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Resonance Cassie-Wenzel Wetting Transition for Horizontally Vibrated Drops Deposited on a Rough Surface Edward Bormashenko,* Roman Pogreb, Gene Whyman, and Mordehai Erlich The College of Judea and Samaria, The Research Institute, 44837 Ariel, Israel ReceiVed June 4, 2007. In Final Form: July 30, 2007 The transition between the Cassie and Wenzel wetting regimes has been observed under horizontal vibrations of a water drop placed on the rough micrometrically scaled polymer pattern. The observed transition has a distinct resonance character. The resonance frequencies as established experimentally coincide with the calculated eigenfrequencies of capillary-gravity standing waves on the drop surface. The resonance Cassie-Wenzel transition is related to the displacement of the triple line caused by both the inertia force and the increase in the Laplace pressure. This strengthens the idea that the Cassie-Wenzel wetting transition is most likely a 1D affair stipulated by the triple-line behavior. The study of the vibrated drop deposited on the rough surface supplied valuable information concerning the Cassie-Wenzel wetting transition.
1. Introduction Wetting is an essential phenomenon in many technological processes such as filtration, printing, and impregnation of textiles. An understanding of wetting is also important for soil and climate science and plant biology. The wetting of rough surfaces has attracted much attention during the past decade.1-10 Most natural and artificial solid surfaces are rough to some extent, and it must be emphasized that the wetting of rough surfaces is not completely clear and calls for further experimental and theoretical insights. In spite of the fact that the main theoretical approaches to the wetting of highly developed reliefs were developed by Cassie and Wenzel 50 years ago, the problem is still attractive to investigators.8-29 Gao and McCarthy in their recent paper even (1) de Gennes, P. G.; Brochard-Wyart, F.; Que˘ re˘ , D. Capillarity and Wetting Phenomena; Springer: Berlin, 2003. (2) Erbil, H. Y. Surface Chemistry of Solid and Liquid Interfaces; Blackwell Publishing: Oxford, U.K., 2006. (3) Cassie A. B. D.; Baxter, S. Trans. Faraday Soc. 1944, 40, 546-551. (4) Cassie, A. B. D. Discuss. Faraday Soc. 1948, 3, 11-16. (5) Gao, L.; McCarthy, Th. J. Langmuir 2006, 22, 2966-2967. (6) Gao, L.; McCarthy, Th. J. Langmuir 2006, 22, 6234-6237. (7) Lafuma, A.; Que´re´, D. Nat. Mater. 2003, 2, 457-460. (8) Bico, J.; Thiele, U.; Que´re´, D. Colloids Surf., A 2002, 206, 41-46. (9) Nosonovsky, M. J. Chem. Phys. 2007, 126, 224701. (10) Li, W.; Amirfazli, A. AdV. Colloid Interface Sci. 2007, 132, 51. (11) Marmur, A. Langmuir 2003, 19, 8343-8348. (12) Marmur, A. Soft Matter 2006, 2, 12-17. (13) Yoshimitsu, Z.; Nakajima, A.; Watanabe, T.; Hashimoto, K. Langmuir 2002, 18, 5818-5822. (14) McHale, G.; Aqil, S.; Shirtcliffe, N. J.; Newton, M. I.; Erbil, H. Y. Langmuir 2005, 21, 11053-11060. (15) Shirtcliffe, N. J.; McHale, G.; Newton, M. I.; Perry, C. C. Langmuir 2005, 21, 937-943. (16) Thiele, U.; Brusch, L.; Bestehorn, M.; Ba¨r, M. Eur. Phys. J. E 2003, 11, 255-271. (17) Herminghaus, S. Europhys. Lett. 2000, 52, 165-170. (18) Shibuichi, A.; Onda, T.; Satoh, N.; Tsujii, K. J. Phys. Chem. 1996, 100, 19512-19517.1 (19) He, B.; Lee, J.; Patankar, N. A. Colloids Surf., A 2004, 248, 101-104. (20) Barthlott, W.; Neinhuis, C. Planta 1997, 202, 1-8. (21) Patankar, N. A. Langmuir 2004, 20, 7097-7102. (22) Liu, B.; Lange, F. F. J. Colloid Interface Sci. 2006, 298, 899-909. (23) Jeong, H. E.; Lee, S. H.; Kim, J. K.; Suh, K. Y. Langmuir 2006, 22, 1640-1645. (24) Bormashenko, E.; Stein, T.; Whyman, G.; Bormashenko, Ye.; Pogreb, R. Langmuir 2006, 22, 9982-9985. (25) Bormashenko, E.; Bormashenko, Ye.; Whyman, G.; Pogreb, R. J. Colloid Interface Sci. 2006, 302, 308-311. (26) Nosonovsky, M. Langmuir 2007, 23, 3157-3161. (27) Ishino, C.; Okumura, K. Europhys. Lett. 2006, 76, 464-470. (28) Extrand, C. W. Langmuir 2003, 19, 3793-3796. (29) Gao, L.; McCarthy, Th. J. Langmuir 2007, 23, 3762-3765.
