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Langmuir 2008, 24, 14074-14077
Drop Impact on Porous Superhydrophobic Polymer Surfaces R. Rioboo,* M. Voue´, A. Vaillant, and J. De Coninck Centre de Recherche en Mode´lisation Mole´culaire, UniVersite´ de Mons-Hainaut, Parc Initialis, AV. Copernic 1, B-7000 Mons, Belgium ReceiVed September 4, 2008. ReVised Manuscript ReceiVed October 2, 2008 Water drop impacts are performed on porous-like superhydrophobic surfaces. We investigate the influence of the drop size and of the impact velocity on the event. The Cassie-Baxter/Wenzel transition is observed to be a function of the drop size, as well as the outcomes of the impact or deposition process, which can be deposition, rebound, sticking, or fragmentation. A quantitative analysis on the experimental conditions required to observe rebound is provided. Our analysis shows that the wettability hysteresis controls the limit between deposition and rebound events. This limit corresponds to a constant Weber number. A survey of literature results on impact over patterned superhydrophobic surfaces is provided as a comparison.
Introduction For more than a century, drop impact on solid surfaces has been investigated,1-3 resulting in a general sketch of the outcomes and of the time evolution of the physical process.4-10 Nevertheless, the interactions between inertia, viscous dissipation, and free surface movement and the effects due to the physicochemistry of the experimental system (contact line friction, possible deformation of the solid surface, or superhydrophobicity) result in a lack of predictability of the outcome of the deposition or impact for many cases. On the other hand, superhydrophobicity has been intensively investigated for only one decade, and it was shown that complete rebound of the drop during impact was only observed at the surface of superhydrophobic materials.5,11 Because of their spectacular property of water repellency, their promising technological applicability, and their scientific challenges, these materials have attracted the attention of many scientific teams around the world.12-17 Most of the time, superhydrophobicity is encountered when common hydrophobic materials have their specific surface drastically increased by roughness effects. The * To whom correspondence should be addressed. E-mail: romain.rioboo@ crmm.umh.ac.be. (1) Worthington, A. M. Proc. R. Soc. London 1876, 2-5, 261–271. (2) Rein, M. Fluid Dyn. Res. 1993, 12, 61–93. (3) Yarin, A. L. Annu. ReV. Fluid Mech. 2006, 38, 159–192. (4) Pasandideh-Fard, M.; Qiao, Y. M.; Chandra, S.; Mostaghimi, J. Phys. Fluids 1996, 8, 650–659. (5) Rioboo, R.; Tropea, C.; Marengo, M. Atomization Sprays 2001, 11, 155– 165. (6) Rioboo, R.; Marengo, M.; Tropea, C. Exp. Fluids 2002, 33, 112–124. (7) Roisman, I. V.; Rioboo, R.; Tropea, C. Proc. R. Soc. London, A 2002, 458, 1411–1430. (8) Rioboo, R.; Bauthier, C.; Conti, J.; Voue´, M.; De Coninck, J. Exp. Fluids 2003, 33, 112–124. (9) Clanet, C.; Beguin, C.; Richard, D.; Que´re´, D. J. Fluid Mech. 2004, 517, 199–208. (10) Rioboo, R.; Ada˜o, M. H.; Voue´, M.; De Coninck, J. J. Mater. Sci. 2006, 41, 5068–5080. (11) Richard, D.; Que´re´, D. Europhys. Lett. 2000, 50, 769–775. (12) Nakajima, A.; Hashimoto, K.; Watanabe, T. Monatsch. Chem. 2001, 132, 31–41. (13) Blossey, R. Nat. Mater. 2003, 2, 301–306. (14) Que´re´, D. Rep. Prog. Phys. 2005, 68, 2495–2532. (15) Ma, M. L.; Hill, R. M. Curr. Opin. Colloid Interface Sci. 2006, 11, 193– 202. (16) Li, X. M.; Reinhoudt, D.; Crego-Calama, M. Chem. Soc. ReV. 2007, 36, 1350–1368. (17) Lau, K. K. S.; Bico, J.; Teo, K. B. K.; Chhowalla, M.; Amaratunga, G. A. J.; Milne, W. I.; McKinley, G. H.; Gleason, K. K. Nano Lett. 2003, 3, 1701–1705.
