Article pubs.acs.org/Langmuir
In Situ Observation of Dynamic Wetting Transition in Re-Entrant Microstructures Yang He,* Qingqing Zhou, Shengkun Wang, Ruyuan Yang, Chengyu Jiang, and Weizheng Yuan* Key Laboratory of Micro/Nano Systems for Aerospace, Ministry of Education and Shaan’xi Key Provincial Laboratory of Micro and Nano Electromechanical Systems, Northwestern Polytechnical University, Xi’an 710072, P. R. China S Supporting Information *
ABSTRACT: Re-entrant microstructures exhibit excellent wetting stability under different pressure levels, but the underlying mechanism determined by wetting transition behavior at the microscale level remains unclear. We propose the “wetting chip” method for in situ assessment of the dynamic behavior of wetting transition in re-entrant microstructures. High sag and transverse depinning were observed in re-entrant microstructures. Analysis indicated that high sag and transverse depinning mainly influenced the stability of the structures. The threshold pressure and longevity of wetting transition were predicted and experimentally verified. The design criteria of wetting stability, including small geometry design, hydrophobic material selection, and sidewall condition, were also presented. The proposed method and model can be applied to different shapes and geometry microstructures to elucidate wetting stability.
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INTRODUCTION The microstructure surface that maintains a stable Cassie state under pressure is a crucial factor for broad applications, such as hydrophobic coating and underwater drag reduction.1−7 Cassie state8 refers to liquid suspended on the top of a microstructure; it is metastable9 and will be converted into Wenzel state10 when the liquid on the surface suffers from external disturbances, such as varied levels of pressure,11,12 vibration,13 impact,14,15 evaporation,16 and others.17 The materials lose their wetting stability because of wetting transition from Cassie state to Wenzel state. Studies1,2,5,18−22suggested that re-entrant microstructures display considerable wetting stability under different pressure levels. Wetting stability is determined by wetting transition behavior at the microscale level. The traditional wetting transition behavior of straight sidewall microstructures (such as pores or pillars) follows two processes, namely, sag and depinning.23 Despite progress achieved in studies of wetting transition, the mechanism underlying the excellent wetting stability of reentrant microstructures remains unclear. In situ imaging of the dynamic behavior of pressure-induced wetting transition in re-entrant microstructures is necessary to understand the stability mechanism. Experimental methods, such as optical microscopy,24 cryogenic-focused ion beam milling and SEM imaging,25 confocal microscopy,26 X-ray microcomputed tomography,27 and synchrotron X-ray radiography28 are used to study the wetting behavior at the microscale level. However, the use of these methods is limited to dynamic observation of the internal morphologies of the liquid−solid interface in complex structures. In this study, we propose a novel method named “wetting chip” in which a slice is cut from a 3D droplet to obtain the © XXXX American Chemical Society
profile section of the microstructure through microfluidic chip technology (Figure 1). The proposed method can be used for in situ imaging of the dynamic behavior of wetting transition, fabricating different microstructures and manipulating different pressure levels. We observed the high sag and transverse depinning phenomena during wetting transition in re-entrant microstructures. We then developed a model to describe the dynamics of wetting transition. Analysis indicated that high sag and transverse depinning are key factors affecting wetting stability. We also predicted the threshold pressure and longevity of wetting transition by using the proposed model and experimentally verified the results. On the basis of the model, we present a design criterion of wetting stability for design optimization and actual applications.
