Application of Superhydrophobic Edge Effects in Solving the Liquid

In this paper, we discuss various edge effects on the outflow behaviors of water ... used for characterizing the stability of water around an edge, wh...
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Langmuir 2007, 23, 3230-3235

Application of Superhydrophobic Edge Effects in Solving the Liquid Outflow Phenomena Jihua Zhang,†,‡ Xuefeng Gao,*,† and Lei Jiang*,† Institute of Chemistry, Chinese Academy of Sciences, Beijing 100080, People’s Republic of China, and Graduate School of the Chinese Academy of Sciences, Beijing 100049, People’s Republic of China ReceiVed October 12, 2006. In Final Form: December 14, 2006 In this paper, we discuss various edge effects on the outflow behaviors of water around the edge to solve the troublesome problem that frequently brings about great inconvenience in daily lives. A simple method of pressing a drop over the edges of a conical frustum was adopted here to explore the stability of a suspended drop around the edges. On the basis of experiments and theoretical analyses, the critical pressure Pc and the pressing work ∆Ew were used for characterizing the stability of water around an edge, which were found to be closely related to the geometric morphologies, the microstructures of sides, and the material characteristics. The stability of suspended drops around the edge may be enhanced by increasing the rise angle ω, the actual rise angle φ, and the size of edge circles and by using low surface energy materials. Thus, a facile and effective strategy has been successfully developed. We believe that these findings will help to design novel tubes and bottles without a liquid outflow problem.

Introduction Surface wettability is an important characteristic of solid materials, which is involved with molecular microscopic surface structures and macroscopic geometrical morphologies.1-3 Up to now, researchers have paid great attention to the control of surface wettability by chemical composition and microstructures.4-18 However, studies on the effect of edges on surface wettability are few, although certain specified morphologies of edges and their effects have been skillfully adopted in scientific research and industrial applications. For example, it is the existence of the specific shaped edge that makes a drinking glass with a sharp rim able to hold more than its volume of liquid and reproduce a well-defined drop in pendent drop methods for measuring the surface tension of liquids.19 As each coin has two sides, the edge effect also has the disadvantage and brings us great inconve* Corresponding authors. E-mail: (X.G.) [email protected] and (L.J.) [email protected]. † Institute of Chemistry, Chinese Academy of Science. ‡ Graduate School of the Chinese Academy of Science. (1) Adamson, A. M. Physical Chemistry of Surfaces, 6th ed.; John Wiley and Sons: Toronto, 1997; Ch. 1. (2) Chappuis, J. In Multiphase Science and Technology; Hewitt, G. F., Delhaye, J. M., Zuber, N., Eds.; Hemisphere Pub. Corp.: Washington, DC, 1985; Vol. 1, p 387. (3) de Gennes, P. G. ReV. Mod. Phys. 1985, 57, 827. (4) Que´re´, D. Phys. A 2002, 313, 32. (5) McHale, G.; Shirtcliffe, N. J.; Aqil, S.; Perry, C. C.; Newton, M. I. Phys. ReV. Lett. 2004, 93, 36102. (6) (a) Feng, L.; Li, S.; Li, H.; Zhai, J.; Song, Y.; Jiang, L.; Zhu, D. Angew. Chem., Int. Ed. 2002, 41, 1221. (b) Gao, X.; Jiang, L. Nature 2004, 432, 36. (7) Onda, T.; Shibuichi, S.; Satoh, N.; Tsujii, K. Langmuir 1996, 12, 2125. (8) Shibuchi, S.; Onda, T.; Satoh, N.; Tsujii, K. J. Phys. Chem. 1996, 100, 19512. (9) McCarthy, T. J.; Oner, D. Langmuir 2000, 16, 7777. (10) Yoshimitsu, Z.; Nakajima, A.; Watanabe, T.; Hashimoto, K. Langmuir 2002, 18, 5818. (11) Blossey, R. Nat. Mater. 2003, 2, 301. (12) Xie, Q.; Xu, J.; Feng, L.; Jiang, L.; Tang, W.; Luo, X.; Charles, C. H. AdV. Mater. 2004, 16, 302. (13) Shi, F.; Wang, Z.; Zhang, X. AdV. Mater. 2005, 17, 1005. (14) Miwa, M.; Nakajima, A.; Fujishima, A.; Hashimoto, K.; Watanabe, T. Langmuir 2000, 16, 5754. (15) Gau, H.; Herminghaus, S.; Lenz, P.; Lipowsky, R. Science 1999, 283, 46. (16) Lam, P.; Wynne, K. J.; Wnek, G. E. Langmuir 2002, 18, 948. (17) Wenzel, R. N. Ind. Eng. Chem. 1936, 28, 988. (18) Cassie, A. B. D; Baxter, S. Trans. Faraday Soc. 1944, 40, 546. (19) Princen, H. M. In Surface and Colloid Science; Matijeviæ, E., Ed.; John Wiley and Sons: New York, 1969; Vol. 2, p 254.