topography of such surfaces can be defined by many roughness parameters, but when considering static or dynamic wetting properties, it is commonly accepted that the relevant roughness parameter is Wenzel’s roughness. It is defined as the ratio between the real and the projected planar surface areas. When the Wenzel roughness of a hydrophobic material is high enough,18 superhydrophobicity is expected. However, although important, surface roughness is not the sole parameter controlling superhydrophobicity of a surface; it also depends on the details of the topography and the intrinsic wettability of the flat material. In practice, two regimes are observed: a composite wetting regime usually referred to as the Cassie-Baxter regime19 and a sticking or pinning wetting regime, the Wenzel regime.20 They differ by the details of the underlying wettability mechanisms. In both cases, the advancing contact angle is increased compared to the angle on the smooth surface of the same material, while only the composite wetting allows very high receding contact angles. Self-cleaning and drop rebound are direct consequences of such very high receding contact angles. The transition between these two regimes has been investigated in terms of the solid surface features using, most of the time, tailored topographies with periodic and single-scale structures.21,22 For a given surface the transition between Cassie-Baxter and Wenzel regimes depends also on the way the drop is deposited or impacted23 on the surface and, possibly, on the size of the drop.24,25 Only a few studies have shown the effect of the impact of a drop on the superhydrophobicity of the system. He et al.23 were the first to show that, on needle-like surfaces made of an array of pillars, impacting instead of depositing the drop could result in a Cassie-Baxter/Wenzel transition. They showed that the distance between the pillars was a critical parameter to keep the (18) Borgs, C.; De Coninck, J.; Kotecky, R.; Zinque, M. Phys. ReV. Lett. 1995, 74, 2292–2294. (19) Cassie, A. B. D.; Baxter, S. Trans. Faraday Soc. 1944, 40, 546–551. (20) Wenzel, R. N. Ind. Eng. Chem. 1936, 28, 988–994. (21) De Coninck, J.; Ruiz, J.; Miracle-Sole, S. Phys. ReV. E 2002, 65, No. 036139, 1-4. (22) De Coninck, J.; Dobrovolny, C.; Miracle-Sole´, S.; Ruiz, J. J. Stat. Phys. 2004, 114, 575–604. (23) He, B.; Patankar, N. A.; Lee, J. Langmuir 2003, 19, 4999–5003. (24) Figure 6 in ref 25 that shows this possible effect refers to two drops of different sizes with different regimes (Cassie-Baxter or Wenzel) but deposited also at various impact velocities (D. Que´re´, personal communication). (25) Callies, M.; Que´re´, D. Soft Matter 2005, 1, 55–61.
10.1021/la802897g CCC: $40.75 2008 American Chemical Society Published on Web 11/11/2008
Drop Impact on Porous Superhydrophobic PP
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Figure 1. Scheme of the outcomes of a drop impacting a superhydrophobic surface.
drop in a Cassie-Baxter regime. Reyssat and co-workers,26 Bartolo and co-workers,27 and, more recently, Jung and Bushan28 have quantified this effect of the impact or deposition velocity for a given drop size on needle-like surface topographies. When the drop velocity is increased by changing, for example, the height of fall of the drop, the liquid is forced to touch the bottom of the “valleys” of the material rough surface23,26,27 and the drop is no longer suspended on the top of the needles. Figure 1 presents a sketch which summarizes the state-of-the-art knowledge on the outcome of an impacting water drop on a superhydrophobic surface when the Wenzel roughness and impact velocity are increased. It is important to stress here that, when a drop is deposited on a surface, its impact velocity can be a few tenths of a meter per second and inertia effects could be non-negligible, even when the drop is “gently” deposited. For this reason, the distinction between the terms “deposition” and “impact” will no longer be made in the remaining paragraphs of this paper. Various criteria based on the topography parameters (distance between needles, height of needles,...) have been proposed to explain the behavior of structured surfaces. In particular, for regular geometries, theoretical predictions have been developed.21,22 Considering drops much larger than the surface topography features, predictive models give the critical velocities separating these outcomes.26,27 These critical velocities are independent of the drop size, except for the limit between deposition and rebound.26 In such a case, the kinetic energy is equated to the energy stored by the wettability hysteresis, H, of the system, which is the difference between the advancing and receding static contact angles, θa and θr, respectively. The limit impact velocity to observe rebound, VC, scales as the inverse square root of the drop size:26
VC ≈
2σ Fd
Figure 2. SEM image of a superhydrophobic polypropylene surface (scale bar 10 µm).
