which is perpendicular to the surface.
3. Roll-off Angle Models 3.1. Contact Angle Hysteresis-Based Model
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In Contact Angle Hysteresis-Based Model, the weight of the droplet is balanced by the surface tension force at the onset of the droplet sliding. This model was verified by Furmidge [20] and has been considered in this paper as follows: 𝑚𝑔sin 𝛼 = 2𝑅𝛾𝐿𝐺(cos 𝜃𝑅 ― cos 𝜃𝐴)
(2)
where 2𝑅 is a characteristic length representing the size of the droplet contour, 𝛾𝐿𝐺 is the surface tension, 𝜃𝑅 is the receding angle, 𝜃𝐴 is the advancing angle, 𝑔 is the gravitational acceleration, and 𝛼 is the roll-off angle. We define R is the radius of the droplet prior to deformation, which can be estimated by using the following equation [32]: 𝑅=
(
3𝑉 𝜋(1 ― cos 𝜃)2(2 + cos 𝜃)
1 3
)
(3)
where 𝑉 is the drop volume and is the apparent contact angle.
Combining eqs. (2) and (3) yields the following equation: sin 𝛼 =
2𝛾𝐿𝐺 𝑚𝑔
(cos 𝜃𝑅 ― cos 𝜃𝐴)
(
1 3
3𝑉
𝜋(1 ― cos 𝜃)2(2 + cos 𝜃)
)
(4)
ElSherbini et al. [22] introduced a shape-factor 𝑘 ( = 24/𝜋3) in Eq. (2). Therefore, Eq. (4) can be modified as:
sin 𝛼 =
2𝑘𝛾𝐿𝐺 𝑚𝑔
(cos 𝜃𝑅 ― cos 𝜃𝐴)
(
3𝑉 𝜋(1 ― cos 𝜃)2(2 + cos 𝜃)
1 3
)
9
(5)
Fig. 6. Illustration of the tilted surface at a specific droplet roll-off angle 𝛼.
3.2. Lateral Retention Force-Based Model We define the detachment of the receding edge of the three-phase contact line (TCL) as the onset of motion. In this model, the lateral component of the gravitational force 𝐹𝑔 for the droplet on tilted surface under gravity, as shown in Fig. 6, is given as (6)
𝐹𝑔 = ― 𝜌𝑔𝑉sin 𝛼
where 𝜌 and 𝑉 denote the density of the liquid drop and the volume of the drop, respectively. Accounting for the lateral component of the gravitational force and lateral retention force at the moment that a droplet starts to move yields the following equation: (7)
𝐹𝑙𝑎𝑡 + 𝐹𝑔 = 0
Based on our lateral force measurement, combining eqs. (1), (6), and (7) yields the following equation: sin 𝛼 =
𝑚𝜔2𝐿
(8)
ρV𝑔
This roll-off model determines 𝛼 by the measured lateral force (centrifugal force) and the gravitational force. 10
4. Results and discussion 4.1. Contact Angles of Water Droplets on Micropillar-structured Superhydrophobic Surfaces The advancing, receding, and static contact angles and the contact angle hysteresis for different sizes of water droplets on the micropillar structured surfaces with different spacings are plotted in Fig. 7. The plot reveals that the advancing, receding, and static contact angles are not a function of drop size for those small droplets. Contact angle hysteresis is defined as the difference between the advancing and the receding contact angles. Comparing different surfaces, Fig. 7 shows that contact angle hysteresis reduces as pillar spacing increases, though the advancing contact angles keep consistent. Also, surfaces with larger pillar spacing—which causes a smaller area fraction and a higher static contact angle— generally exhibit a smaller contact angle hysteresis than surfaces with smaller pillar spacing, which causes a larger area fraction and a lower static contact angle. These differences in static contact angles are in an agreement with Hou et al.’s work which shows the static contact angle increases with increasing pillar spacing until it reaches a maximum value (70 μm) [33] which is beyond the largest pillar spacing of our surfaces (50 μm). It indicates that the wetting state is Cassie–Baxter’s state caused by the microscale structures, which provide spaces for air to be trapped between the droplet and the surface, and this air pocket acts as a cushion to support the water drops existing between the micropillars.
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Fig. 7. Advancing, receding and static contact angles and the contact-angle hysteresis of the droplets with different volumes on (a) surface #1 (25 μm spacing), (b) surface #2 (37.5 μm spacing), and (c) surface #3 (50 μm spacing). Red-advancing contact angle, blue-static contact angle, green-receding contact angle.
