Droplet Detachment by Air Flow for Microstructured Superhydrophobic

Article pubs.acs.org/Langmuir

Droplet Detachment by Air Flow for Microstructured Superhydrophobic Surfaces Pengfei Hao,* Cunjing Lv, and Zhaohui Yao Department of Engineering Mechanics, Tsinghua University, Beijing 100084, China S Supporting Information *

ABSTRACT: Quantitative correlation between critical air velocity and roughness of microstructured surface has still not been established systematically until the present; the dynamics of water droplet detachment by air flow from micropillar-like superhydrophobic surfaces is investigated by combining experiments and simulation comparisons. Experimental evidence demonstrates that the onset of water droplet detachment from horizontal micropillar-like superhydrophobic surfaces under air flow always starts with detachment of the rear contact lines of the droplets from the pillar tops, which exhibits a similar dynamic mechanism for water droplet motion under a gravity field. On the basis of theoretical analysis and numerical simulation, an explicit analytical model is proposed for investigating the detaching mechanism, in which the critical air velocity can be fully determined by several intrinsic parameters: water−solid interface area fraction, droplet volume, and Young’s contact angle. This model gives predictions of the critical detachment velocity of air flow that agree well with the experimental measurements.

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INTRODUCTION Interest in superhydrophobic surfaces has been growing rapidly in recent years. Because of their special wetting properties, superhydrophobic surfaces have shown wide applications in self-cleaning, water collection, friction-drag reduction, anticorrosive protective coatings, and microfluidics.1−5 Detachment of a liquid droplet from the solid surface, as well as its corresponding dynamic behavior, is among the fundamental problems of wettability and its applications. In many practical applications, such as self-cleaning,5 the dynamical process of droplet detachment off a microstructured surface is a key issue. The droplet will run away if the adhesive force (generated from contact surface) is overcome by the external drag forces (generated from gravity,6−12 vibration,13−17 air flow,18−22 etc.). Sliding behaviors of a water droplet on an inclined microstructured superhydrophobic surface under a gravity field has been reported in previous work.6−12 Suzuki et al.6 evaluated the relationship between sliding acceleration and dynamic contact angle hysteresis of water droplets on a fluoroalkylsilane-treated silicon surface. Song7 investigated the static and dynamic hydrophobicities of water droplets on a patterned surface prepared using fluoroalkylsilane with different molecular chain lengths. These results suggested that it is feasible to control the sliding acceleration of water droplets over hydrophobic surfaces by changing the surface structure patterns and chemical composition. Lv et al.9 established an explicit analytical model in which the sliding angle could be fully determined by the intrinsic parameters of the system, and detachment of a droplet mainly determined by the rear contact line was revealed, which was consistent with results of other researchers.23,24 Compared with detachment driven by gravity field, air flow is an easier method to remove droplets on © 2013 American Chemical Society

superhydrophobic surfaces, and it is widely used in applications such as avoidance of airfoil icing, water management in fuel cells, and cleaning.18−22,25,26 For example, Zhang18 studied the mechanisms of water droplet removal from the fuel cell gas diffusion membrane surface as well as the gas channels, employing the air flow over surface technique. Fan25 revealed three modes of motion about a liquid droplet on a hydrophilic smooth surface under air flow. Sommers26 presented a model to calculate the critical air flow force for water droplet departure from vertical surface with microgrooves, but the advancing and receding contact angles need to be taken into account. Cho21 computed drag forces of water droplet in a PEFC gas flow channel, the detachment velocity is analyzed by comparing the wall adhesion and drag forces, and an expression relating the Weber number to the Reynolds number using the detachment velocity is developed. However, there was a lack of any experimental data to validate his analytical solutions. Milne22 investigated shedding of droplets by laminar airflow on surfaces with various wetting properties. It was found that the contact angle is very influential in determining the minimum required air velocity for droplet shedding. Their experimental data showed the lowest critical air velocity for droplet shedding on a superhydrophobic substrate. However, research on the detachment behavior of droplets off superhydrophobic surfaces under air flow remains limited, and some fundamental issues are still not solved. For example, quantitative correlation among adhesion force, the critical velocity and roughness distribution, Received: December 10, 2012 Revised: March 15, 2013 Published: April 4, 2013 5160