in our previous paper.29 The aim of the present investigation is to fill that gap and to study superhydrophobic surfaces with porous-like topographies and the possible outcomes of the drop interactions with the surface when either the impact velocity or drop size is increased. Such surfaces present topographical features at various length scales29 and are, at least on that point, more complex than the surfaces considered in previous studies.11,23,26,27
Experimental Procedure Isotactic polypropylene (iPP) (molecular weights Mn ) 5000 and Mw ) 12 000) and p-xylene (99+%) were purchased from SigmaAldrich (Germany). Polypropylene sheets (1 mm thick, PP333100/ 13) were purchased from Goodfellow (United Kingdom). Surface Preparation. Superhydrophobic surfaces were prepared according to the method proposed by Rioboo et al.29 and briefly summarized here. A polymer solution (0.1 g/mL) was prepared by dissolution of iPP at reflux (135 °C) in xylene. A glass cylinder, sealed with wax to a degreased iPP sheet acting as a substrate, was filled with the polymer solution (10 mm height). The xylene in the solution was allowed to evaporate during one day at room temperature. During that time, the iPP slowly crystallized and produced porouslike surfaces. Drop Impact Experiments. Milli-Q water was used throughout all our experiments. Drops of millimetric size or above were formed using precision syringes and needles of various diameters. Droplets of submillimetric size were created using various sprays where the outlet nozzle diameter could be varied to change the density of the spray and the size of the drops. Imaging the impact was performed with a high-speed camera (CMOS Vosskhu¨ler HCC-1000) at 923 images per second and a Navitar 6000 zoom lens system.
Results and Discussion (1)
where F, σ, and d are respectively the density of the liquid, its surface tension, and the diameter of the drop. In the analysis by Reyssat and co-workers, a prefactor quantifying the effect of the hysteresis in ∆ cos θm, where θm is an average contact angle, is approximated by 1. To the best of our knowledge, no quantitative study on the different transitions between these outcomes has been carried out for porous superhydrophobic surfaces such as those presented (26) Reyssat, M.; Pe´pin, A.; Marty, F.; Chen, Y.; Que´re´, D. Europhys. Lett. 2006, 74, 306–312. (27) Bartolo, D.; Bouamrirene, F.; Verneuil, E.; Buguin, A. Europhys. Lett. 2006, 74, 299–305. (28) Jung, Y. C.; Bhushan, B. Langmuir 2008, 24, 6262–6269.
Surface Characterization. Isotactic PP superhydrophobic surfaces were prepared by the casting method. According to our previous study,29 these surfaces can be characterized by the average of the advancing and receding static contact angles. This mean angle is close to 150°, and the hysteresis varies between less than 1° and 25° due to the surface heterogeneity. Scanning electron microscopy (SEM) was used to image some of the surfaces without metallization of the sample. A typical example is given in Figure 2, showing that the surface presents a porouslike morphology formed by 4-5 µm granular structures. Drop Impact. The impact experiments were carried out at various impact speeds (0.017-7.17 m/s) and various drop (29) Rioboo, R.; Voue´, M.; Vaillant, A.; Seveno, D.; Conti, J.; Bondar, A. I.; Ivanov, D. A.; De Coninck, J. Langmuir 2008, 24, 9508–9514.
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Figure 3. Outcomes of the deposition/impact events at various drop sizes, d, and impact velocities, V (fragmentation, open triangles; rebound, open circles; deposition, filled circles; sticking, filled triangles). Experimental R/F and D/R limits from the works of Reyssat et al.26 (open rectangles) and Bartolo et al.27 (filled rectangles) are also reported for comparison. Key: solid line, R/F limit (We ) 60); dashed line, D/R limit calculated from eq 4 (θm ) 150°, H ) 2°) and corresponding to WeC ) 0.2; dashed-dotted lines, transition lines calculated from the lower (0.2°) and upper (25°) values of the contact angle hysteresis.