4.2. Lateral Force Measurement Water drops of various volumes were placed on a horizontal microstructure surface that was fixed in the chamber. It was observed that when the lateral force measurement system starts running, the drops experience an increasing lateral force (centrifugal force) that is parallel to the surface. The angular velocity of the rotation increases linearly at the rate of 0.7 rpm/s. Fig. 8 denotes the shapes of the drop during different phases of its motion. Initially, when the lateral force is unable to overcome the lateral retention force, the TCL is pinned to the surface with increasing advancing contact angles and decreasing receding contact angles as the drop deforms. Fig. 8b shows the moment that the receding edge of a 10 μL water drop is about to move under 33 μN lateral force. When lateral force 𝐹𝑙𝑎𝑡 > 33 N, the receding edge depins and the drop starts moving. We observe that after the receding edge detaches from the surface, it “jerks” to the next pillar, and this motion is consistent with the sliding phenomena of water droplets on the inclined micropillar-structured superhydrophobic surfaces. As a function of lateral force 𝐹𝑙𝑎𝑡, the drop undergoes a fast motion after 𝐹𝑙𝑎𝑡 > 39 N.
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Fig. 8. A series of four pictures (a-d) showing a 10 μL water drop sliding on a microstructure surface #1 (25 m spacing) under lateral forces (a) 𝐹𝑙𝑎𝑡 = 0, (b) 𝐹𝑙𝑎𝑡 = 33 N, (c)&(d) 𝐹𝑙𝑎𝑡 = 39 N. From (a) to (b) the receding edge of the drop pinned on the surface with increasing lateral force. The time interval is 0.067 s between (c) and (d), so there is no significant increase in lateral force.
As the representative examples, we plotted the length, the advancing and receding positions, and the average velocity of the receding edge as a function of lateral force for a 10 μL water drop sliding across the micropillar-structured surfaces with different spacings (Fig. 9). The length of the drop is defined as the distance from the advancing edge to the receding edge of the TCL. The mass and volume of the drop were considered as constant, due to the suppression of the evaporation [34]. There was no visible change in the length before the onset of motion for each run, while with wider pillar spacing, namely higher hydrophobicity, the length at the initial position decreased, which corresponds to the 14
reducing contact area. The onset of motion is marked on the plot of position for each surface (Fig. 9A(d), 9B(d) and 9C(d)). It is easy to distinguish the onset of motion on the plot, since there would be a small decrease on the receding edge of position curve (Fig. 9A(d), 9B(d) and 9C(d)). Additionally, comparing the recorded sequential images (15 frames per second), we can find the visible motion of the drop. When the lateral force is below this threshold, the drop is at rest on the surface. After the drop starts moving, the motion is not smooth. After the receding edge of the drop jumps to the next pillar, which is closer to the advancing edge, it may experience a few jumps before it moves fast (Fig. 9d).
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Fig. 9. Plots of length (a), position of advancing and receding edges (b), and velocity (c) as a function of lateral force for a 10 μL water droplet sliding on the microstructure surfaces (cf. Fig. 2). Zoom in the plot of position for showing the onset of motion (d). A) surface #1 (25 μm spacing), B) surface #2 (37.5 μm spacing), C) surface #3 (50 μm spacing).
Fig. 10 shows the lateral forces required to slide the drops as a function of droplet volume on different micropillar array surfaces. As the size of drop increases from 8 μL to 12 μL, the retention force increases on these three surfaces. The highest retention force is recorded on the surface with a spacing of 25 μm. In comparison, the surface with the wider spacing requires less force for the drop to slide. These differences in retention force result from the change in pillar spacings. The surface with wider spacing has smaller roughness ratio which is defined as the ratio between the real surface area and projected area.[35] Namely, smaller spacing causes more contact area between drop and the surface; therefore, the retention force is stronger. Surprisingly, the differences in spacing between the three surfaces are the same (12.5 μm); however, the differences in retention force between the surface with 25 μm spacing and the surface with 37.5 μm spacing are approximately twice the difference between the surface with 37.5 μm and 50 μm spacing for the same drop size.
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40 Surface #1 Surface #2
F (N)
35
Surface #3
30 25 20 15
8
9
10
11
12
Volume (L) Fig. 10. Lateral adhesion forces for the water drops on the microstructure surfaces. These lateral forces are gained from the plots of position (c.f. Fig. 9d). Red-surface #1 (25 μm spacing), green-surface #2 (37.5 μm spacing), blue-surface #3 (50 μm spacing).
4.3. Roll-off Angles Previous studies have shown that the roll-off angles of water droplets decrease as the weights of the droplets increase [36–38]. For the tilting plate experiments, when measuring the roll-off angle, the analyzer was gradually tilted (see Fig. 11). It was observed that the TCL appears to be pinned down at the surface until the receding contact angle reached a minimal value. Based on the contact angle hysteresis, the information regarding water-repelling kinetics could be obtained, since the retention force against the drop motion is governed by contact angle hysteresis, as shown in Eq. (2). In addition, the retention forces can be measured directly from the lateral force measurements. According to Eq.
