pubs.acs.org/Langmuir © 2009 American Chemical Society
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Characteristics of Water Strider Legs in Hydrodynamic Situations Pal Jen Wei,‡ Yan Xing Shen,‡ and Jen Fin Lin*,‡,§,
Department of Mechanical Engineering and §Center for Micro/Nano Science and Technology and Institute of Nanotechnology and Microsystems Engineering, National Cheng Kung University, Tainan 701, Taiwan, )
‡
Received January 16, 2009. Revised Manuscript Received March 18, 2009 This study investigated the forces and the cross-section images of a water strider’s leg through experimental observations. In the vertical direction, the spring coefficients were found to be 0.6 N/m for the leg and 0.3 N/m for the water, which provide a water-treading stiffness of 0.2 N/m. In the horizontal directions, besides the alignment of the microsetae, the large cuticle forces were also related to the resistant side in a Wenzel state.
1. Introduction Water striders are remarkable with their hydrophobic legs, which generate a curvature of the water surface such that their weight is supported by the surface tension force.1-3 They have flattened bodies and thin legs covered with setae to remain nonwetted.3-6 They can stroke with driving legs to gain high speeds;7 in contrast, they can stand at rest on the water surfaces of rivers and seas with variable vibrations and flows.8,9 Substantial advances have been made in the hydrodynamics underlying the surface of locomotion,1,3,7-12 and stroke forces have been measured to be approximately 10 times their body weight.11 The mechanism of water-repellent legs4-6 was found to result from the microsetae structures and covered wax. Feng et al.6 predicted the contact angles of the water strider’s legs through the proposed equation for the oriented structures together with an investigation of the supporting force and dimple depth. Wei et al.13 proposed the direct measurement of the contact angle through observations of a cross section of a water strider’s leg. However, the contact angles of a surface are strongly related to its wetting states;14-16 therefore, the contact angles of the body vary with the state of the cuticle. For a water strider’s leg, the contact angles exhibit a range of between 167° for a CassieBaxter state and 60° for a Wenzel state.7 Previous hydrodynamic investigations focused on the alignment of microsetae. The tiny friction forces against forward flow and large stroke forces against lateral flow were argued to result from the anisotropy of the cuticle.7,8 In this study, we investigated *Corresponding author. E-mail:
[email protected]. Tel: +886-62757575. Fax: +886-6-2352973. (1) Andersen, N. M. Vidensk Meddr Dansk Naturh Foren. 1976, 139, 337. (2) Keller, J. B. Phys. Fluids 1998, 10, 3009. (3) Hu, D. L.; Chan, B.; Bush, J. W. M. Nature (London) 2003, 424, 663. (4) Gao, X.; Jiang, L. Nature (London) 2004, 432, 36. (5) Sun, T. L.; Feng, L.; Gao, X.; Jiang, L. Acc. Chem. Res. 2005, 38, 644. (6) Feng, X. Q.; Gao, X.; Wu, Z.; Jiang, L.; Zheng, Q. S. Langmuir 2007, 23, 4892. (7) Bush, J. W. M.; Hu, D. L.; Chan, B. Adv. Insect Physiol. 2008, 34, 118. (8) Cheng, L. Nature (London) 1973, 242, 132. (9) Dickinson, M. Nature (London) 2003, 424, 621. (10) Dickinson, M. H.; Farley, T. C.; Full, R. J.; Koehl, M. A. R.; Kram, R.; Lehman, S. Science 2000, 288, 100. (11) Perez Goodwyn, P.; Fujisaki, K. Entomol. Exp. Appl. 2007, 124, 249. (12) Perez Goodwyn, P.; Wang, J. T.; Wang, Z. J.; Ji, A. H.; Dai, Z. D.; Fujisaki, K. J. Bionic Eng. 2008, 5, 121. (13) Wei, P. J.; Chen, S. C.; Lin, J. F. Langmuir 2009, 25, 1526. (14) Wenzel, R. N. Ind. Eng. Chem. 1936, 28, 988. (15) Cassie, A. B. D.; Baxter, S. Trans. Faraday Soc. 1944, 40, 546. (16) Wenzel, R. N. J. Phys. Colloid. Chem. 1949, 53, 1466.