diameters (93 µm to 4.72 mm). On the impact image sequences, four outcomes have been identified: deposition (D), rebound (R), sticking (S), and fragmentation (F). They are schematically reported in Figure 1 and briefly described here. (1) Deposition occurs when, after touching the surface, the drop presents some oscillations but stays on it without modification of the wettability of the system. In this case, the drop still exhibits a Cassie-Baxter regime and can be very easily removed from the solid surface. (2) Rebound occurs when the drop is completely bouncing. (3) Sticking corresponds to an event when the drop is impaled on the solid and thus presents a Cassie-Baxter/Wenzel transition due to the impact pressure. In such a case, the drop can also partially rebound,5 but the drop part sticking to the surface is in a Wenzel regime. (4) Fragmentation corresponds to the formation of various droplets due to impact pressure. Receding breakup and possibly prompt splash are observed.5,30 In this last case, the behavior of the resulting droplets still corresponds to a Cassie-Baxter regime. Once identified, the outcomes were represented as a function of the drop diameter and of the impact speed (Figure 3). Two limits are easily identified. They correspond to the rebound/ fragmentation (R/F) limit and to the deposition/rebound (D/R) limit. The experimental conditions according to which these transitions are observed are discussed here. Let us first consider the R/F limit. The influence of the drop size is clearly visible for the R/F limit. The smaller the drops, the higher the impact velocity, V, to observe its fragmentation. The Weber number (We), which is the ratio between inertia and surface forces, is defined by We ) FdV2/σ. This means that, on a log-log scale, a plot of V versus d corresponds to a straight line with a -1/2 slope. Empirically, the F and R events can be appropriately separated at We ) 60 (Figure 3, solid line) for these surfaces. Higher values of We lead to the fragmentation of the impacting drop. In the same way, the limit for D and R events is also a function of the drop size, but the limit does not appear to be as regular (30) Rioboo, R. Impact de gouttes sur surfaces solides et se`ches. Ph.D. Thesis, Universite´ Pierre et Marie Curie (Paris VI), France, February 2001.
Rioboo et al.
as the R/F limit. A possible explanation of this difference is the inhomogeneity of our random-like surfaces, which results in fluctuating contact angle hysteresis.29 According to the analysis of Reyssat et al. leading to eq 1, the hysteresis is scaled with a difference of cosines which is approximated by 1. But for our surfaces, the hysteresis can vary a lot. Thus, the prefactor which is a function of θm, i.e., the average of the advancing and the receding “static” contact angles and of the hysteresis of the surface, can vary over at least 1 order of magnitude, and its effect can no longer be neglected. When the liquid spreads onto the surface, it reaches a maximum diameter before receding back.7 Simultaneously, the drop contact angle changes from the advancing to the receding one. It is experimentally observed that for a small impact velocity, which is the case for the limit between rebound and deposition, the drop is not strongly deformed. Therefore, approximating the shape of the drop at the moment of its maximum spreading diameter by a spherical cap is appropriate. This assumption is also confirmed when considering the forces involved in the problem. In Figure 3, the line corresponding to We ) 0.2 follows the limit between rebound and deposition, with an empirical hysteresis around 2°. As We is low and viscous effects negligible (water drops), capillary forces are dominant. Let us denote di the diameter of a spherical cap formed by the liquid on the surface having a contact angle with the solid of θi. From the volume of the drop and simple geometry arguments based on the spherical cap approximation, di and d, the diameter of the impinging drop, are related by
di ) f(θi) ) [1 - (1 + cos θi)3 - (3 sin2 θi)(1 + cos θi)]1/3 d (2) with θi > 90°. The hysteresis energy, EH, is the energy stored in the difference of free surfaces of two configurations of the same drop of a given volume but with respectively contact angles of θa and θr. Thus, EH can be estimated as
EH ) σπ(dr2 cos θr - da2 cos θa) ) σπd2[(cos θr)f2(θr) (cos θa)f2(θa)] (3) Equating the kinetic energy of the impacting droplet (1/12Fπd3V2) to its hysteresis energy leads to the following condition to determine the minimum velocity, VC, allowing rebound to be observed:
VC ≈
[(cos θ )f (θ ) - (cos θ )f (θ )] 12σ Fd 2
r
2
r
a
a
(4)
This condition generalizes eq 1 when the effect of the hysteresis can no longer be neglected. As the mean contact angle, θm, and the contact angle hysteresis, H, are only functions of the advancing and receding static contact angles, θa and θr, eq 4 can be used to evaluate θm and H from the R/D limit. For our polypropylene porous-like surfaces, the best separation of the D and R events is obtained for H ) 2° at θm ) 150° (Figure 3, dashed line). These values are compatible with the ones presented in our previous paper. Keeping θm ) 150° and probing the effect of the contact angle hysteresis, H, in the range 0.2-25° can be visualized by the lower and upper dashed-dotted lines in Figure 3 which determine the shaded area. Furthermore, to each line representing the limit between deposition and rebound in Figure 3 corresponds a constant Weber number. Let us note this critical Weber number by WeC. From the definition of We, its value can be related to the advancing and receding constant angles by