Figure 1. Water outflowing from an oblique smooth hydrophilic glass tube.

niences. Most people have encountered such a nuisance as shown in Figure 1 that, when decanting a liquid such as water and alcohol from a bottle (or tube), the liquid usually moves over the top, then adheres to the side and flows along it, resulting in some residue on the side wall and even splashing droplets on the ground. Thus, it is very important to study the role of edge effects in surface wettability, especially for solving the liquid outflow problem. In the 1870s, Gibbs first proposed the wetting relations of a sharp edge composed of two adjacent smooth surfaces.20 Afterward, Oliver et al. perfectly deduced Gibbs’ conclusions and proved them via experiments.21 It was well-known that apparent contact angle hysteresis (CAH) phenomena widely occur when a liquid drop or fluid spreads on a flat solid, especially when the front advances to the corner of the edges, which was partly ascribed to the edges possessing edge energy.20-24 Although the energy is small, it is sufficient to resist the progress of the contact line. So far, most of the works reported have focused on cases of smooth edges. However, real solid surfaces are actually not smooth but very rough with pores, undulations, and other (20) Gibbs, J. W. The Collected Works of J. Willard Gibbs; Yale University Press: New Haven, CT, 1961; Vol. 1, p 326. (21) Oliver, J. F.; Huh, C.; Mason, S. G. J. Colloid Interface Sci. 1977, 59, 568. (22) Oliver, J. P.; Huh, C.; Mason, S. G. Colloids Surf. 1980, 1, 79. (23) Huh, C.; Mason, S. G. J. Colloid Interface Sci. 1977, 60, 11. (24) Oliver, J. F.; Mason, S. G. Colloid Interface Sci. 1977, 60, 480.

10.1021/la063006w CCC: $37.00 © 2007 American Chemical Society Published on Web 01/25/2007

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θc ) θa,0 + ω

(1)

where ω is the rise angle of the side; θa,0 is the intrinsic advanced angle; and R is the edge angle subtended by the top.

R ) 180° - ω

(2)

Critical Pressure. Since the water drop does not spread between the superhydrophobic surface and the edges, the force state may be considered as the quasi-balance. The vertical component of water surface tension, γ, may be calculated (the downward forces are taken as positive) by the following equation:31,32

f ) -2πr0γ cos(θ - 90°) Figure 2. (a) Schematic illustration for describing the method of using a superhydrophobic surface pressing a drop over the edge. (b-f) Time sequence CCD images of the Al sample at the conditions of ω ) 60°, ψ ) 23.8°, and d0 ) 4 mm. Scale bar: 1 mm.