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(4), (5), and (8), the predicted roll-off angles are calculated and plotted in Fig. 12, which also shows the measurements of the roll-off angles for the surfaces with 25 μm, 37.5 μm and 50 μm micropillar spacing. From the results, the measured roll-off angles and predicted angles from three models show a visible decrease with increasing drop size on surface #1 and surface #2, and a slight decrease on surface #3 (~ 3). These findings are consistent with the previously reported results [39,40]. Furthermore, roll-off angle decreases with pillar spacing because there is less surface area in contact with the liquid droplet as spacing increases. Thus, our experiments revealed that the larger micropillar spacing surface, which has smaller area fraction and more hydrophobicity, is related to the more significant rolling ability of a water droplet.
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Fig. 11. The series of pictures shows a 10 μL water drop sliding on a microstructure surface #1 (25 m spacing) by tilting the contact angle analyzer counterclockwise (a) inclination angle = 0 (b) inclination angle = 10, the receding edge of the drop (the right edge of the droplet) still pinned on the surface (c) inclination angle = 19, receding edge was about to move (d) inclination angle = 19.5, the three phase contact line of the droplet started to move (e) inclination angle = 21 (f) inclination angle = 21.5
The comparisons in Fig. 12 indicate that the lateral retention force-based model of Eq. (8) excellently agrees with the measurements by tilting plate method on the micropillar- structured surfaces with different spacings. The deviations appear between our measurements and the contact angle
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hysteresis-based model of Eq. (4) for 25 μm and 37.5 μm spacings, while the deviations are not notable 24
for 50 μm spacing. Adding the correction factor, 𝑘 ( = 𝜋3 ) [22], the contact angle hysteresis-based model (Eq. (5)) partially fit our experimental measurements. The notable deviations between the experimental results and predictions of the sliding angles from the contact angle hysteresis-based models can be attributed to the overvalued or underestimated retention forces between the droplets and the surfaces in the models. However, the trend in the variation of roll-off angles with droplet volume for different surfaces has still been captured very well by the models.
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Fig. 12. Roll-off angles of droplets measured and calculated by different methods with different volumes on (a) surface #1 (25 μm spacing), (b) surface #2 (37.5 μm spacing), and (c) surface #3 (50 μm spacing). Dark cyan up-triangle - measured values from tilting plate method, magenta down-triangle - lateral retention force-based method, black square - contact angle hysteresis-based method with 𝑘 = 1 , blue circle - contact angle hysteresis-based method with 𝑘 = 24/𝜋3 [22].
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5. Conclusions In this study, we proposed a robust experimental method for determining lateral retention force, which was utilized to predict roll-off angles of water droplets on micropillar-structured surfaces, with spacing ranging from 25 μm to 50 μm. For lateral force measurement, the onset of motion was considered as the instant of the detachment of the receding edge of the three-phase contact line, and this motion was consistent with the sliding phenomena of water droplets on the inclined micropillarstructured superhydrophobic surfaces. We also introduced three models to explain the sliding behavior of a water droplet on an inclined surface. The lateral retention force-based model shows an excellent agreement with the experimental measurements. In addition, our experimental data reveals that roll-off angle was noticeably affected by droplet size and contact angle hysteresis. These findings and the proposed methods herein can be used to design micro-structured surfaces with specific wetting and droplet detachment characteristics. Also, for future study, these models can be a hint to predict the sliding angle of micro-structured hydrophilic surfaces if a droplet is able to slide off the surface without any residue.
Acknowledgment This work was supported by Center for Advances in Port Management (CAPM) of Lamar University, and Research Enhancement Grant (REG) Award at Lamar University. The authors would like to thank Carrie Martin for her assistance during SEM characterization. The authors appreciate the Center for
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Innovation, Commercialization and Entrepreneurship (CICE) at Lamar University for providing lab space. The authors acknowledge support by NSF Grants CMMI-1405109, 523 CBET-1428398, and CBET-0960229.
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26
Sliding of Water Droplets on Micropillar-structured Superhydrophobic Surfaces
Chun-Wei Yao a,*, Sirui Tangb, Divine Sebastiana, Rafael Tadmorb,c
A series of four pictures (a-d) showing a 10 μL water drop sliding on a microstructure surface (e) under lateral forces.
27
Highlights:
A robust experimental method was proposed for determining lateral retention force of a water droplet on a micropillar-structured superhydrophobic surface, which was utilized to predict roll-off angles of water droplets.
The lateral retention force-based model agrees well with the roll-off angle measurements.
The effects of droplet sizes and contact angle hysteresis on the roll-off angle were investigated.
