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Adhesion Forces and Contact Angles of Water Strider Legs Pal Jen Wei,† Sheng Chao Chen,† and Jen Fin Lin*,†,‡,§ Department of Mechanical Engineering, Center for Micro/Nano Science and Technology, and Institute of Nanotechnology and Microsystems Engineering, National Cheng Kung UniVersity, Tainan 701, Taiwan ReceiVed October 1, 2008. ReVised Manuscript ReceiVed NoVember 23, 2008 This study investigated the adhesion (pull-off) force and contact angles of a water strider’s leg. During hydrostatic experiments, the adhesion force was found to be 2 dyn. The image of a cross section of a live leg contacted with a deformed water surface provided the contact angle of 168.8°. A numerical scheme was proposed to determine the water surface on a groove wall of a seta. The results showed that the asperities of a seta are almost wetted, and the fraction of the wetted projection area was 0.69. Thus, the contact angle of a seta was 124.8°.
1. Introduction Wetting of solid substrates by liquids is one of the most important properties widely used by many technological applications.1,2 Besides the effects of surface stains and adsorption of molecular substances, the wetting ability of a solid surface also strongly depends on the surface roughness3,4 and the interfacial energy, which is related to the counterfacing properties and the fluid medium. The lotus effect, which is a lotus leaf regarded as one such typical application in nature, now means a hydrophobic property due to the surface structure.5,6 The wetting ability of a surface is characterized by the static (equilibrium) contact angle, or simply contact angle, made between a liquid droplet and a surface, which was found to strongly depend on the morphology of the surface.7 Theoretical models for liquid droplets on topologically rough and chemically inhomogeneous surfaces have been in existence for a long time,8-10 and these models have recently been used to rationalize the lotus effects on hydrophobicity11-14 and adhesion.15,16 Currently, biomimetics is an effective method for developing advanced materials and solving engineering problems.17-19 In nature, water striders are a type of insect with remarkable abilities to stand, slide, and jump on water surfaces using their * Corresponding author. E-mail:
[email protected]. Tel.: +886-62757575. Fax: +886-6-2352973. † Department of Mechanical Engineering. ‡ Center for Micro/Nano Science and Technology. § Institute of Nanotechnology and Microsystems Engineering.
(1) Adamson, A. W. Physical chemistry of surfaces; Wiley: New York, 1990. (2) Bhushan, B. Introduction to Tribology; Wiley: New York, 2002. (3) Wang, R.; Hashimoto, K.; Fujishima, A.; Chikuni, M.; Kojima, E.; Kitamura, A.; Shimohigoshi, M.; Watanabe, T. Nature 1997, 388, 431. (4) Baier, R. E.; Shafrin, E. G.; Zisman, W. A. Science 1968, 162, 1360. (5) Barthlott, W.; Neinhuis, C. Planta 1997, 202, 1. (6) Neinhuis, C.; Barthlott, W. Ann. Bot. 1997, 79, 667. (7) Vaibhav, B.; Suresh, V. G. Langmuir 2007, 23, 4918. (8) Wenzel, R. N. Ind. Eng. Chem. 1936, 28, 988. (9) Cassie, A. B. D.; Baxter, S. Trans. Faraday Soc. 1944, 40, 546. (10) Wenzel, R. N. J. Phys. Colloid Chem. 1949, 53, 1466. (11) Marmur, A. Langmuir 2003, 19, 8343. (12) Quere, D.; Lafuma, A.; Bico, J. Nanotechnology 2003, 14, 1109. (13) Patankar, N. A. Langmuir 2004, 20, 8209. (14) Otten, A.; Herminghaus, S. Langmuir 2004, 20, 2405. (15) Autumn, K.; Hansen, W. J. Comp. Physiol. A 2006, 192, 1205. (16) Feng, L.; Zhang, Y. A.; Xi, J. M.; Zhu, Y.; Wang, N.; Xia, F.; Jiang, L. Langmuir 2008, 24, 4114. (17) Yuan, Z. Q.; Chen, H.; Tang, J. X.; Gong, H.; Liu, Y. J.; Wang, Z. X.; Shi, P.; Zhang, J. D.; Chen, X. J. Phys. D: Appl. Phys. 2007, 40, 3485. ¨ ner, D.; Youngblood, J.; (18) Chen, W.; Fadeev, A. Y.; Hsieh, M. C.; O McCarthy, T. J. Langmuir 1999, 15, 3395. (19) Ball, P. Nature 1999, 400, 507.