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RESULTS AND DISCUSSION The re-entrant microstructures with closed channels were designed and fabricated inspired from springtail.4,5 A 10 kPa pressure (relative pressure) was applied to drive DI water into the wetting chip. The dynamic behavior of wetting transition in re-entrant microstructures was observed in situ. The varying contact angle (CA), which is located between the meniscus and sidewalls at different time points, was measured. Further details are provided in Supporting Information S1−S3. The meniscus morphology in different states during wetting transition is shown in Figure 2a. Critical changes of the meniscus during wetting transition are highlighted in Figure 2b. At 1−2 states, Received: January 23, 2017 Revised: March 19, 2017 Published: April 10, 2017 A
DOI: 10.1021/acs.langmuir.7b00256 Langmuir XXXX, XXX, XXX−XXX
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than the traditional sag height. This result represents a new phenomenon, named high sag, because the deformation of the meniscus is higher than that of traditional sag. At 3−4 states, the meniscus was depinned from the corner and transversely spread along the horizontal sidewall. The transverse depinning of the triple line agrees with previous studies.29−33 At 4−5 states, the meniscus touched the bottom sidewall. At 5−6 states, the meniscus slid between horizontal and bottom sidewalls, which could be regarded as a depinning recycling process because depinning process between horizontal and bottom sides occurred repeatedly. Analysis using the proposed method indicted two phenomena, namely, high sag and transverse depinning (Figure 2d), which differ from traditional sag and depinning (Figure 2c). We further analyzed the relationship of the forces of microdroplet to establish a model for explaining the stability mechanism of re-entrant microstructures. The vector relationship of forces during wetting transition in the re-entrant microstructure is shown in Figure 3a. The bond number is
Figure 1. Schematic of “wetting chip” method. (a) Concept of wetting chip. (b) Experiment setup. (c) Geometric parameters of the wetting chip. The actual measured parameters are shown in the following: a = 143 μm, b = 145 μm, c = 238 μm, h = 142 μm, e = 47 μm, and δ = 56 μm.
Figure 3. Model of force analysis. (a) Vector relationship of forces. (b) Geometrical relationship of R1. (c) Geometrical relationship of R2.
given by Bo = Δρgδ2/γ = 0.42 < 0.5 (details are presented in Supporting Information S4). Bond number indicates that gravity exerts small effects, which could be ignored in modeling, and the meniscus profile is approximately circular cross sections34 (Figure 3c). A quasi-static state was achieved when the water moved relatively slowly. The equilibrium equation for describing the relationship of driving and resisting forces can be written simplified as pl ≈ Δp + pg(t) + pv. Details of modeling and simplification are provided in Supporting Information S5. Thus we defined the threshold pressure of wetting transition (pt) as pt = Δp + pg (t ) + pv
Figure 2. Dynamic behavior of wetting transition in re-entrant microstructures and the two phenomena. (a) Critical meniscus morphology during wetting transition. Scale bar, 100 μm. (b) Changes in critical meniscus during wetting transition. (c) Traditional sag and depinning. (d) Two phenomena, namely, high sag and transverse depinning.
(1)
When the driving force (water static pressure pl) is larger than the critical resisting force (threshold pressure pt), the water drop will move and result in wetting transition. The details of eq 1 are discussed in the following. Young−Laplace pressure (Δp), the first item in the right part of eq 1, can be written as follows
an essential traditional depinning process took place in vertical sidewall microstructures. This result coincides with that of traditional depinning theory, in which depinning occurs when CA is larger than the advancing CA (θa). At 2−3 states, the meniscus was deformed largely, which could not be interpreted using traditional sag theory. The meniscus height of traditional sag23 (h0) satisfied h0 < R(1 − sin θa), where R is the radius of the meniscus and θa is the advancing CA. According to the geometric relationship of traditional sag shown in Figure 2c, R = −b/(2 cos θa). When the measured parameter value of the reentrant microstructure, shown in Figure 1c, was substituted into the equation (b = 145 μm, θa = 97°), the calculated result is h0 < R(1 − sin θa) = 5 μm. However, the measured height of meniscus (H), as shown in Figure 2d, is 74 μm, which is higher
⎛1 ⎛ sin θ cos θa ⎞ 1 ⎞ ⎟ Δp = γ ⎜ + − ⎟ = 2γ ⎜ ⎝ D R2 ⎠ δ ⎠ ⎝ R1
(2)
where R1 and R2 are the microdroplet principal radii of curvature. The geometrical relationship of R1 and R2 is shown in Figure 3b,c. θ is the measured CA between the meniscus and horizontal sidewall. D is the contact length of microdroplet and characterizes the degree of transverse spread of meniscus. Moreover, when t = 0, D is equal to b, which is the space of the re-entrant microstructure (Figure 3b). The gas partial pressure of the trapped air, pg(t), the second item in the right part of eq 1, varied with time because the trapped air resolved in water or permeated through B
DOI: 10.1021/acs.langmuir.7b00256 Langmuir XXXX, XXX, XXX−XXX
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Langmuir polydimethylsiloxane (PDMS) gradually. The volume of permeated air through the unit area of PDMS in unit time could be described as eq 335 (the deduction process is presented in Supporting Information S6) N (t ) =
P0[1 + m(pg (t ) − pg,0 )](pg (t ) − pg,0 ) L
(3)
where N is the steady-state penetrant flux through the polymer film and P0 is the permeability coefficient at ΔP = 0. The slope, m, characterizes the pressure dependence of permeability, pg(t) is the feed or upstream pressure, that is, the pressure of air trapped in chambers, pg,0 is the permeate or downstream pressure, that is, atmospheric pressure around chip, and L is the film thickness. The air resolved in water26 could be described in eq 4 A(t )DG d n r (t ) =− [pg (t ) − spg,0 ] dt lK G
(4) Figure 4. Different phases based on variation in R1 and Δp. Phase 1, depinning, 0−20 s; phase 2, high sag, 20−80 s; phase 3, transverse depinning, 80−200 s; phase 4, collapse, 200−240 s; phase 5, recovery, 240−280 s; phase 6, depinning recycling, 280−320 s; and phase 7, approximate wetting, 320−420 s.