asperities. On the basis of the newly developed knowledge of roughness-induced superhydrophobicity and extremely low adhesion,25-30 we believe that introducing fine micropattens on the hydrophobic edges with different rise angles of the side and exploring their effects on the surface wettability are very important, especially in solving the problem of liquid outflowing from the edge. In this paper, a simple method of pressing a drop around edges was adopted to study the dynamic behavior of a water drop over the edge. Some sharp edges with sawtooth microstructures were prepared, and the outflowing processes of water over the edges were observed by a high-speed CCD camera and analyzed based on the measurement of advanced angles. Subsequently, we analyzed in detail the effects of the sharp edges with different rise angles and textured micropatterns on the stability of water over the edge. Finally, we proposed a facile strategy to solve the outflowing problem of edges (Figure 1) by applying the cooperative effect of rough microstructures with low surface energy material, instead of tailoring the special morphology such as the hawk mouth commonly used in domestic products. We believe that these findings would help to improve certain products involved with the problem of liquid outflowing over edges and bring about great convenience in our daily lives and industrial processes.

Theory Geometrical Conditions. To study the role of edge effects in the surface wettability and the stability of water flowing over the edge, the method of pressing a drop around edges was adopted here as shown in Figure 2a. A certain amount of water was dropped on the top of the conical frustum to ensure that the contact line reached the edges. Subsequently, a superhydrophobic surface placed parallel to the top surface and began to press the drop downward very slowly. As a result, the drop suddenly flowed over the edges as being flattened to a certain depth. Before the shape of the drop was distorted and the drop moved over the edge, the critical advanced angle, θc, should satisfy the Gibbs’ equation, which may be derived from a purely geometrical extension20 (25) Extrand, C. W. Langmuir 2005, 21, 10370. (26) Lafuma, A.; Que´re´, D. Nat. Mater. 2003, 2, 457. (27) Extrand, C. W. Langmuir 2002, 18, 7991. (28) Extrand, C. W. Langmuir 2004, 20, 5013. (29) Extrand, C. W. Langmuir 2006, 22, 1711. (30) Carbone, G.; Mangialardi, L. Eur. Phys. J. E 2005, 16, 67.

(3)

where θ is the CA around the edge, and r0 is the radius of the edge circle. As the drop is pressed, the apparent CA increases from θ0 to θ, and the change of the upward surface tension may be given by

∆f ) -2πr0γ (sin θ - sin θ0)

(4)

Considering the spring effect of a drop,33-37 the pressure P should be approximately equal to the changes in the vertical surface tension. Here, the CA of the superhydrophobic surface is high (i.e., the advanced angle close to 180°). Thus, the critical pressure may be simply expressed as

Pc ) -2πr0γ (sin θc - sin θ0)

(5)

where the effect of gravity is ignored due to the radius of the drop being smaller than the capillary constant. Experimental Procedures Sample Preparation. Single asperities of various shapes and sizes were machined from aluminum alloy (Al) rods (Keyi factory, Beijing, China). These rods were machined into small conical frusta (the accuracy of finish was (0.01 mm) with rise angles of ω ) 30, 45, 60, and 90° (a right angle, cylinder). Rough sawtooth microstructures on the side of the conical frusta were achieved with cutter shape, cutter orientation, and cutter speed. All these tops of asperities were carefully ground with various sand papers and then polished with a 100-grit diamond rag wheel. The root-mean-square roughness of the smooth top and edges was controlled below 0.1 µm (AFM observations, Seiko Instruments Inc., Tokyo, Japan). The polishing Al conical frusta were ultrasonically washed in benzene, acetone, alcohol, and Mill-Q water for about 15 min, respectively. Afterward, the samples were dried using N2 gas and immediately immersed into a 1.0 wt % ethanol solution of hydrolyzed heptadecafluorodecyltrimethoxysilane (FAS-17, CF3(CF2)7CH2CH2Si(OCH3)3, Shin-Etsu Chemical Co., Ltd., Tokyo, Japan) for 3 h at room temperature.38 Finally, the FAS-modified samples (FAS-Al) were taken out and heated at 140 °C in the oven for 1 h. Characterization. The pendent droplet method was used to measure the intrinsic water advanced angle θa,0 on the top of each (31) There is the vertical pressure of liquid drop around the edges caused by the curvature. Washburn40 derived an equation for the pressure needed to either force a liquid into or expel it from a capillary, the CA of the liquid with capillary wall, θ, and capillary radius, r: P ) 2γ cos θ/r. We can obtain the downward force suspending the liquid drop: f ) 2πrγ cos(θ - 90°), analogous to the capillary. (32) Wapner, P. G.; Hoffman, W. P. Langmuir 2002, 18, 1225. (33) Richard, D.; Que´re´, D. Europhys. Lett. 2000, 50, 769. (34) Richard, D.; Que´re´, D. Europhys. Lett. 1999, 48, 286. (35) Clanet, C.; Que´re´, D. J. Fluid Mech. 2002, 460, 131. (36) Okumura, K.; Chevy, F.; Richard, D.; Que´re´, D.; Clanet, C. Europhys. Lett. 2003, 62, 237. (37) Richard, D.; Clanet, C.; Que´re´, D. Nature 2002, 417, 811. (38) Li, H.; Wang, X.; Song, Y.; Lin, Y.; Li, Q.; Jiang, L.; Zhu, D. Angew. Chem., Int. Ed. 2001, 40, 1743.