Drop Impact on Porous Superhydrophobic PP
WeC ) 12[(cos θr)f2(θr) - (cos θa)f2(θa)]
Langmuir, Vol. 24, No. 24, 2008 14077
(5)
These WeC values, calculated from eq 5, have been added to Figure 3. This means that, for a given random-like superhydrophobic surface (θm and H constant), increasing the Weber number of the drop will enable it to pass through the D/R limit at a given constant Weber number, depending on the hysteresis of the system, and undergo rebound. The experimental transitions observed by Reyssat et al. and Bartolo et al. only for 2 mm drops impinging surfaces patterned with pillars, i.e., with a single-length-scale type of corrugation, are quantitatively different from ours. To facilitate the comparison, these transitions have been reported in Figure 3 by open and filled squares, respectively. Fragmentation occurs at lower impact velocity on our multiscale surfaces than on the patterned surfaces of Reyssat et al. This can be explained by the way the spreading lamella radially expands over a rough surface. As previously described,30 when the liquid lamella arrives over an asperity of the surface due to its inertia, it is deviated and its thickness decreases at places preceding the asperity because of mass and momentum conservation. In this way, the breakup of the lamella is enhanced by surface asperities. On surfaces with a periodic and dense structure of pillars of same height, it is more likely that the liquid smoothly spreads over their tops. On the other hand, on our random-like rough surfaces, asperities are easily encountered by the liquid lamella and breakup is more likely. It is believed that this difference between random-like surfaces and surfaces with a dense pattern of pillar of same height is genuine. The difference observed between our results and Bartolo’s results in terms of the D/R limit can be explained by the difference of hysteresis of the surfaces. Our surfaces present a mean hysteresis around 2° and an average mean static contact angle around 150°, but it is possible that values of the mean static contact angle as high as 163° can be locally encountered. In Bartolo study,27 the hysteresis value on patterned elastomer surfaces is not given, but the advancing static contact angle equals 154°. The regular patterning of their surfaces allows us to suppose a homogeneous and constant hysteresis. On the other hand, elastomer smooth materials are characterized, independently of the advancing and receding static contact angles, by low receding dynamic contact angles during drop impact. This prevents rebound as the deformation of the material allows a dissipation of energy during drop impact.31 In this way, it is possible to explain and show the importance of the hysteresis on the possibility to observe drop rebound. Figure 4 confirms such results: theoretical values of WeC for the D/R limit, calculated from eq 5, are displayed for various θm values and various values of hysteresis. Clearly, the (31) Voue´, M.; Rioboo, R.; Bauthier, C.; Conti, J.; Charlot, M.; De Coninck, J. J. Eur. Ceram. Soc. 2003, 23, 2769–2775.
Figure 4. Influence of the hysteresis and the mean static contact angle, θm, on the critical Weber number, WeC, defining the limit between deposition and rebound.
D/R limit is a function of the mean static contact angle but mainly depends on the hysteresis: whatever θm, increasing the hysteresis from 0.1° to 10° induces a change of a factor 102 in the value of the critical Weber number.
Conclusion We have shown that, on polymer superhydrophobic surfaces with multiscale type roughness, the outcome of the process of depositing or impacting a water drop is a function of the drop size and that this parameter has to be taken into account when the wettability of such surfaces is studied. In particular, the Wenzel/Cassie-Baxter transition and therefore the wettability of the system are functions of the drop size. The smaller the drop, the higher the deposition or impact velocity to get sticking of the liquid to the surface. We experimentally confirm that the minimum velocity to observe drop rebound follows a law in the inverse square root of the drop diameter. Moreover, we show that this limit depends on the contact angle hysteresis of the surface and corresponds to a constant Weber number, WeC. The same trend in terms of drop size is found for the minimum velocity to pass from rebound to fragmentation. The limit between rebound and fragmentation is expected to be lower on random-like surfaces than for surfaces with a dense array of pillars of same height. Acknowledgment. We acknowledge Prof. D. A. Ivanov and his team (Institut de Chimie des Surfaces et Interfaces, Mulhouse, France) for providing the SEM image of the polypropylene surface. The partial financial support of the FNRS and the Re´gion Wallonne are also acknowledged. LA802897G