where nr(t) is the mole number of the gas remaining in closed chamber, A(t) is the surface area of the meniscus, DG and KG are the diffusion coefficient and Henry’s constant, respectively, l is the characteristic diffusive length, and s represents the degree of gas saturation. We further calculated the mole number ratio between resolved air in water and permeated air through PDMS (details are provided in Supporting Information S7). The calculated ratio was 12.55, which indicated that the gas partial pressure of the trapped air was dominated by air dissolution in water during wetting transition. The water-saturated vapor pressure, pv, the third item in the right part of eq 2, is equal to 2.3 kPa at 20 °C. Drop condensation, which could be interpreted with water-saturated vapor pressure, was observed when DI water was injected into the wetting chip (Supporting Information S8). We further analyzed the meniscus curvature R1 and the corresponding Young−Laplace pressure Δp. The R1 of a series of images during wetting transition was measured using ImagePro Plus, and the corresponding Young−Laplace pressure Δp was calculated using eq 3. The results are shown in Figure 4. Δp varied accordingly with R1 (the detail of R1 analysis is presented in Supporting Information S9). The entire wetting transition process was divided into seven phases, considering varied R1 and Δp. In depinning phase, Δp minimally changed. In high sag phase, Δp increased significantly, providing resistance for wetting transition. When Δp increased and exceeded the threshold value, transverse depinning occurred. The threshold value was the demarcation point of high sag and transverse depinning, which is marked in the Δp curve. After a time period, Δp decreased sharply, thereby demonstrating a meniscus collapse process, then slightly increased, indicating a meniscus recovery process, and became nearly unchanged again, demonstrating a depinning recycling process. Finally, Δp became infinitely large and unmeasurable until full wetting was accomplished. The threshold value of depinning force acting on the unit length of the triple-line could be calculated as γdepin = 27.8 mN/m. The calculation details are provided in Supporting Information S10. When the driving pressure was removed when it was less than the threshold pressure, the meniscus recovered again; that is, the water drop shrank back and the meniscus curvature increased and changed as the former value. When the driving pressure is larger than the threshold pressure, the meniscus
curvature is difficult to recover even when the pressure is removed. This suggests that the adhesion work dominates the recovery (or dewetting) behavior of droplets.36 The adhesion between the water and the solid surface serves as an energy barrier for the recover. Smaller contact area before the transverse depinning results in a reduced adhesion work, which promotes the recovery and vice versa. The duration of the seven phases was obtained based on Figure 4. Depinning, high sag, transverse depinning, collapse, recovery, and depinning recycling lasted for 20, 60, 120, 40, 40, and 40 s, respectively; the approximate wetting phase lasted for 100 s until the full wetting process was completed. The entire process consumed ∼420 s. Meanwhile, high sag, and transverse depinning lasted for 180 s, which occupied 42% of the entire process. Above all, these two phases are critical for the longevity of wetting stability of re-entrant microstructures. Equation 2 was used to predict the threshold pressure and longevity of the re-entrant microstructure. According to calculation, wetting transition could occur only when the pressure exceeded 3.5 kPa, and the longevity of wetting transition decreased with increasing driving pressure. Further details are provided in Supporting Information S11. To verify our theoretical analysis, we conducted a series of experiments with different pressure levels to obtain the threshold value and the relationship between driving pressure and transition time. The result is shown in Figure 5. When the driving pressure pl is below 3.5 kPa, the meniscus is pinned at the top sidewall of the re-entrant microstructure. When the driving pressure is higher than the threshold, transition occurs. The transition time, which is a function of driving pressure, decreased exponentially (the fitting coefficient is −2.25) as the driving pressure increased. The experimental results coincide with the theoretical prediction. Finally, we presented the design criterion for the wetting stability of re-entrant microstructures. To improve wetting stability, small geometric parameters should be designed, or hydrophobic material should be used, and sidewall condition should be satisfied C
DOI: 10.1021/acs.langmuir.7b00256 Langmuir XXXX, XXX, XXX−XXX
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Figure 5. Experiment verification of threshold pressure and longevity. Wetting state transition could occur only when the pressure was larger than the threshold value (3.5 kPa), and longevity decreased exponentially when pressure increased.