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and wetting property of the superhydrophobic surfaces is still not established. In the present study, the relationship between the surface topology and the critical velocity of air flow is investigated systematically with specific designed micropillar-like superhydrophobic substrates with low contact angle hysteresis. On the basis of experimental observations about the onset of detachment and numerical simulations of the drag forces on a droplet, the same mechanism of detachment by gravity and air flow is revealed, and an explicit analytical model is proposed for studying the detachment mechanism driven by air flow. In this innovative model, the critical air velocity Uc can be predicted by the area fraction f of water−solid interface area, droplet volume V, and Young’s contact angle ϕ0, and such a physical model is proposed for studying the detachment mechanism for the first time.

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Table 1. Geometrical Parameter about the Samples no.

length L (μm)

space S (μm)

area fraction f

height H (μm)

1 2 3 4 5

4 4 4 4 4

4 6 8 12 16

0.25 0.16 0.1111 0.0625 0.04

20 20 20 20 20

EXPERIMENTAL SECTION

A series of micropillar-like surfaces were fabricated by photolithography and etching of inductively coupled plasma (ICP).9 After the etching process, the remaining protective layers were removed from the silicon wafer. To make the silicon wafer hydrophobic, a selfassembled monolayer (SAM) of a hydrophobic substance was applied onto the surface: Octadecyltrichlorosilane (OTS) of formula C18H37Cl3Si (Acros Organics) was used for this purpose. The surface was first treated with a “Piranha” solution, composed of 70% sulfuric acid (H2SO4) solution with 98% concentration and 30% hydrogen peroxide (H2O2) solution with 20% concentration. The process consists of immersing the surface in the “Piranha” solution and keeping it at a constant temperature of 90 °C for 30 min inside a heater. The surface was then rinsed with deionized water and dried. In a completely dry container, 0.1 mL of OTS is mixed with 25 mL of hexadecane. The surface was rinsed with this new solution and baked in an oven for 20 min. Then the surface was treated with chloroform for 15 min to remove any dust, and finally the surface was soaked in anhydrous alcohol for 30 min and dried. After chemical modification, the Young’s contact angle ϕ0 was measured to be 112° ± 2° on the smooth surface. Topology of harvested microstructured surfaces with square pillars is shown in Figure 1a,b, in which L is the side length of the square

Figure 2. Schematics of the experimental setup used to capture the dynamic wetting properties of a water droplet on a microstructured superhydrophobic surface under air flow. pressure regulator and the air velocity is adjusted by a throttle valve. The air flow velocity on the upstream of the water droplet is measured by an air velocity meters (8385 TSI Cop. USA) with accuracy of 0.01 m/s. When a droplet rests (is sessile) on a substrate and is exposed to air flow, the droplet will be moved if the adhesion force of the droplet on the surface is overcame by the external drag forces on the droplet. Here, we define this air flow velocity as the critical velocity Uc. In our experiment, first, a 10 μL sessile droplet is placed on the micropillarlike superhydrophobic surfaces. Then the velocity of the air flow is increased smoothly by adjusting the throttle valve until the droplet begins to move (see Figure 3 and Movies 1,2, Supporting Information). Before the onset of movement of the water droplet, there is a small deformation and oscillation occurs on the droplet under the action of air drag. When the velocity of the air flow reaches the critical value, the contact line of the water droplet starts to move (see Figure 3c). The moving details of water droplets exposed to air flow are taken by a high-speed computer-controlled digital camera (200fps, PIKE F032, AVT Ltd., Germany) connected to the contact angle meter.

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RESULTS AND DISCUSSION Figure 3 shows the details of the onset of moving a 10 μL droplet on the micropillar-like superhydrophobic surface (L = 20 μm and S = 30 μm), with respective enlarged pictures of the front and the rear contact lines. As shown in Figure 3a,b, first, the advancing contact angle θA of the droplet increases and the receding contact angle θR decreases under the air flow. Figure 3c shows clearly that the rear contact line (as indicated by the yellow arrow) detaches from the micropillar and moves forward; accordingly, the center of gravity of the droplet moves forward along the direction of the air flow. But at this moment, the front contact line (as indicated by the white arrow) is still pinning the micropillar. In Figure 3d, deformation of the water droplet is recovered because of the surface tension, and the center of gravity retreats; at this moment, neither the front line nor the rear contact line moves. In Figure 3e, the advancing contact angle continues to increase to almost 180°; the front contact line adheres to the next pillar but the rear contact line is still pinning (see Movie 1, Supporting