3232 Langmuir, Vol. 23, No. 6, 2007 asperity of the Al and FAS-Al samples (DataPhysics OCA 20, the advancing speed of water is 1 µL/s). Water was deposited on the top surface of the conical frusta through a 1 mL microsyringe equipped in the contact angle system. The deposited volume of water was calculated by the formula in the Appendix, and the initial deposited angle θ0 was set to be 110°. A superhydrophobic surface with an apparent water CA of 165° was prepared by photolithography to construct arrayed square posts on silicon wafers and then were treated with the previous silane agents. Its back was attached to a thin rod. Then, it was hung on a microelectronic balance of the dynamic contact angle measurement (DCAT11, DataPhysics Instruments GmbH, Filderstadt, Germany) in a vertical orientation, as shown in Figure S1. The superhydrophobic surface moved downward at a speed of 0.05 mm/s until the front of the drop advanced over the edges. Afterward, the superhydrophobic surface was elevated to the initial position. All test processes and the collection of data were automatically controlled through the software SCAT12 (version 1.01). Meanwhile, they were monitored via a high-speed CCD camera and recorded in image format at intervals of 200 and 3.3 ms (HCC1000F, VDS Vossku¨hler GmbH, Osnabru¨ck, Germany). Software ImageViewer v2.0.2 was used with all image information. The tests of each sample were repeated 5 times, and the sample was dried by N2 gas after the test was finished. The test conditions were restricted at 25 °C and a relative humidity of 30%. The density and viscosity of water in the tests were 0.9882 g/cm3 and 1.0 mPa s, respectively, and the surface tension was measured by the Whilhelmy technique, 72.56 ( 0.01 mN/m. Outflow of Water in Tubes. Smooth polytetrafluoroethylene tubes (Teflon, Jiangyin Huanyu Rubber and Plastic Co., Ltd., Jiangyin, China) were purchased, and afterward, the tops of tubes were further polished to eliminate water CA hystereses due to the roughness. We used an autocontrol sampler to control the flowing velocity. A needle and sealants were adopted to connect the Teflon tube and the syringe in the sampler. Then, water was affused into Teflon tubes at a constant flowing velocity of 20 mL/h, which was slow enough to observe the dynamic behavior of water around the edges of Teflon tubes. The same CCD camera was also used to record the outflow processes of water from various tubes.