28
Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
29
S0169-4332(19)33309-4 https://doi.org/10.1016/j.apsusc.2019.144493 APSUSC 144493
To appear in:
Applied Surface Science
Received Date: Revised Date: Accepted Date:
14 August 2019 19 October 2019 22 October 2019
Please cite this article as: C-W. Yao, S. Tang, D. Sebastian, R. Tadmor, Sliding of Water Droplets on Micropillar-structured Superhydrophobic Surfaces, Applied Surface Science (2019), doi: https://doi.org/10.1016/ j.apsusc.2019.144493
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© 2019 Published by Elsevier B.V.
Sliding of Water Droplets on Micropillar-structured Superhydrophobic Surfaces
Chun-Wei Yao a,*, Sirui Tangb, Divine Sebastiana, Rafael Tadmorb,c
a Dept.
of Mechanical Engineering, Lamar University, Beaumont, TX, 77710, USA
b Dan
F. Smith Department of Chemical Engineering, Lamar University, Beaumont, TX 77710, USA
c Dept
of Mechanical Engineering, Ben Gurion University of the Negev, Beer Sheva 8410501, Israel
* Correspondence: [email protected]; Tel.: +1-409-880-7008
Keywords: Sliding angle, Wetting properties, Micro textured surfaces
ABSTRACT Understanding the specific behavior of water droplet detachment from a micropillar-structured superhydrophobic surface is essential in a variety of potential applications. Herein, the sliding behavior of water droplets on three different micropillar-structured superhydrophobic surfaces was studied. From tilting plate experiments and retention force measurements, we probed the motion of water droplets with different volumes. The effects of droplet sizes and contact angle hysteresis on the roll-off angle were also investigated. Furthermore, three different models are proposed to estimate a roll-off angle. The lateral retention force-based model agrees well with the roll-off angle measurements, and the other two contact angle hysteresis-based models capture the trend in the variation of the roll-off angle.
1
1. Introduction Superhydrophobic surfaces have been in the limelight of the scientific community over the last decade owing to the plethora of applications ranging from membrane distillation to anti-icing and selfcleaning [1–3]. Generally, superhydrophobic surfaces are designed using materials with low surface energy and specific surface morphology [4,5]. Micro-textured hydrophobic surfaces have been studied in an effort to understand the effects of micro-structures on hydrophobicity [6–12]. Such surfaces are characterized by their high contact angles, which result from the fractal micro- or nanostructure of the surface [5]. The behavior of a droplet sliding off a micro-structured surface remains a challenge in many applications; therefore, many studies to date have focused on the sliding behavior of water droplets on inclined micro-textured superhydrophobic surfaces under the influence of gravity. Recent studies have also modified the classical Cassie-Baxter relation and proposed theoretical models [13–19]. For example, Cunjing Lv et al. [16] proposed an energy-based model that is suitable for calculating the sliding angle of the droplet in terms of known physical properties such as area fraction, droplet volume, and Young’s contact angle. However, experimental results have shown some inconsistency with theoretical predictions. It has been widely accepted that the retention force of liquid droplets sliding on solid surfaces is critically related to the contact angle hysteresis and the roll-off angle [20–22]. Various efforts to study the lateral adhesion force have been included in recent studies [23–26]. The most prominent one among them is the tilted plate method, which can be employed to effectively investigate static lateral adhesion
2
forces [23,27,28]. In the tilted plate method, the inclination of the surface where the droplet rests is controlled, and the motion of the droplet is recorded by a high-speed camera; thus, the roll-off angle can be accurately measured [23]. The static lateral adhesion forces can be conveniently calculated by considering the gravitational force necessary for the initiation of the droplet’s motion. A limitation to this approach is that it cannot be employed for accurate measurement of static lateral adhesion forces for smaller droplets (a few microliters), as their gravitational forces are too small to overcome the adhesion; thus, this method is applicable only with considerably larger droplets. Nguyen Thanh-Vinh et al. [29] used a MEMS-based two-axis force sensor array and measured the lateral adhesion force when a water droplet moves on the array of micropillar during sliding. However, this method is also valid only with a large droplet. As for the other methods, D.W. Pilat et al. [30] directly measured the lateral adhesion force when they moved drops over micropillar surfaces using a capillary tube. This method provided information about lateral adhesion forces only for very small volumes of up to 2 μL. Even though the relation between the lateral adhesion force and rolling ability of a water droplet on micro-structured surfaces was investigated in some recent studies, the sliding mechanism of the droplet on the micropillar-structured superhydrophobic surfaces has not yet been fully understood. This research considers the effect of surface hydrophobicity on droplet roll-off angles with specific micropillar-structured superhydrophobic surfaces, and proposes a possible way to effectively measure the lateral retention force and estimate a more accurate roll-off angle by different models. Moreover,
3
the effects of droplet size on contact angle hysteresis, roll-off angle, and moving velocity were investigated.