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the hydrodynamic characteristics of a water strider’s legs through experimental observations. For stably standing on the water surface, the six legs of water striders were found to provide independent water-treading stiffness, which is combined with the deflection of a leg and the deformation of the water surface. When the driving leg was against a lateral flow, the resistant side was found to remain in a Wenzel state, which is helpful for the large cuticle forces.
2. Experimental Section A series of experiments were conducted with an in situ measurement system of force data and photographs, as shown in Figure 1a. Two directional forces of a water strider’s leg against a water surface were measured by fixing the leg to a transducer of a TriboScope system (Hysitron) and moving a water vessel with the stage of an SP 3800N SPM (Seiko, Japan). To simulate the contact angles of a leg against a lateral flow, the water vessel was shaken at a 180 μm distance at a specific frequency, and the shaking direction was parallel to the direction of the horizontal force measurement.
3. Results and Discussion 3-1. Antivibration Mechanism: The Water-Treading Stiffness. To observe the contact conditions, the leg tip was placed very near the wall of the water vessel, as shown in Figure 1b. Therefore, the image shown in Figure 2a focuses on the front of the deformed water surface on the vessel wall, and both the tip and back sections of the leg are out of focus. According to the profiles of the water surface and the estimated cross section of the leg, the contact angle in a Cassie-Baxter state was 165 ( 3°, which agrees with reported values.4,6,7,13 The filling angle of the leg’s tip was 162 ( 5° under a float of 33 ( 5 μN, which is close to the situation when a water strider stands on the water at rest. Compared to the leg’s side, the tip has distinct wetting properties.7,13 The tip of the leg was wetted during water treading, and an adhesion force of 21 ( 4 μN was found when the leg lost contact with the water surface. Because the cross section of the leg is not exactly circular,17 the Gibbs inequality18 should be applied to determine the receding contact angle, as illustrated in Figure 2c. The angle measured from the vertical direction φ, as (17) Liu, J. L.; Feng, X. Q.; Wang, G. F. Phys. Rev. E 2007, 76, 066103. (18) Gibbs, J. W. The Collected Works of J. Willard Gibbs; Yale University Press: New Haven, CT, 1961; Vol. 1, p 326.
Published on Web 04/14/2009
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Figure 1. (a) Scheme of the developed measurement system. (b) Scheme of imaging the cross-section images during hydrostatic experiments.
shown in Figure 2b, was found to be 17 ( 3°. According to the image under a scanning electric microscope (SEM), as shown in Figure 2c, the setae at the bottom of the leg are closer to the leg’s sidewall because of being against water pressure all the time. The average distances of setae from the leg’s sidewall, RS, were found to be at a maximum of 50 μm at the top and at a minimum of 0.5 μm at the bottom. Accordingly, the constructed cross section of the leg, as shown in Figure 2c, provides the tangential angle from the vertical direction, ω = 43 ( 2°. The critical receding contact angle θr = φ + ω was evaluated to be 59 ( 4° when the leg’s tip was in a Wenzel state. During upward movement of the water vessel, the vertical forces increased linearly with an approximate slope of 0.2 N/m,6,13 which is composed of the deflection of the leg hl and the deformation of the water surface hw, as shown in Figure 3a. According to the images, hl ≈ hw/2, meaning that the stiffness of the leg kl was approximately double the stiffness of the water kw. Considering the two springs in series, as shown in Figure 3b, the values of the stiffness were kl = 0.6 N/m and kw = 0.3 N/m, which indicates that the small water-treading stiffness has a partial contribution from the flexibility of a water strider’s leg. The SEM image of the cross section of a peeled leg, as shown in Figure 4, was found to be hollow with 4/5 diameter, which not only lessens the weight of the insect and provides more buoyancy but also allows the leg to be more flexible. In fact, each leg is like a spring reacting independently to outgoing forces; its six legs construct a spring matrix, as shown in Figure 5a. The water strider’s legs can flexibly adjust when the water surface is unstable and maintain the balance of its entire body, as demonstrated in Figure 5b. 3-2. Tiny Friction and Large Thrust. For a water strider’s leg, the drag forces against forward flows were found to be much smaller than those against lateral forces. According to fluid dynamics, a drag force resulted from the friction and pressure forces. The diameter of a driving leg is approximately 0.2 mm, Langmuir 2009, 25(12), 7006–7009
Figure 2. (a) Images used to determine the contact angles in a Cassie-Baxter state by water surface B in contact with the water strider’s leg. (b) Images and adhesion forces when the leg leaves the water surface. (c) Illustration used to determine the contact angle in a Wenzel state.