Results and Discussion Figure 2b-f shows the typical CCD images of a superhydrophobic surface pressing a drop over the edge (Al, ω ) 60° and d0 ) 4 mm). The record time was evaluated by the frame frequency and number. After contacting the superhydrophobic surface, the drop began to deform and flattened. Meanwhile, the apparent CA gradually increased during the process. As the time of the superhydrophobic surface pressing on the drop reached 2.719 s (Figure 2c), its apparent CA around the asperity increased to 133.1°, larger than the initial one (110°) in Figure 2b. As predicted by the Gibbs’ equation (eq 1), the effect of the edges can enhance the apparent CA of water on the solid surface due to the rise angle ω > 0. However, the collapse of the drop around the edge suddenly occurred at the right corner (Figure 2d, t ) 13.358 s). In this case, the advanced angle may be considered as the critical value θc. Afterward, the drop flowed along the side of the conical frustum as shown in Figure 2e. However, as the time passed about 30 s, the superhydrophobic surface was stopped and elevated (Figure 2f). Because of the strong CA hystereses and adhesion on smooth hydrophobic surfaces, water did not flow along the side any longer and settled on the right corner between the top and the side. Apparently, no remains were found on the superhydrophobic surface after the experiments. Note that it was not all the cases around the edges and that the movement of the drop over the edge only occurred in the right side of the conical frustum, although the CA of a drop on a two-dimensional surface is usually homogeneous. This might be ascribed to the

Zhang et al.

Figure 3. (a) Actual micrograph of the sawtooth microstructures on the side of conical frustum with ω ) 45°. (b) Schematic illustration for describing the geometrical relations between the intrinsic advanced angle θa,0 of water at the edge and the rise angle of the side as the micropatterns were introduced on the side.

slight deviation in the parallel direction between the top of conical frusta and the superhydrophobic surface. To explore the effect of microscopic structures and macroscopic morphologies on the behaviors of water flowing around the edge, we first machined fine micropatterns on the sides based on ref 25. Figure 3a showed a representative optic view of the side features in the case of the rise angel ω ) 45°. Clearly, the sawtooth microstructure covered the whole side. In our experiments, fine micropatterns introduced on the sides make the relations between the surface wettability and the macroscopic geometrical features more complex, which was suggested and experimentally verified by Extrand.25 Figure 3b sketches the geometrical details of the drop advancing over the edges. Clearly, the actual rise angle should be ω + ψ in this case. Similar to Extrand’s equation,25 the critical advanced angle θc, beyond which the drop moved over the edge, can be written as

θc ) θa,0 + ω + ψ

(6)

It was found that the experimental values θc agreed well with those calculated by eq 6 (see Supporting Information Table 1). Previous studies have indicated that the incomplete parallelism and fine structures at the sub-micrometer scale by machining may influence these experimental θc values.5 Interestingly, the θc value may be even beyond 180° for the top surface (see Figure S2), although it is well-known that the theoretical CA value is not more than 180° for a droplet on a solid surface in the air. Thus, the issue on the surface wettability and the outflow behaviors of water at the edges of the flat top surface and textured sides would be more complex than a simple mode of the twodimensional smooth solid surface.25 Figure 4 shows the recorded pressure-position plots when a superhydrophobic surface pressed a drop over the edge (d0 ) 4 mm) of the FAS-Al samples with varied macroscopic morphologies: the rise angle of the side ω ) 30, 45, 60, and 90°, respectively. With a drop gradually being pressed, the pressure dramatically increased. We found in the experiments that the initial change of the pressure-position plots had the same trend just as predicated by eq 5, similar to the sinusoids at the range between the deposited angle θ0 and the measured critical advanced angle θc. Besides, there were turning points in the force plots (a, b, c, and d points) after a drop was pressed to move over the edge and the pressure suddenly decreased. Here, the critical point Pc can be determined according to the initial state of a drop

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Figure 4. Pressure-position plots of FAS-Al conical frusta with the top diameter d0 ) 4 mm. To illustrate clearly, we make these plots parallel to move some distance along the x coordinates.