noted that the number of publications citing the classical Wenzel and Cassie work has increased exponentially during past decade.29 (This is primarily due to intensive research on the superhydrophobicity phenomenon revealed in various natural and artificial systems.18,20,24) According to the Cassie model,3,4 air can remain trapped below the drop, forming “air pockets”. Thus, hydrophobicity is strengthened because the drop sits partially on air. However, according to the Wenzel model, the roughness increases the surface area of the solid, which also geometrically modifies the hydrophobicity.1,2,7-8,11 In both the Cassie and Wenzel approaches, the apparent contact angle is dictated by the interfacial contact area between the liquid and the rough solid. The Wenzel and Cassie approaches allowed the prediction of apparent contact angles on a variety of rough surfaces. However, several authors argued that contact angles are determined by the interaction that occurs at the contact line, not in the interfacial contact area.28-30 One of the most intriguing topics is the so-called CassieWenzel wetting transition.7,13,14,22,27 It has been shown that both the Cassie and the Wenzel wetting regimes can coexist on the same surface. Moreover, the Cassie regime could be switched to the Wenzel one under an external stimulus such as pressure.7,22 The theoretical model considering transition via nucleation between the Cassie and the Wenzel states has been reported recently by Ishino and Okumura.27 In this model, supported by experimental data from Lafuma and Que´re´,7 the Cassie-Wenzel transition looks like a 2D affair that begins from the center of the drop.27 We have already demonstrated that the Cassie-Wenzel wetting transition of the drop could be caused by the vertical vibration of the drop.31-32 (The vibration of sessile drops has been intensively studied recently.33-37) Our experimental finding (30) Bartell, F. E.; Shepard, J. W. J. Phys. Chem. 1953, 57, 455-458. (31) Bormashenko, E.; Pogreb, R.; Whyman, G.; Bormashenko, Ye.; Erlich, M. Appl. Phys. Lett. 2007, 90, 201917-1-201917-2. (32) Bormashenko, E.; Pogreb, R.; Whyman, G.; Bormashenko, Ye.; Erlich, M. Langmuir 2007, 23, 6501-6503. (33) Lyubimov D. V.; Lyubimova, T. P.; Shklyaev, S. V. Phys. Fluids 2006, 18, 012101-1-012101-11. (34) Daniel, S.; Chaudhury, M. K. M. K.; De Gennes, P. G. Langmuir 2005, 21, 4240-4248. (35) Celestini, F.; Kofman, R. Phys. ReV. E 2006, 73, 041602-1-041602-6. (36) Noblin, X.; Buguin, A.; Brochard-Wyart, F. Eur. Phys. J. E 2004, 14, 395-404.
10.1021/la7016374 CCC: $37.00 © 2007 American Chemical Society Published on Web 10/23/2007
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Figure 1. (a) Image of the PS honeycomb pattern used as a substrate for horizontal drop vibration experiments. (b) Drop on the substrate with a smooth spot.