2. Experimental 2.1. Surface fabrication Micropillar array surfaces were fabricated using a photolithography process. The substrates used were single-side polished silicon wafers. The desired pattern consisting of an array of 25 m x 25 m micropillars was developed by using plasma and chemical resistant positive photoresist (SPR-220) with an adhesion promoter (AP8000). A total of three designs were exposed on the photoresist with a mask aligner, with edge-to-edge spacings of 25 m, 37.5 m and 50 m, respectively. The wafer then underwent an anisotropic dry etch process for 50 min to etch around the photoresist squares and towers was made at least 75 m in height. The wafer was then submerged in photoresist stripper AZ 400T for 24 hr to remove the photoresist. The substrate underwent an anisotropic dry etch process (Plasmatherm ICP-DRIE) to etch around the photoresist squares. The substrate then was left in the ICP-DRIE, and C4F8 plasma was run for 1 min to deposit a thin layer of Teflon-like hydrophobic material ((C2F4)n) on the whole surface. The combination of micro-pillar structures and the chemical coating makes surfaces superhydrophobic. The desired samples consisting of a micropillar array of 25 m x 25 m were made as shown in Fig. 1. At least 75 m height of micropillars was measured using optical profilometry (see Fig. 2).
4
Energy-Dispersive X-Ray Spectrouscopy (EDX) data indicates that the surfaces include a Carbon and Fluorine signature, suggesting the deposition of ((C2F4)n) on the surface as shown in Fig. 3.
Fig. 1. SEM images of the micro textured surfaces with a micropillar array with spacing values of (a) 25 m (b) 37.5 m, and (c) 50 m. All micropillar-structured surfaces exhibit a hydrophobic property when water droplets (10 L) are gently placed on them as shown in inserted pictures.
5
Fig. 2. (a) 3D Profilometer image of the micropillar surface with 37.5 m spacing and (b) the pillar height measurements.
Fig. 3. EDX spectrum analysis of the micropillar array surface. (𝑎)2
The area fraction of the solid-liquid interfaces (f) could be defined as 𝑓 = (𝑎 + 𝑏)2, where 𝑎 is the micropillar width, 𝑏 is the pillar spacing. The values of 𝑓 for the spacings of 25 μm, 37.5 μm and 50 μm surfaces are 0.25, 0.16 and 0.11, respectively.
2.2. Experiment setup Contact angle measurements were performed using a contact angle analyzer with tilting table (DSA25E, Krüss) for each spacing design. Advancing, receding, static, and roll-off angles were determined using droplet volumes in the range from 8 to 12 μL at room temperature (23℃). These angle values were obtained by averaging five measurements per sample. Advancing and receding contact angles were measured right before the droplet started to move and roll off the surface by tilting the 6
contact angle analyzer at a rate of 0.5°/s. The inclined angle of the tilting system was recorded as the roll-off angle of each droplet. Lateral retention force measurements were performed using a customized Centrifugal Adhesion Balance apparatus (see Fig. 4) [24,31], which can measure the lateral retention force directly. There is a shaft that can rotate with the help of a motor, and a centrifugal arm is attached to the shaft. When the shaft rotates, the centrifugal arm rotates in the horizontal plane. At the end of the centrifugal arm, there is a chamber in which a camera is mounted to monitor the motion of the drop. Sequential images were taken at the rate of 15 frames per second. The samples (surface and liquid drop) were placed in the goniometer inside the chamber.
Fig. 4. Images of the Centrifugal Adhesion Balance. a) Structure of CAB, b) details of the goniometer inside the chamber. (1) Camera (lens), (2) mirror (45 ° tilted), (3) sample stage, (4) light source, (5) satellite drops, and (6) central drop. Reprinted with permission from [31]. Copyright (2019) American Chemical Society.
7
In this study, we defined the forces which are parallel to the surface as the lateral force 𝐹𝑙𝑎𝑡 as shown in Fig. 5 [24,31]. Namely, the lateral force 𝐹𝑙𝑎𝑡 is the centrifugal force which starts from zero and increases with set angular acceleration, and can be calculated as 𝐹𝑙𝑎𝑡 = 𝑚𝜔2𝐿
(1)
where 𝑚 is the mass of the liquid drop, 𝜔 is the angular velocity of the rotation of the centrifugal arm, and 𝐿 is the distance from the central axis of the system to the center of the drop.
Fig. 5. Schematic illustration of a drop resting on the horizontal, rotating plate of the apparatus. During the rotation, the drop experiences a centrifugal force in the lateral direction which is parallel to the surface and a gravitational force which is perpendicular to the surface.