sliding over the edge. In other words, Pc may be used to characterize the stability of a drop sliding around the edges since the macroscopic movement of the drop would occur once the pressure was beyond Pc. However, the initial movement of a drop sliding over the edge did not indicate that it necessarily flowed along the side. Actually, even beyond the critical value, the pressure may further slowly increase, for the example of ω ) 30°, accompanied with some fluctuations in the force plots during the late process. In contrast, the pressure would dramatically reduce after the critical point d in the case of ω ) 90° and have almost no fluctuations in the plot. As compared with the qualitative analyses of CCD images, the pressure-position plot can be used to quantitatively characterize the dynamic behaviors of a drop sliding around the edge, and the critical pressure may be adopted to characterize its outflow stability. For the same size of edges, the larger the Pc, the steadier a drop flow over the edge, that is, it is more difficult for the drop to go off the edge. To clearly elucidate the effects of the surface microstructures, the rise angle of sides, and the edge sizes on the stability of a drop flowing over the edge, we introduced the parameter of actual rise angle φ into the following discussions, which included the contributions of ω and ψ (Supporting Information Table 1). As shown in Figure 3b, the φ value is equal to ω + ψ. Consequently, eq 6 can be simplified: θc ) θa,0 + φ. As for the Al samples, the plots of the critical pressure Pc versus the actual rise angle φ are shown in Figure 5a. Apparently, the Pc value increased with the increase of the actual rise angle φ and the size of the edge circles. For a certain material, the larger the actual rise angle φ, the larger the critical advanced angle θc, which indicated that it was more difficult off the edge. Moreover, for FAS-Al samples with a lower surface energy, the Pc values became larger than those of the Al samples, although they possessed similar increasing trends with the actual rise angle of the side and the size of the edge as shown in Figure 5b. Just as is predicated by eqs 1 and 5, the effect of the intrinsic advanced angle θa,0 on the stability of a suspended drop moving over the edge was indeed observed; that is, the larger the intrinsic advanced angle θa,0 of materials, the steadier the suspended drop moving over the edge. However, the inherent dewetting property governed by low surface energy molecules actually was not the only key factor to control the stability of a drop moving over the edges, which was not like the smooth surface.25 Here, the effect of geometrical features must be considered. For example, the Pc

Figure 5. Plots of the critical pressure Pc vs the actual rise angle φ. (a) Al and (b) FAS-Al.

value (0.6215 mN) in the FAS-Al case of φ ) 41.7° was smaller than the one (1.0503 mN) in the Al case of φ ) 100.5° on the same condition of edge circle d0 ) 4 mm. The drop around the edge of the Al sample was steadier in such cases, although the intrinsic advanced angle of Al (83.6 ( 2.1°) is smaller than that of FAS-Al ones (110 ( 1.7°). Thus, the state of a drop around the edge may be strongly influenced by the geometrical features, including the rise angle and the surface microstructures of sides. Note that the experimental values of Pc agree well with the theoretical ones calculated by eq 5 and that moving the superhydrophobic surface at a range of 0.01-0.1 mm/s did not cause any obvious changes to our results, which indicates that the system used here was feasible to study the outflow problem of liquid around the edge. The slight errors in the experiments might result from incomplete parallelism, pressure loss of superhydrophobic surfaces, and hydrostatic pressure of a drop.26,30 Although the critical pressure Pc was useful to determine the stability of a drop around the edges, the size effect of edge circles may interfere with the comparison of Pc. It was difficult to determine the combined effect of sizes and these geometrical angles (ω and ψ) on the stability of a drop only by the Pc values. For example, the Pc value of the Al sample was 0.5534 mN in the case of φ ) 100.2° and d0 ) 2 mm, smaller than the one (0.6123 mN) in the case of φ ) 83.8° and d0 ) 4 mm. Although the latter had a larger Pc value with a steadier state of drop around the edge, the φ value was less than that of the former, which indicated the contradiction of less distortion (the difference between the critical θc and the deposited θ0) causing less stability of the drop. Thus, the pressing work ∆Ew was required to further analyze the stability of a drop around the edge in different cases.