Figure 1. Pillar-like microstructured surfaces: (a) top schematic view of the substrate; (b) scanning electron microscope (SEM) images of one sample (L = 4 μm, S = 12 μm, H = 30 μm, f = 0.0625). pillar, S is the spacing between the neighboring pillars, and H is the height of the pillar. In our experiments, the height H of the pillars is fixed at 20 μm, and the side length L is held constant at 4 μm. Finally, 5 types of samples are investigated in the experiments, and the corresponding area fractions f = L2/(L + S)2 are 0.04, 0.0625, 0.1111, 0.16, and 0.25 (see Table 1). The static contact angle and the sliding angle were measured by employing a commercial contact angle meter (JC2000CD1). The experimental setup for the air flow test is schematically shown in Figure 2. A 200-mm-long stainless tube with inner diameter 15 mm is set up in front of the test sample and is connected to an air compressor. The distance between the outlet of the tube and the water droplet is about 15 mm. The pressure of the air flow is adjusted by a 5161

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Figure 3. Observation of onset of movement of a 10 μL water droplet on a micropillar-structured surface (L = 20 μm and S = 30 μm) under controlled horizontal air flow: (a) schematic view of the water droplet under horizontal air flow; (b) the state before onset of the droplet moving; (c) the rear contact line (yellow arrow) detaches from the micropillar and moves forward, but the front contact line (white arrow) is still pinning; (d) deformation of the droplet is recovered, and the center of gravity retreats because of the surface tension; (e) the advancing contact angle continues to increase and the front contact line adheres to the next pillar (see also Movie 1, Supporting Information.).

Figure 4. Wetting properties of a 10 μL water droplet on the micropillar-structured superhydrophobic surfaces with different area fractions: (a) critical air velocity Uc vs area fraction f; (b) apparent contact angle ϕ vs area fraction f; (c) sliding angle α vs area fraction f.

explicit analytical model, by which the sliding angle is fully determined by the water−solid interface area fraction f, droplet volume V, and Young’s contact angle ϕ0:

Information). In this case, an approximate estimation about the horizontal translation of the water droplet gravity center is (L + S). The detailed process shown in the above pictures reveals that the onset of movement of a water droplet under horizontal air flow on micropillar-structured hydrophobic surfaces always starts with the detachment of the rear contact lines of the droplet from the pillar tops, which is consistent with the sliding phenomena of a water droplet on an inclined micropillarstructured hydrophobic surface under gravity.9,10 Therefore, we conclude that the mechanisms of motion are the same for water droplets under air flow and gravity. In our previous work,9 we obtained the relationship between the sliding angle and the adhesion force for a water droplet sliding on a micropillarstructured hydrophobic surface. We will show that the adhesion forces for a droplet on the same substrate under air flow and gravity are equivalent to each other, and we could further obtain the critical flow velocity Uc based on our experimental observations and theoretical analysis. Figure 4a gives the relationship between the critical velocity and the water−solid interface area fractions of a 10 μL water droplet on the micropillar-structured superhydrophobic surfaces. The critical air velocity increases with the area fraction, which indicates that the adhesion force of the water droplet on such surfaces with smaller area fraction is lower and the droplet could be removed by the air flow more easily. We also performed a series of experiments to measure the contact angles and the sliding angles9 of water droplets on such superhydrophobic surfaces. Figure 4b shows that the measured values of the apparent contact angles are consistent with Cassie’s theory.27 Furthermore, solid squares in Figure 4c show the relationship between the measured value of the sliding angles and the area fraction f. Recently, Lv et al.9 established an

sin α =

2 3 3 γLV ρw g 3 πV 2 2(1 + cos ϕ0) − (1 + cos ϕ0)2 f

× 3

4 − 3(1 + cos ϕ0)2 f 2 + (1 + cos ϕ0)3 f 3

× (1 + cos ϕ0)f

(1)

where α, γLV, ρw, and g are the sliding angle, liquid−vapor surface tension, density of water, and acceleration of gravity, respectively. By comparisons shown in Figure 4c, we can see there is excellent agreement between the experimental data and the predictions using eq 1. The deduction of eq 1 depends on the assumption that the increase of the total interfacial energy equals the decrease of the gravity potential during the onset of water droplet detachment. Here, we want to emphasize that this idea could be used to predict the critical air flow velocity for droplet detachment on such superhydrophobic surfaces. Moreover, the drag force Fd for the droplet on such tilted surfaces under gravity is given as9 Fd = ρw gV sin α