strengthened the idea that interaction occurring at the contact line is actually responsible for the Cassie-Wenzel wetting transition.32 In the present work, we also discuss the case of horizontal vibrations promoting the Cassie-Wenzel transition. The observed transition is characterized by distinct resonance behavior. The possibility of the wetting regime controlled by vibration may be of primary importance in the context of the rapid development of microfluidic devices.34,38-40
3. Results and Discussion First, let us consider drop vibration irrespectively of the CassieWenzel transition. When the drop is vibrated, both volume and surface modes are excited. For a rough estimation of the nth volume eigenfrequency ωn of the drop, the well-known Rayleigh equation could be used
ωn2 )
2. Experimental Section Two types of surfaces were prepared. The first one was a micrometrically scaled polystyrene honeycomb surface prepared with the fast dip-coating method described in great detail earlier.41 Polystyrene (PS) (5 wt %) was dissolved in a mixture of chloroform (CHCl3, 7.6 wt %) and dichloromethane (CH2Cl2, 87.4 wt %). Thoroughly cleaned polypropylene (PP) substrates were pulled at a high speed of V ) 20-50 cm/min from the polymer solution and dried immediately with infrared lamps at a temperature of 80 °C. Thus, the 2D PS honeycomb structures (such as that depicted in Figure 1) were formed. The second two-component surface was a PS honeycomb relief, prepared as described above comprising a smooth spot (in the spirit of recent work reported by Gao andMaCarthy).29 A smooth spot within a rough field was prepared with room-temperature vulcanized (RTV) polyorganosilane/siloxane supplied by Dow Corning (Dow Corning 1-2577). The diameter of the spot D was 2 mm (Figure 1b). A drop of radius R ) 2.6 mm (V ) 50 µL) was deposited on the two-component surface as depicted in Figure 1b. Droplets of distilled water of 10-150 µL volume were carefully deposited on the PS honeycomb relief of the first type with a precise microdosing syringe. The apparent contact angle (APCA in terms of abbreviations introduced by Marmur)12 was measured with a laboratory-made goniometer. The substrate with the drop was bound up with the moving part of the Frederiksen 2185.00 vibration generator, driven by synthesized function generator DS 345. The horizontal helium-neon laser beam illuminated the entire drop profile and produced its enlarged image on the screen using the system of lenses. The frequency interval was from 5 to 350 Hz; the amplitude was changed from 0.02 to 2 mm. (37) Meiron, T. S.; Marmur, A.; Saguy, I. S. J. Colloid Interface Sci. 2004, 274, 637-644. (38) Nosonovsky, M.; Bhushan, B. Microsyst. Technol. 2005, 11, 535-549. (39) Intonti, F.; Vignolini, S.; Tu¨rck, V.; Colocci, M.; Bettotti, P.; Pavesi, L.; Schweizer, S. L.; Wehrspohn, R.; Wiersma, D. Appl. Phys. Lett. 2006, 89, 211117. (40) Beyssen, D.; Le Brizoual, L.; Elmazria, O.; Alnot, P. Sens. Actuators, B 2006, 118, 380-385. (41) Bormashenko, E.; Pogreb, R.; Stanevsky, O.; Bormashenko, Ye.; Stein, T.; Cohen, R.; Nunberg, M.; Gaisin, V.-Z.; Gorelik, M. Mater. Lett. 2005, 59, 2461-2464.
n(n - 1)(n + 2)γ FR3
(1)
where γ and F are the surface tension and density of water, respectively, and R is the radius of the drop. For the hemispherical sessile drop, as has been shown recently by Lyubimov and coworkers, eigenfrequencies depend on the boundary conditions at the triple line and, for a freely sliding contact line, coincide with the natural frequencies of spherical drop.33 It could be seen that for the water drop with R ≈ 1-3 mm, F ) 103 kg/m3, and γ ) 72 mJ/m2 the fundamental frequency (n ) 2) is in the 20-120 Hz range. For the fixed triple line, the equation obtained in ref 35
ω1 )
x
6γh(θ) R-3/2 F(1 - cos θ)(2 + cos θ)
(2)
gives for the volume mode of water droplets of sizes 1-3 mm the frequencies in the 10 - 60 Hz interval. (The dependence of the geometrical factor h on the APCA θ is found in ref 35.) This range of volume modes intersects with that of surface ones (5-250 Hz); however, as will be shown below, in the case of a horizontal vibration only the surface modes are responsible for the Cassie-Baxter wetting transition. With the exception of one mode of the lowest frequency, all modes considered in this work correspond to the fixed triple line. As a result of the horizontal drop vibration, waves appeared on the drop surface (Figure 2), extending over the meridian stripe parallel to the vibration direction. Quite surprisingly, these waves may be described in the framework of the same simple approach developed by Noblin et al. for the vertical drop vibration.36 According to that, the surface waves obey
qj )
1 2π π(j - /2) ) λj p
(3)
where λ/2 is half of the wavelength, equal to the mean distance
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Figure 2. Profiles of oscillating drops. Modes with j ) 1 (A), 3/2, (B) 5/2 (C), and 7/2 (D). Depressions on the drop surface are hidden by the front part of the drop.
wavelengths: with increasing frequency, the wavelength becomes substantially lower than the drop size, justifying the use of this model for the spherical surfaces. It is clear from Figure 2 that one of important factors governing the nonequilibrium drop behavior is the increase in the Laplace pressure in the regions with large values of the surface curvature. In a rough approximation, the deviation of the drop surface from the spherical form may be expressed as Figure 3. Scheme of the drop profile corresponding to the antisymmetric surface mode with j ) 5/2.