c>
b(1 − cos θa) b ; h> sin θa 2sin θa
AUTHOR INFORMATION
Corresponding Authors
*Y.H.: E-mail:
[email protected]. Tel: +86 29 88460345. Fax: +86 29 88495102. *W.Y.: E-mail:
[email protected]. ORCID
Yang He: 0000-0003-4659-9349
(5)
Notes
where b, c, and h are the parameters of re-entrant microstructures (Figure 1c) and θa is the advancing CA of meniscus movement during transverse depinning. Further details are provided in Supporting Information S12.
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS We are grateful for support from National Natural Science Foundation of China (Grant Nos. 51005187, 51375398), Fundamental Research Funds for the Central Universities (Grant No. 3102014JCS05001, 3102015ZY088), 111 Project (Grant No. B13044), Seed Foundation of Innovation and Creation for Graduate Students in NPU (Grant No. Z2016086), and Fundamental Research Funds of ShenZhen City(JCYJ2016022917313). We acknowledge the helpful discussion with Professor Yanbo Xie and Professor Wei Tian at NPU.
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CONCLUSIONS A “wetting chip” method was proposed for in situ observation of dynamic wetting transition in re-entrant microstructure on the microlength scale. The high sag and transverse depinning phenomena were observed during pressure-induced wetting transition in re-entrant microstructures with closed cavities by using wetting chip method. The force model was presented to precisely describe the dynamic wetting transition. The threshold pressure and unit depinning force of the triple-line as well as longevity of wetting transition in the re-entrant microstructure were predicted. The experiments verified that transverse depinning only occurred when the driving pressure was larger than the threshold value, and longevity decreased exponentially when the pressure increased. Experiments and theoretical analysis revealed that high sag and transverse depinning are key factors affecting the wetting stability of reentrant microstructures. The design criteria for wetting stability including geometry parameters, material selection, and sidewall condition were further presented. The presented method could enable in situ observation of dynamic wetting behavior in different shapes and geometry microstructures on the micron length scale. The proposed model could also help scientists and engineers design stable re-entrant microstructures and predict their pressure-enduring capability and longevity. The methods and findings may have potential in wide applications including hydrophobic coating and underwater drag reduction.
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between resolved air in water and permeated air, experimental phenomenon and analysis of drop condensation, details of varying R1 during wetting transition, calculation of the threshold value of depinning force acting on the unit length of the triple-line, prediction of the threshold pressure and longevity of the re-entrant microstructure, and details of design criteria of wetting stability in re-entrant microstructure. (PDF) Dynamic behavior of wetting transition in re-entrant microstructures (AVI)
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ASSOCIATED CONTENT
* Supporting Information S
The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.7b00256. Fabrication of wetting chip, in situ observation of dynamic behavior of wetting transition, dynamic behavior of wetting transition in re-entrant microstructures at driving pressure of 10 kPa, bond number, simplification of eq 1, permeated formula of PDMS, mole number ratio D
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