(2)

Instead of gravity, as shown in Figure 3, for a droplet exposed to the air flow, at the onset of detachment, all forces on a droplet, including the water−solid interface adhesion force Fa, are balanced to keep the droplet stationary. The drag force Fd created by air flow exerted on the droplet is the sum of the pressure Fp and viscous forces Fv: 5162

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1 ρ U 2AcCd (3) 2 a where ρa is the density of the air, U is the free-stream air velocity, Cd is the drag coefficient, Ac is the frontal area (crosssection, as shown in Figure 3a) of the water droplet, which could be estimated approximately as Ac = R2(ϕ − sin ϕ cos ϕ) where R is the radius of the water droplet and ϕ is the apparent contact angle of the droplet on the micropillar-like superhydrophobic surface. For a static droplet exposed to air flow, the total drag force will be balanced by the water−solid interface adhesion force arising from the surface tension. The maximum adhesion force of the water droplet on the surface will equal the total drag force under critical air velocity. When air velocity exceeds the critical value, the droplet starts to move. However, to the best of the author’s knowledge, there was no analytical solution to calculate the accurate total drag force of a spherical cap on a plate under air flow. In this paper, by employing a CFD (Computational Fluid Dynamics) simulation, we obtained the accurate total drag force Fd exerted on the static droplet under air flow by integrating the pressure distribution and the viscous friction over its spherical cap. When Fd is obtained, accordingly, we can further get Cd by eq 3. In the simulation, we assume negligible deformation of the droplet and nonslip boundary condition between the air flow and the droplet surface. In other words, the water droplet is assumed to be a solid spherical cap in the plate surface. Air flow is introduced at the inlet boundary with uniform speed and it exits through the outflow boundary. A commercial CFD code (Fluent 6.3.26) was used to solve the 3D nonlinear governing equations (Navier−Stokes equations). As shown in Figure 5, the red solid triangles are the simulation results of the total drag force Fd of a 10 μL water

below 0.2, which also means the adhesion forces under two different working conditions are equivalent to each other. For a droplet on a substrate with the largest area fraction ( f = 0.25), the drag force seems smaller, as if caused by gravity. One reasonable explanation is that as we know, the drag force/ adhesion force will increase with the water−solid area fraction, so a larger value of air flow velocity is needed to blow the droplet away; in this case, the deformation of the droplet will be considerable. Serious oscillation of the water droplet may cause turbulence near the water−air interface, which will lead to the increase of the drag force. Drag force increased by turbulence could not be considered in CFD: we believe this is the main source of the errors. The agreement of drag force/adhesion force for f ≤ 0.2 under air flow and gravity is contrary to the findings in Milne’s work.22 In Milne’s experiments, difference between θmax and θmax under air flow was 31.9° ± 8.9°, which was much larger than the value 20° ± 5.5° for the droplet on a tilted plate under gravity. However, considering the relatively large uncertainty of the contact angle measurement due to oscillation of the droplet under air flow and the heterogeneity of the superhydrophobic surface, such differences are not very significant. In our experiment, for example, a 10 μL water droplet on the superhydrophobic surface with L = 4 μm, f = 0.0625, differences between θmax and θmin are 20.4° ± 3.5° under air flow and 16.9° ± 2.3° under gravity, respectively. On the basis of the experimental observations (Figure 3 and ref 9) and the measurements of the drag force (Figure 5), we reveal that there are similar dynamic characteristics of droplet detachment on superhydrophobic surfaces under air flow as that caused by gravity on a tilted plate. As we know, the drag coefficient Cd changes with the droplet shape and the Reynolds number.22 Previously, Al-Hayes et al. studied detachment of gas bubbles from hydrophilic smooth surface in flowing liquids,28 and they gave estimations of the relationship between the drag coefficient and the Reynolds number in the range of 4 to 400. However, no reported correspondence could be found between Cd and the Reynolds number in the range of this study. On the basis of the Stokes law,29 we present an improved simple formula to predict Cd for different Reynolds number and droplet shape:

Fd = Fp + Fv =

Cd =

24 +a Re

(4)

Here, Re is the Reynolds number of the droplet determined by Re = Udρa/μ, where d is the diameter of the droplet and ρa and μ are the mass density and the dynamic viscosity of the air. In eq 4, a is used to describe the influence on the drag coefficient for an object with nonspherical shape. As we know, the different between the advancing and the receding contact angles is small on superhydrophobic surface, so the shape of the droplet under air flow is not far away from a spherical cap. For convenience, it is reasonable for us to assume that a is only dependent on the static contact angle of the water droplet. Figure 6a shows that the value of a decreases with increase of the contact angle by CFD. By means of the least-squares method, a linear function could be obtained as

Figure 5. Drag force Fd of a 10 μL droplet on the micropillar-like surface with various area fractions; the red solid triangles are the simulation results of the total drag force under the critical air flow velocity, and the black solid circles are the experimental results of the drag force on such tilted surfaces under gravity.

droplet under the critical air flow velocity by CFD (see the Supporting Information), which also indicated that the water− solid interfacial adhesion force increases with the solid area fraction. The black solid circles are the experimental data of the drag force Fd of the same water droplet but on tilted surfaces calculated by eq 2. It is found that the maximum drag force of the water droplet on the micropillar-like superhydrophobic surfaces under critical air flow velocity agrees very well with the drag force of the same droplet on the same inclined surfaces under gravity when the value of the water−solid area fraction is

a = 1.6355 − 0.00788ϕ

(5)

From the above analysis, it shows that, on one hand, we can predict the value of Cd analytical by combination of eq 4 and eq 5, but on the other hand, we can get the value of Fd by eq 3. Figure 6b shows the drag coefficients Cd of a 10 μL water droplet on a microstructured surface ( f = 0.0625, ϕ = 161°, a = 5163

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Figure 6. (a) Parameter a of a 10 μL droplet as a function of contact angle; (b) drag coefficient Cd as a function of the Reynolds number.

Figure 7. Critical air velocity of experimental measurements and predicted value: (a) relationship between Uc and f for a 10 μL water droplet; (b) relationship between Uc and the droplet volume when f = 0.0625; (c) comparison of eq 7 with other reference data from water−SHS system (see Figure 5, ref 22).

showed the relationship between Uc and f of a 10 μL water droplet under air flow on the micropillar-like superhydrophobic surfaces, in which the predictions (red hollow circles) by our analytical model (eq 7) are in good agreement with the experimental measurements (black solid squares). We also studied the relationship between Uc and V on substrate with f = 0.0625 in Figure 7b; the experimental data and the predicted results by employing eq 7 are consistent with each other. Both experimental and prediction data indicated that the critical velocity of the air flow increased with the decrease of the droplet volume. This means that the smaller droplets are more difficult to remove than the larger ones. This conclusion is consistent with the experimental observations by Milne22 and the simulation data by Cho.21 Interestingly, although our analytical model (eq 7) is developed based on the dynamic mechanisms for squareshaped pillar-like structured surfaces, we find it could be still applicable for superhydrophobic surfaces with other types of microstructures.22 Figure 7c is plotted from the measured critical velocity for water−SHS system in Milne’s experiments.22 Even though there is no detailed information about the wetting at the liquid−solid interface, it is plausible to assume the water droplet was in Cassie−Baxter wetting state because it has very large apparent contact angle and very low contact angle hysteresis (see line 19, column 2, column 4, and column 6, Table 1, ref 22). Without loss of generality, it is reasonable to get the wetting properties of a water−SHS system by employing Young’s contact angle ϕ0 = 108° and solid area fraction f = 0.1; we can see that these measured results agree very well with the prediction from eq 7. Even though our theoretical model is applicable on such superhydrophobic substrates with homogeneous roughness,

0.37) for Reynolds number ranging from 130 to 400 by CFD (black squares) based on eq 3. The simulation results agree well with the predictions (red line) by the analytical model given by eq 4 and eq 5. When detachment happens under the critical air flow velocity Uc, the drag force can be obtained by putting Cd in eq 4 to eq 3 Fd =