between the wave nodes (Figure 2), q is the corresponding wave vector, p is the half-perimeter of the maximal meridian cross section of the drop, and j is an integer or half-integer. The authors of ref 36 have observed surface modes with a fixed drop triple line corresponding to j ) 2, 3,... and those with a mobile triple line described by eq 3 with j ) 3/2, 5/2,... Note that the mentioned modes generated by vertical vibration are fully axisymmetrical. We have also revealed the modes that are antisymmetric relative to the symmetry plane of the drop orthogonal to the vibration direction (images in Figure 2 and the scheme in Figure 3). Also, the lowest frequency mode with a moving triple line and one node was observed (j ) 1, Figure 2A). To find the frequency of the modes, the authors of ref 36 have used the dispersion relation for 1D capillary-gravity waves in a liquid bath42
(
ω2 ) gq +
γ 3 q tanh(qH) F
)
(4)
where the mean depth H of the drop may be set equal to
H)
V π(R sin θ)2
(5)
with V being the drop volume. As it turns out, eqs 3 and 4 also successfully describe the antisymmetrical modes (half-integer j) with the fixed triple line. In the Table, the eigenfrequencies calculated according to eqs 3 and 4 are compared to the measured ones. The latter were fixed visually using the pictures on a screen as in Figure 2 and scanning a frequency until the maximal value of the wave amplitude was reached. The overall correspondence of observed and calculated values in the Table is satisfactory. Deviations for low-frequency modes (j < 2.5) are explained by the use of the plane bath model that is not suitable for long (42) Landau, L.; Lifshitz, E. Fluid Mechanics, 2nd ed.; ButterworthHeinemann: Oxford, U.K., 1987.
z ) A sin
2πx λ
(6)
where z is the deviation of the drop surface from equilibrium at the position x along the arc and A is the amplitude of z. The positive curvature radius r is minimal at the maxima in eq 6 and obeys
| | ( )
d2z 2π 2 1 ) 2 )A r λ dx
(7)
The corresponding Laplace pressure is
P)
8π2Aγ λ2
(8)
where λ is defined by eq 3 or may be measured directly from images such as those in Figure 2. The values of P calculated from images according to eq 8 are in the 120-150 Pa interval at intermediate and high resonance frequencies, independent of the mode number. It should be emphasized that this value agrees well with the typical pressures accompanying the Cassie-Wenzel wetting transition.7,31,32 To elucidate the influence of the vibrational frequency on this transition, the water drop had been exposed to the horizontal vibration of the increased amplitude at various frequencies until the wetting transition took place, and the amplitude corresponding to the Cassie-Wenzel transition was measured, when the APCA decreased approximately from 90 to 60°. In Figure 4, these critical amplitudes of exciting oscillations are plotted versus the corresponding frequencies. The latter are also presented in the Table. Obvious resonance character of the curve in Figure 4 can be recognized. The curves obtained for the honeycomb reliefs comprising a smooth spot coincide with those established for the original surfaces. This important observation supports the idea that the Cassie-Wenzel transition does not occur via a nucleation mechanism beginning from the center of the drop as discussed recently by Ishino and Okumura27 but is
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Table 1. Frequencies (Hz) of Symmetrical (Integer j) and Antisymmetrical (Half-Integer j) Modes V ) 30 µL
mode j 1a 1.5 2b 2.5 3 3.5 4c 4.5 5
resonant calcd exptl 12 33 60 92 128 168 211 257 306
11 25 88 120 160 210 260 280
V ) 50 µL resonant wetting transition 12 24 40-50 88 120 160
resonant calcd exptl 9.7 26 47 72 100 130 164 200 238
9 20 40 65 102 120 155 180
V ) 100 µL resonant wetting transition 10 21 41 70 102 135
resonant calcd exptl 7.9 20 35 52 71 93 116 142 169
7 14 48 63 85 105 135 165
resonant wetting transition 14 26 50 60-70 95
a The antisymmetric mode with a moving triple line. b The axially symmetric modes (j ) 2-5) are hardly observed in the case of horizontal-vibration excitation, which, unlike vertical excitation, has no full axial symmetry. c For the highest modes, the wetting transition takes place at very low amplitudes, which could not be measured. In this case, the inertial force that is proportional to the squared frequency seems to give rise to the transition.