3234 Langmuir, Vol. 23, No. 6, 2007

Figure 6. Dependence of the pressing work ∆Ew on various sizes of edges and actual rise angle φ. (a) Al and (b) FAS-Al.

Figure 6 shows the experimental pressing work ∆Ew of the drops around various edges of the conical frusta. To state the relation between ∆Ew and φ more explicitly, the solid lines as empirical curve fitting by software ORIGIN (version 7.0) were plotted in Figure 6. Clearly, ∆Ew of the Al or FAS-Al samples increased with the increase of the actual rise angle and the size of the edge circles, and the value of the FAS-Al sample was always larger than that of the Al sample for the edge with the same size and actual rise angle. Although the experimental work ∆Ew was only for cases at the deposited angle θ0 ) 110°, the geometrical effects, including the rise angle, the surface microstructures of sides, and the size of edges, on the stability of a drop moving over the edge can be determined. For example, by comparing ∆Ew, we may easily conclude that the drop in the previous case of edge circle d0 ) 4 mm (0.2136 µJ) was steadier than that of d0 ) 2 mm (0.0957 µJ). So, the stability of a suspended drop around edges can be improved by the following ways: tuning macroscopic geometrical features to increase the rise angle ω, introducing rough microstructures on the sides to increase the actual rise angle φ, increasing the size of edge circles, and using materials with a lower surface energy. On the basis of the previous analyses, we could solve the troublesome outflowing problem of fluid along the sides of bottles as shown in Figure 1 by simply introducing rough microstructures on the sides and modifying them with materials of lower surface energy. Actually, our aim is to make the fluidic flow around the edge so steady to a certain extent that it suddenly ruptures and falls down without adhering to the side, avoiding the occurrence of the outflow along the side at the beginning. To better elucidate

Zhang et al.

Figure 7. Distinct behaviors of water outflowing around Teflon capillaries. (a-c) No apparent outflowing occurred for the capillary with rough micropatterns on the sidewalls. (c-f) Typical outflowing for the capillary with smooth untreated sidewalls.

it, we have performed a controlled experiment as follows. Since tubes are the most used configuration in our daily lives, for example, bottles for holding beer, soy, and wine, we chose commercial Teflon capillary as the mode, which had a rise angle of 90° and a lower surface energy with an intrinsic advanced angle of 121.3 ( 0.3°. To obtain a larger actual rise angle φ, we machined sawtooth microstructures as shown in Figure 3a on the surface of the sides and then introduced finer sub-micrometer scale roughness with sand paper, which could not only improve the stability of water around the edge so as to maintain a perfect spherical shape before the fracture but make the sides superhydrophobic so as to greatly reduce the adherence of water to the sides.6-14 Figure 7 showed several representative optical micrographs of water outflowing from the smooth and textured Teflon tube with an outer diameter of 1.5 mm and an inner diameter of 0.5 mm. When water was affused into the textured Teflon tubes with the root-mean-square roughness of edge at a range of 0.851-1.560 µm at a constant velocity of 20 mL/h, the drop suspended on the top would gradually grow and reach the edge (Figure 7a). Interestingly, the adhesive phenomenon and the further flow along the side did not occur in successive seconds and the water front did not advance over the edge any longer. Afterward, water flow suddenly ruptured (see Figure 7b) and slid out of the tube without any remains around the sidewall as shown in Figure 7c. However, it was not the case if the rough microstructure was not introduced on the sides. As shown in Figure 7d-f, the problem of water outflowing over the edge and

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around the edge. Thus, a facile and effective strategy was developed to make liquid suspended around the edge so steady that it suddenly ruptures and falls down without adhering and flowing along the side at the beginning. For example, the bothersome problem of water outflowing over the tube mouth, adhering, and flowing along the side would disappear only by introducing rough multiscale microstructures on the side of the Teflon tube, although it inevitably occurs for a smooth hydrophobic Teflon tube, especially for a hydrophilic tube as shown in Figure 1. Therefore, we believe that these findings would be very helpful to guide innovative design of some tubes and bottles involved with the outflow problem of liquid at the edges.