⎞ ⎛ 24μ 1 ρa Uc2Ac⎜⎜ + a⎟⎟ 2 ⎠ ⎝ Ucdρa

(6)

It is not difficult to get Uc from the above equation Uc =

−12μAc +

144μ2 Ac2 + 2Fdaρa Acd 2 aρa Acd

(7)

On the basis of our experimental observations (Figure 3 and ref 9) and comparisons in Figure 5, when detachment happens, the value of Fd in eq 2 is equivalent to its value in eq 3. So, when the geometrical material parameters (such as ϕ0, f, and V) and the physical constants (such as γLV, ρw, and g) are given, we can get Fd, d, and Ac by eq 1 and eq 2; accordingly, we know Fd in eq 3. Then, put Fd and other physical constants (such as μ, ρa) in eq 7 (ϕ in eq 5 could be determined by Cassie’s theory27), and we can finally get Uc. Actually, the physical parameters are usually constant in real material systems, so the advantage of our analytical model (eq 7) is that the critical air velocity could be fully determined in terms of several intrinsic parameters (area fraction f, droplet volume V, and Young’s contact angle ϕ0), instead of relying on an unknown coefficient such as Lb/A in ref 22 or the uncertain advancing and receding angles. To validate this analytical model, a series of experiments was performed. Figure 7a 5164

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material is available free of charge via the Internet at http:// pubs.acs.org.

there are also some open questions: (1) the validity of our model for general hydrophobic surface wetting in Cassie− Baxter state should be checked further; (2) the potential mechanism about the Wenzel mode of wetting and superhydrophobic microgrooved surface with wetting anisotropy is different from what we studied in this work; a more generalized mode needs to be constructed in the future; (3) previously, Mahadevan30 reported that the small viscous droplet will roll down on the inclined plane as long as the Reynolds number Re ≪ 1. Hao11 revealed that both rolling and slipping motions happened for a water droplet during its sliding-down on a superhydrophobic surface by employing micro-PIV and microPTV techniques. Detailed information about the internal flow field of a droplet under air flow should also be revealed in the future.

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Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS Financial support from the NSFC under grant Nos. 11072126 and 11272176 is gratefully acknowledged.

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CONCLUSIONS In this paper, various micropillar-like structures on silicon wafers are fabricated using the photolithography method, then coated by a layer of octadecyltrichorosilane (OTS). The influence of the surface topology (water−solid area fraction) on sessile droplet detachment under air flow has been systematically investigated. Detachment onset of the droplet on such micropillar-like surfaces is experimentally studied, and the mechanism of the droplet detachment under air flow is investigated, which is similar to the detachment caused by a gravity field on a tilted plate. In order to confirm these experimental results, adhesion force of the water droplet on various superhydrophobic surfaces under critical air velocity has been investigated using 3D CFD simulations. It is found that the adhesion force of the water droplet on these surfaces under critical air flow velocity is consistent with that on the inclined surfaces under gravity. On the basis of experiments and simulation comparison, an explicit analytical model is established for the first time to determine the critical air velocity. This innovative model is written in terms of several intrinsic parameters: area fraction of the water−solid interface, droplet volume, and the Young’s contact angle. The proposed model agrees well with experimental measurements for a number of superhydrophobic surfaces with different area fractions. Prediction of such a proposed model also matches well with experimental measurements by other researchers for some types of substrate with homogeneous roughness.22 This proposed model for quantitatively correlating critical air velocity directly with the roughness distribution of the superhydrophobic surface will be widely used for superhydrophobic surfaces designed to realize practical applications. The internal flow field of a droplet under air flow, the general validity of the prediction mode for various pillar cross sections, and the size effect of the roughness will be studied in our future research.

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AUTHOR INFORMATION

REFERENCES

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ASSOCIATED CONTENT

S Supporting Information *

Movie 1: Detailed information about the onset of a 10 μL water droplet detachment on a micropillar-structured surface with L = 20 μm and S = 30 μm. Movie 2: Observation about the detachment and horizontal motion of the same water droplet on such micropillar-structured surface driven by the critical air flow velocity. The actual speed of the frames in experiments is 10 times higher than that shown in Movie 2. The dynamic behaviors of the water droplet under air flow were taken by a high-speed computer-controlled digital camera (200 fps). This 5165

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