Figure 4. Threshold amplitude of the Cassie-Wenzel wetting transition caused by horizontal vibration. The drop volume is 50 µL.
caused by the displacement of the triple line as it is demonstrated in our previous paper.32 In our opinion, the mentioned wetting transition is conditioned by two factors, which are the inertia force and the Laplace pressure (eq 8). The minima of the curve in Figure 4 correspond well to the resonance frequencies of the surface waves (Table 1). In this case, the Laplace pressure is maximal and gives rise to the transition. However, far from the resonance frequencies the main role is played by the inertia term, which is proportional to the amplitude and squared frequency of substrate oscillations;31 therefore, the maxima of the amplitude of the curve in Figure 4 tend to decrease with frequency growth. For instance, the most distinct peaks at 50 and 110 Hz, which are well separated from adjacent resonances, correspond to excitation amplitude values Ae ) 460 and 105 µm, respectively, and give values close to the inertia force per unit length of the triple line FVAeω2/l ) 140 and 150 mN/m (V ) 50 µL, l ) 16.3 mm). Previously, it was argued32 that in the case of vertical vibration it is the force per unit length of the triple line that governs the wetting transition. The obtained values of 140 and 150 mN/m are comparable to the critical value of 200 mN/m for vertical vibrations.32 It could also be seen that at the frequencies corresponding to peaks of the resonance curve in Figure 4 the energies of the drop are determined mainly by its translational displacement as a whole, together with the substrate, E ≈ (1/2)FVAe2ω2. Unlike these, in the vicinity of the “dips”, where the amplitude Ae is 2 orders of magnitude smaller, the energy excess of the drop, E ≈ γ∆S, is connected with the capillary-gravity waves (∆S is the change in the drop surface). It is clear that the above energy value may be considered to be an energy barrier of the CassieWenzel wetting transition. However, we prefer to use the “force” criterion for this purpose.32 The wetting transition occurs when the triple line is de-pinned. Pinning is caused by both the roughness
of the surface and long-range forces, and it resembles the phenomenon of static friction, as has been discussed recently by Yaminsky in much detail.43 Pinning forces are large but lowenergy, that is why the critical force per length unit criterion is suitable for the characterization of the wetting transition.43 Note that the investigated transition is dynamic in nature. Indeed, the vibrating surface contains not only convex parts but also concave ones where the Laplace pressure is negative (Figures 2 and 3). It seems reasonable to suggest that the transition happens when the crest of a wave is near the triple line that gives rise to the local increase in the Laplace pressure, leading to the triple-line displacement and subsequent wetting transition. This also stresses the 1D character of the Cassie-Wenzel transition in the case of the horizontal vibration of the drop.
Conclusions This article continues the previous investigations performed by the authors and is devoted to the Cassie-Wenzel wetting transition observed with vibrated drops deposited on the rough surfaces. Polymer honeycomb relief and the same relief comprising a smooth spot smaller than the diameter of the drop were also studied in this work. The Cassie-Wenzel transition has been observed for both kinds of substrates under horizontal vibrations of the drop. As was shown above, when the drop is vibrated horizontally the wetting transition has a distinct resonance character. The frequencies corresponding to the minimal amplitudes of vibration coincide with the mode frequencies of surface capillary-gravity waves inherent in the vibrated drop. The resonance frequencies were the same for both kinds of (43) Yaminsky, V. V. Molecular Mechanisms of Hydrophobic Transitions. In Apparent and Microscopic Contact Angles; Drelich, J., Laskowski, J. S., Mittal, K. L., Eds.; VSP BV: Utrecht, The Netherlands, 2000; pp 47-95.
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substrates. It could be concluded that under vertical and horizontal vibrations the behavior of the triple line is responsible for the dynamic Cassie-Wenzel wetting transition.32 In our opinion, the displacement of the triple line leading to the wetting transition is due to the increase in the Laplace pressure in the vicinity of the resonance or is due to the inertia force when the frequency is far from resonance. The presented results strengthen the previously discussed hypothesis that only the effects occurring closest to the triple line are invoked in the Cassie-Wenzel wetting transition.
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Acknowledgment. This work was supported by the Israel Ministry of Absorption. We are grateful to Professor M. Zinigrad for his generous support of our experimental activity and Dr. Mordechai Hakham Itzhaq for fruitful discussions. This article is dedicated to the blessed memory of Professor Yakov Yevseevitch Gegusin, prominent scientist and teacher, who directed our attention to the physical phenomena occurring in droplets. LA7016374