Appendix Figure 8. Side view of a drop deposited on the top of a conical frustum in a partial wetting situation: (a) θ0 < 90° and (b) θ0 > 90°. R is the radius of curvature of the spherical cap formed by the drop.

adhering to the side continued to occur in the case of smooth Teflon tubes (the edge root-mean-square roughness was 38.90 ( 2.37 nm), although its degree was less than that of the smooth hydrophilic glass tube in Figure 1 because Teflon has a lower surface energy. Apparently, it was not ideal for solving the troublesome outflow problem if only using low surface energy material to modify the tube surface, without combing it with rough microstructures introduced on the sidewall. Thus, these findings will be of significant value in future practical applications, although engineers have currently realized that the use of low surface energy polytetrafluoroethylene as the top material of bottles for holding soy and oil may greatly reduce the outflow of fluid over the edge. Our strategy for solving the problem of liquid outflowing and adhering to the side would bring great convenience and economical savings in our daily lives and as well as in industrial productions.

Conclusion To solve the troublesome problem of liquid outflowing over the edge and adhering to the side that frequently occurs, we discussed various edge effects on the surface wettability and the outflow behaviors of water around the edge in detail. A simple method of pressing a drop over the edge was adopted here to explore the stability of a drop suspended around the edges. On the basis of experimental observations and theoretical analyses, the critical pressure Pc and the pressing work ∆Ew were proposed successively for characterizing the stability of a suspended drop around the edge. It was found that the geometric morphologies, the surface microstructures, and the molecule characteristics play an important role in controlling the stability. The increase of the rise angle ω, the actual rise angle φ, the size of edge circles, and the use of hydrophobic FAS molecules with a lower surface energy may greatly enhance the stability of suspended drops

Ignoring the effect of gravity, a drop deposits on the top of a small solid conical frustum and then forms a spherical cap around the edge circle, as shown in Figure 8, where R is the radius of curvature of the drop, and θ0 is the apparent CA (Figure 8a, θ0 < 90°; Figure 8b, θ0 > 90°). The volume of the drop, V, can be expressed as a function of θ0 and R39

π V ) R3(1 - cos θ0)2(2 + cos θ0) 3

(7)

According to eq 7, we can obtain the required volume of the drop on the condition of the known θ0 and R. Because of the known length of the contact line, namely, the diameter d0 of the top surface of the conical frustum, R can be derived from the simple relations

R)

d0 2 sin θ0

(8)

The volume of the drop, V, can be expressed again as a function of θ0 and the diameter d0

V)

2 π 3(1 - cos θ0) (2 + cos θ0) d0 24 sin3 θ

(9)

0

As known from the Gibbs’ equation, the stability condition of a liquid drop around the edges is θ < θa,0 + ω. So, the initial θ0 of the drop deposited on the edges can be determined as θr,0 < θ0 < θa,0 + ω (θr,0 is the intrinsic receded angle of the drop on the smooth surfaces). Acknowledgment. The Graduate School of the Chinese Academy of Sciences and National Center for Nanoscience and Technology is thanked for supporting this work. Also, thanks to X. Sheng for helpful discussions and suggestions. Supporting Information Available: Graphs of additional information concerning the experimental setup and results of advanced angle around the edges measured by CCD images. This material is available free of charge via the Internet at http://pubs.acs.org. LA063006W (39) Que´re´, D.; Azzopardi, M. J.; Delattre, L. Langmuir 1998, 14, 2213. (40) Washburn, E. W. Proc. Natl. Acad. Sci. U.S.A. 1921, 7, 115.