3. Roll-off Angle Models 3.1. Contact Angle Hysteresis-Based Model
8
In Contact Angle Hysteresis-Based Model, the weight of the droplet is balanced by the surface tension force at the onset of the droplet sliding. This model was verified by Furmidge [20] and has been considered in this paper as follows: 𝑚𝑔sin 𝛼 = 2𝑅𝛾𝐿𝐺(cos 𝜃𝑅 ― cos 𝜃𝐴)
(2)
where 2𝑅 is a characteristic length representing the size of the droplet contour, 𝛾𝐿𝐺 is the surface tension, 𝜃𝑅 is the receding angle, 𝜃𝐴 is the advancing angle, 𝑔 is the gravitational acceleration, and 𝛼 is the roll-off angle. We define R is the radius of the droplet prior to deformation, which can be estimated by using the following equation [32]: 𝑅=
(
3𝑉 𝜋(1 ― cos 𝜃)2(2 + cos 𝜃)
1 3
)
(3)
where 𝑉 is the drop volume and is the apparent contact angle.
Combining eqs. (2) and (3) yields the following equation: sin 𝛼 =
2𝛾𝐿𝐺 𝑚𝑔
(cos 𝜃𝑅 ― cos 𝜃𝐴)
(
1 3
3𝑉
𝜋(1 ― cos 𝜃)2(2 + cos 𝜃)
)
(4)
ElSherbini et al. [22] introduced a shape-factor 𝑘 ( = 24/𝜋3) in Eq. (2). Therefore, Eq. (4) can be modified as:
sin 𝛼 =
2𝑘𝛾𝐿𝐺 𝑚𝑔
(cos 𝜃𝑅 ― cos 𝜃𝐴)
(
3𝑉 𝜋(1 ― cos 𝜃)2(2 + cos 𝜃)
1 3
)
9
(5)
Fig. 6. Illustration of the tilted surface at a specific droplet roll-off angle 𝛼.
3.2. Lateral Retention Force-Based Model We define the detachment of the receding edge of the three-phase contact line (TCL) as the onset of motion. In this model, the lateral component of the gravitational force 𝐹𝑔 for the droplet on tilted surface under gravity, as shown in Fig. 6, is given as (6)
𝐹𝑔 = ― 𝜌𝑔𝑉sin 𝛼
where 𝜌 and 𝑉 denote the density of the liquid drop and the volume of the drop, respectively. Accounting for the lateral component of the gravitational force and lateral retention force at the moment that a droplet starts to move yields the following equation: (7)
𝐹𝑙𝑎𝑡 + 𝐹𝑔 = 0
Based on our lateral force measurement, combining eqs. (1), (6), and (7) yields the following equation: sin 𝛼 =
𝑚𝜔2𝐿
(8)
ρV𝑔
This roll-off model determines 𝛼 by the measured lateral force (centrifugal force) and the gravitational force. 10
4. Results and discussion 4.1. Contact Angles of Water Droplets on Micropillar-structured Superhydrophobic Surfaces The advancing, receding, and static contact angles and the contact angle hysteresis for different sizes of water droplets on the micropillar structured surfaces with different spacings are plotted in Fig. 7. The plot reveals that the advancing, receding, and static contact angles are not a function of drop size for those small droplets. Contact angle hysteresis is defined as the difference between the advancing and the receding contact angles. Comparing different surfaces, Fig. 7 shows that contact angle hysteresis reduces as pillar spacing increases, though the advancing contact angles keep consistent. Also, surfaces with larger pillar spacing—which causes a smaller area fraction and a higher static contact angle— generally exhibit a smaller contact angle hysteresis than surfaces with smaller pillar spacing, which causes a larger area fraction and a lower static contact angle. These differences in static contact angles are in an agreement with Hou et al.’s work which shows the static contact angle increases with increasing pillar spacing until it reaches a maximum value (70 μm) [33] which is beyond the largest pillar spacing of our surfaces (50 μm). It indicates that the wetting state is Cassie–Baxter’s state caused by the microscale structures, which provide spaces for air to be trapped between the droplet and the surface, and this air pocket acts as a cushion to support the water drops existing between the micropillars.
11
12
Fig. 7. Advancing, receding and static contact angles and the contact-angle hysteresis of the droplets with different volumes on (a) surface #1 (25 μm spacing), (b) surface #2 (37.5 μm spacing), and (c) surface #3 (50 μm spacing). Red-advancing contact angle, blue-static contact angle, green-receding contact angle.