water-resistant legs.20,21 Hu et al.22,23 designed experiments to study the physical mechanisms of water-walking creatures, such as water striders and spiders, in propelling themselves and climbing menisci and gave an excellent review of the hydrodynamics of water walkers. By directly attaching a force transducer to the backs of water striders, Goodwyn and Fujisaki24 measured stroke forces and concluded that the forces are approximately 10 times the body weights. A water strider has legs with water-resistant side-surfaces; however, the leg tips were found to be hydrophilic25 because there are no setae on them. When its legs are wetted, a water strider will raise the wetted leg from the water surface and clean it with its short front legs. At this time, it has to overcome the adhesion of water to leave the water surface. In this study, hydrostatic experiments including approach and retracting processes were performed to investigate the support and sink forces of water applied to a leg. The contact angles of insects, which denote the importance of surface roughness, have been noted and studied for a long time. The existence of variations in wetting properties can be correlated with processes of cuticle secretion.26 Great interest and effort have been applied to the measurements of biomaterials27,28 and live specimens.25,29,30 Recently, Bush et al.25 found that the contact angle of a body varies with the applied normal force. For a water strider’s leg, the contact angles exhibit a range between 167° for the advancing and 60° for the receding values. By investigation of the supporting force, the dimple depth,31 and the hierarchical structure of microseta and nanogrooves,32 Feng et al.30 proposed the contact angle equation for the oriented microseta structures and predicted the contact angles of the legs and the setae. Following their work, a numerical scheme was proposed in this study to determine the contact angle of a seta in a quantitative manner. In addition, observations of cross section (20) Cheng, L. Nature 1973, 242, 132. (21) Dickinson, M. Nature 2003, 424, 621. (22) Hu, D. L.; Chan, B.; Bush, J. W. M. Nature 2003, 424, 663. (23) Hu, D. L.; Bush, J. W. M. Nature 2005, 437, 733. (24) Perez Goodwyn, P.; Fujisaki, K. Entomol. Exp. Appl. 2007, 124, 249. (25) Bush, J. W. M.; Prakash, M.; Hu, D. L. AdV. Insect Physiol. 2008, 34, 117. (26) Pal, R. Bull. Ent. Res. 1951, 51, 121. (27) Chaudhury, M. K.; Whitesides, G. M. Langmuir 1991, 7, 1013. (28) He, B.; Patankar, N. A.; Lee, J. H. Langmuir 2003, 19, 4999. (29) Feng, L.; Zhang, Y. A.; Xi, J. M.; Zhu, Y.; Wang, N.; Xia, F.; Jiang, L. Langmuir 2008, 24, 4114. (30) Feng, X. Q.; Gao, X.; Wu, Z.; Jiang, L.; Zheng, Q. S. Langmuir 2007, 23, 4892. (31) Gao, X.; Jiang, L. Nature 2004, 432, 36. (32) Holdgate, M. W. J. Exp. Biol. 1955, 32, 591.
10.1021/la803223r CCC: $40.75 2009 American Chemical Society Published on Web 12/22/2008
Adhesion Forces & Contact Angles of Water Strider Legs
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Figure 1. Scheme of the developed measurement system.
Figure 3. Cross-section image of a live leg and deformed water surface which shows that the contact angle of the side of the leg is 168.8°.
Figure 2. Force and image results of hydrostatic experiments with a single leg.
of a live water strider’s leg were proposed for direct measurement of the contact angle.
2. Experimental Section A water strider has a flattened body that is approximately 15 mm long and 10 dyn in weight. In this study, a middle leg was used to investigate the adhesion force and contact angle. An in situ measurement system, which is schematically shown in Figure 1, was used to record force data and photographs during the whole process. The vertical force of a leg against a water surface was measured by fixing it to a transducer of a TriboScope system (Hysitron, US) and moving a water vessel by a stage of SP 3800N SPM (Seiko, Japan). To monitor the deformation of the water surface, an optical microscope lens and a CCD camera system are used to record film at 30 frame/s. The water vessel was moved upward and downward at constant speeds; the resultant force on the leg was balanced; and the vertical force was measured when the TriboScope system was run in open-loop mode. The measured force was adjusted to be zero (i.e., the weight of the indenter column with the leg was compensated) when the leg was far away from the water surface. Once the leg was in contact with the water surface, the force sensor detected a force drop (from zero) due to the adhesion of the water. In contrast, when the leg lost contact with the water surface, a force jump (to zero) was detected. These two sudden events, named jumpinto-contact and jump-off-contact, are helpful for synchronization of the recorded images.