4.2. Lateral Force Measurement Water drops of various volumes were placed on a horizontal microstructure surface that was fixed in the chamber. It was observed that when the lateral force measurement system starts running, the drops experience an increasing lateral force (centrifugal force) that is parallel to the surface. The angular velocity of the rotation increases linearly at the rate of 0.7 rpm/s. Fig. 8 denotes the shapes of the drop during different phases of its motion. Initially, when the lateral force is unable to overcome the lateral retention force, the TCL is pinned to the surface with increasing advancing contact angles and decreasing receding contact angles as the drop deforms. Fig. 8b shows the moment that the receding edge of a 10 μL water drop is about to move under 33 μN lateral force. When lateral force 𝐹𝑙𝑎𝑡 > 33 N, the receding edge depins and the drop starts moving. We observe that after the receding edge detaches from the surface, it “jerks” to the next pillar, and this motion is consistent with the sliding phenomena of water droplets on the inclined micropillar-structured superhydrophobic surfaces. As a function of lateral force 𝐹𝑙𝑎𝑡, the drop undergoes a fast motion after 𝐹𝑙𝑎𝑡 > 39 N.
13
Fig. 8. A series of four pictures (a-d) showing a 10 μL water drop sliding on a microstructure surface #1 (25 m spacing) under lateral forces (a) 𝐹𝑙𝑎𝑡 = 0, (b) 𝐹𝑙𝑎𝑡 = 33 N, (c)&(d) 𝐹𝑙𝑎𝑡 = 39 N. From (a) to (b) the receding edge of the drop pinned on the surface with increasing lateral force. The time interval is 0.067 s between (c) and (d), so there is no significant increase in lateral force.
As the representative examples, we plotted the length, the advancing and receding positions, and the average velocity of the receding edge as a function of lateral force for a 10 μL water drop sliding across the micropillar-structured surfaces with different spacings (Fig. 9). The length of the drop is defined as the distance from the advancing edge to the receding edge of the TCL. The mass and volume of the drop were considered as constant, due to the suppression of the evaporation [34]. There was no visible change in the length before the onset of motion for each run, while with wider pillar spacing, namely higher hydrophobicity, the length at the initial position decreased, which corresponds to the 14
reducing contact area. The onset of motion is marked on the plot of position for each surface (Fig. 9A(d), 9B(d) and 9C(d)). It is easy to distinguish the onset of motion on the plot, since there would be a small decrease on the receding edge of position curve (Fig. 9A(d), 9B(d) and 9C(d)). Additionally, comparing the recorded sequential images (15 frames per second), we can find the visible motion of the drop. When the lateral force is below this threshold, the drop is at rest on the surface. After the drop starts moving, the motion is not smooth. After the receding edge of the drop jumps to the next pillar, which is closer to the advancing edge, it may experience a few jumps before it moves fast (Fig. 9d).
15
16
Fig. 9. Plots of length (a), position of advancing and receding edges (b), and velocity (c) as a function of lateral force for a 10 μL water droplet sliding on the microstructure surfaces (cf. Fig. 2). Zoom in the plot of position for showing the onset of motion (d). A) surface #1 (25 μm spacing), B) surface #2 (37.5 μm spacing), C) surface #3 (50 μm spacing).
Fig. 10 shows the lateral forces required to slide the drops as a function of droplet volume on different micropillar array surfaces. As the size of drop increases from 8 μL to 12 μL, the retention force increases on these three surfaces. The highest retention force is recorded on the surface with a spacing of 25 μm. In comparison, the surface with the wider spacing requires less force for the drop to slide. These differences in retention force result from the change in pillar spacings. The surface with wider spacing has smaller roughness ratio which is defined as the ratio between the real surface area and projected area.[35] Namely, smaller spacing causes more contact area between drop and the surface; therefore, the retention force is stronger. Surprisingly, the differences in spacing between the three surfaces are the same (12.5 μm); however, the differences in retention force between the surface with 25 μm spacing and the surface with 37.5 μm spacing are approximately twice the difference between the surface with 37.5 μm and 50 μm spacing for the same drop size.
17
40 Surface #1 Surface #2
F (N)
35
Surface #3
30 25 20 15
8
9
10
11
12
Volume (L) Fig. 10. Lateral adhesion forces for the water drops on the microstructure surfaces. These lateral forces are gained from the plots of position (c.f. Fig. 9d). Red-surface #1 (25 μm spacing), green-surface #2 (37.5 μm spacing), blue-surface #3 (50 μm spacing).
4.3. Roll-off Angles Previous studies have shown that the roll-off angles of water droplets decrease as the weights of the droplets increase [36–38]. For the tilting plate experiments, when measuring the roll-off angle, the analyzer was gradually tilted (see Fig. 11). It was observed that the TCL appears to be pinned down at the surface until the receding contact angle reached a minimal value. Based on the contact angle hysteresis, the information regarding water-repelling kinetics could be obtained, since the retention force against the drop motion is governed by contact angle hysteresis, as shown in Eq. (2). In addition, the retention forces can be measured directly from the lateral force measurements. According to Eq.
18
(4), (5), and (8), the predicted roll-off angles are calculated and plotted in Fig. 12, which also shows the measurements of the roll-off angles for the surfaces with 25 μm, 37.5 μm and 50 μm micropillar spacing. From the results, the measured roll-off angles and predicted angles from three models show a visible decrease with increasing drop size on surface #1 and surface #2, and a slight decrease on surface #3 (~ 3). These findings are consistent with the previously reported results [39,40]. Furthermore, roll-off angle decreases with pillar spacing because there is less surface area in contact with the liquid droplet as spacing increases. Thus, our experiments revealed that the larger micropillar spacing surface, which has smaller area fraction and more hydrophobicity, is related to the more significant rolling ability of a water droplet.
19
Fig. 11. The series of pictures shows a 10 μL water drop sliding on a microstructure surface #1 (25 m spacing) by tilting the contact angle analyzer counterclockwise (a) inclination angle = 0 (b) inclination angle = 10, the receding edge of the drop (the right edge of the droplet) still pinned on the surface (c) inclination angle = 19, receding edge was about to move (d) inclination angle = 19.5, the three phase contact line of the droplet started to move (e) inclination angle = 21 (f) inclination angle = 21.5
The comparisons in Fig. 12 indicate that the lateral retention force-based model of Eq. (8) excellently agrees with the measurements by tilting plate method on the micropillar- structured surfaces with different spacings. The deviations appear between our measurements and the contact angle
20
hysteresis-based model of Eq. (4) for 25 μm and 37.5 μm spacings, while the deviations are not notable 24
for 50 μm spacing. Adding the correction factor, 𝑘 ( = 𝜋3 ) [22], the contact angle hysteresis-based model (Eq. (5)) partially fit our experimental measurements. The notable deviations between the experimental results and predictions of the sliding angles from the contact angle hysteresis-based models can be attributed to the overvalued or underestimated retention forces between the droplets and the surfaces in the models. However, the trend in the variation of roll-off angles with droplet volume for different surfaces has still been captured very well by the models.
21
Fig. 12. Roll-off angles of droplets measured and calculated by different methods with different volumes on (a) surface #1 (25 μm spacing), (b) surface #2 (37.5 μm spacing), and (c) surface #3 (50 μm spacing). Dark cyan up-triangle - measured values from tilting plate method, magenta down-triangle - lateral retention force-based method, black square - contact angle hysteresis-based method with 𝑘 = 1 , blue circle - contact angle hysteresis-based method with 𝑘 = 24/𝜋3 [22].
22
5. Conclusions In this study, we proposed a robust experimental method for determining lateral retention force, which was utilized to predict roll-off angles of water droplets on micropillar-structured surfaces, with spacing ranging from 25 μm to 50 μm. For lateral force measurement, the onset of motion was considered as the instant of the detachment of the receding edge of the three-phase contact line, and this motion was consistent with the sliding phenomena of water droplets on the inclined micropillarstructured superhydrophobic surfaces. We also introduced three models to explain the sliding behavior of a water droplet on an inclined surface. The lateral retention force-based model shows an excellent agreement with the experimental measurements. In addition, our experimental data reveals that roll-off angle was noticeably affected by droplet size and contact angle hysteresis. These findings and the proposed methods herein can be used to design micro-structured surfaces with specific wetting and droplet detachment characteristics. Also, for future study, these models can be a hint to predict the sliding angle of micro-structured hydrophilic surfaces if a droplet is able to slide off the surface without any residue.
Acknowledgment This work was supported by Center for Advances in Port Management (CAPM) of Lamar University, and Research Enhancement Grant (REG) Award at Lamar University. The authors would like to thank Carrie Martin for her assistance during SEM characterization. The authors appreciate the Center for
23
Innovation, Commercialization and Entrepreneurship (CICE) at Lamar University for providing lab space. The authors acknowledge support by NSF Grants CMMI-1405109, 523 CBET-1428398, and CBET-0960229.
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Sliding of Water Droplets on Micropillar-structured Superhydrophobic Surfaces
Chun-Wei Yao a,*, Sirui Tangb, Divine Sebastiana, Rafael Tadmorb,c
A series of four pictures (a-d) showing a 10 μL water drop sliding on a microstructure surface (e) under lateral forces.
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Highlights:
A robust experimental method was proposed for determining lateral retention force of a water droplet on a micropillar-structured superhydrophobic surface, which was utilized to predict roll-off angles of water droplets.
The lateral retention force-based model agrees well with the roll-off angle measurements.
The effects of droplet sizes and contact angle hysteresis on the roll-off angle were investigated.
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Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:
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