3. Results and Discussion 3.1. Hydrophilic Leg Tip. The loading results of the water strider, as shown in Figure 2, revealed the maximum repulsive force of approximately 2 dyn. The corresponding images showed that the leg gradually depressed the water surface, and an obvious dimple was observed around the treading position. The dimple was observed to increase in size as the water level continued
Figure 4. Geometric relationship used to determine a possible water surface profile located at the seta surface.
upward. According to the theory of floating, the water weight displaced by the dimple is equal to the lift force. This explains that a greater dimple provides a greater lift force (float). The jump-off-contact force of the leg was found to be -2 dyn, which is approximately the magnitude of the measured maximum repulsive force. Because of the hydrophilic tip, the adhesion of water had to be overcome when the leg left the water surface. Considering the maximum attractive force resulted from the vertical surface tension, γ, around the leg bottom, we have a relation between the force F and the diameter of the leg’s tip Dleg as F ≈ π · Dleg · γ. Substituting the surface tension γ ) 0.07 N/m into the relation gives the diameter of the leg’s tip Dleg ) 90.9 µm, which agrees with the observation of the microscopic image (see Figure 3). 3.2. Contact Angle of Leg. On the basis of hydrostatic experiments of the leg, Feng et al.30 proposed the relation between the contact angle and the diameter of the leg. They concluded that the contact angle of the leg must be at least 168°. Bush et al.25 placed a droplet on a water strider’s leg and measured the contact angle to be 167° by microscope images. Here a cross section image of a live water strider’s middle leg provided a direct measurement of contact angle. The image, as shown in Figure 3, focused on the front of the deformed water surface, and both the submerged tip and back sections of the leg were out of
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a groove spacing of 400 nm and an asperity diameter of 165 nm, as shown in Figure 4. However, the free surface of water could not be exactly located at the intersection of groove and asperity. According to the Young-Laplace equation, the pressure difference between a water/air interface ∆p is related to the surface tension of water γ and the principle radius of the interface profile R:
∆p )
Figure 5. (a) Evaluated length of water film has the minimum at the position x ) 126.1 nm, and thus (b) the free surface of water is determined.
focus (see the scheme shown in the right-top corner). According to the profiles of water surface and the estimated cross section of the leg, the contact angle was approximately 168.6°, which agrees with the values provided by Feng et al.30 and Bush et al.25 The cross section image also showed that the leg tip is hydrophilic. 3.3. Contact Angle of Seta. On the basis of the CassieBaxter equation, Feng et al.30 derived the relation between the initial contact angle of wax θ0 and the contact angle of seta θ as
cos θ ) (π - θ0) · f · cos θ0 - (1 - f · sin θ0)
(1)
where f is the fraction of wetted projection area. They assumed that the entire asperities were wetted and the grooves were completely unwetted; therefore, the f was determined to be the ratio of the groove spacing to the asperity diameter. They inferred that the contact angle should be approximately 125° by giving
(
1 γ 1 + )γ· R R1 R2
)
(2)
where R1 and R2 are the orthogonal radii of curvature of the interface profile. For a 2D structure as shown in Figure 4, the principle radius equals the radius of curvature in the x-z plane since the other radius of curvature is infinite. Therefore, the hydrostatic pressure of water leads to a circular profile of interface. For an arbitrary point pair, A and B, of the seta surface with slopes of mA and mB, as shown in Figure 4, the slopes of water surface mA′ and mB′ can be obtained by rotating the mAtangent clockwise and the mB-tangent counterclockwise with the initial contact angle of θ0, respectively. Then the center of curvature O and thus the radius of curvature R can be obtained. The water contact of wax secreted on the legs is θ0 ) 105°,32 and Feng et al.30 indicated that this contact angle is not enough to induce the superhydrophobicity of legs. The length of water surface, which is summed by the water/seta interface S1 and the water/air interface S2, is a function of position, as shown in Figure 5a. The criteria of minimum length was then applied to determine the free surface profile of water at x ) 126.1 nm as shown in Figure 5b, which is slightly lower than the intersection of asperity and groove at x ) 135 nm. The fraction of wetted projection area is evaluated as f ) 0.69, i.e., S1′/(S1′ + S2′) ) 0.21. Substituting the f value into eq 1, the contact angle of seta is 124.8°, which concurs with the prediction of Feng et al.30
4. Conclusions When a water strider cleans its wetted leg, it generally stands on the water with only three legs (one middle leg and two rear legs). The adhesion of water on the single leg was found to be 1/5 of its weight; that is, a water strider has to gain a float of 6/5 weight to raise one single leg. Feng et al.30 found that one single leg can obtain a maximum force of 10 times the weight. It indicates that the superior water repellency is necessary to water striders to adapt to various situations, such as jumping or landing from the water,23 because the adhesion of water is very large to them. Acknowledgment. This work was supported by the Center for Frontier Materials and Micro/Nano Science and Technology Center, National Cheng Kung University, Taiwan (D97-2700). LA803223R