Figure 3. (a) Side- and cross-section images of water-treading experiments show that the total deformation h is composed of the deflection of leg hl and the deformation of the water surface hw; therefore, (b) the contact stiffness is composed of the spring constants of the leg kl and of the water kw in series. DOI: 10.1021/la900185a
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Figure 4. Cross-section image of a water strider’s peeled leg showing a hollow structure with 170 μm inner diameter and 45.8 μm thickness.
Figure 5. Demonstration of (a) the springlike legs of a water strider when standing on the water and (b) the antivibration mechanism.
which is 1/15 the length beneath the free surface. Therefore, the frontal area for the forward flow was much smaller, which resulted in a smaller pressure force. However, the friction force between the leg cuticle and the forward flows was also smaller. Besides the microsetae alignment, remaining in a Cassie-Baxter state also reduces the friction force. According to the filling angle shown in Figure 2a, the wetted area fraction of the leg was smaller than 50%, and the wetted area fraction of setae on the outer surface was around 0.05-0.1.6 To investigate the mechanism of large contact forces against lateral flow, the images obtained during hydrodynamic experiments are presented. Because the leg’s tip was very near the vessel wall, the surrounding water had almost the same velocity as the vessel. The leg was submerged within a few cycles even at low frequency, as shown in Figure 6a-d. Detailed observations revealed that the resistant sides were wetted as a result of the velocity pressure during the first cycle, and then the filling angle soon increased. The maximum in horizontal forces was achieved at almost the middle position of the first stroke, where velocity was maximal and acceleration was minimal. (See the water level.) The contact angle of the wetted side, as shown in Figure 6e, was found to be 67°, which is consistent with the reported value.7 The resistant side in a different state than for the other side, as 7008 DOI: 10.1021/la900185a
Figure 6. (a-d) Series of images in the middle position of strokes showing that the leg became wet and was then submerged with horizontal shaking of the vessel. (e) Image showing that the maximum horizontal force was achieved in the middle position of the first stroke. (f) Illustration of the resistant side in a Wenzel state.
illustrated in Figure 6f, led to not only an unbalanced horizontal force but also great cuticle friction. Because of the strong boundary layer effects, the velocity of the water was not uniform in the longitudinal dirction when the water vessel was shaken. The velocities of the water far from the vessel wall are much smaller. To investigate the leg’s characteristics against uniform flow, experiments at the same frequencies were then performed at the center of the water vessel, which was 2.5 cm away from the wall. The vertical force was 24 μN before shaking the water vessel; and a horizontal force of 6.1 μN was found in the middle position of the first stroke. Because the frequency is the same, the vessel wall has a velocity of 9.2 cm/s; however, it is difficult to determine the water velocity in the center of the vessel precisely. The corresponding image, as shown in Figure 7b,c, significantly showed the nonsymmetric dimples on the two sides of the leg. After 10 cycles, the dimple, as shown in Figure 7d, is smaller than that before shaking the vessel, as shown in Figure 7a, and the vertical force was deduced to be 13 μN. Some portions of the leg were wetted after shaking the vessel because the water was lifted from the free surface when the vessel receded, as shown in Figure 7e,g. In fact, when a water strider strokes, the driving leg is moved not only horizontally (backward) but also vertically (downward), as illustrated in Figure 7h. The gained force from two driving legs in the vertical direction was found to be even Langmuir 2009, 25(12), 7006–7009
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the actual relative velocity of the stroke; therefore, the horizontal forces are smaller as well. Because of the high hydrodynamic pressure induced by strokes, the bottom and the resistant side of a water strider’s leg should be in a Wenzel state.
4. Conclusions
Figure 7. Images and forces of the leg treading the water surface at the center of the vessel (a) before, (b, c) during, and (d) after shaking the vessel and (e, g) then receding the vessel. (h) Illustration showing the movement of a driving leg when a water strider strokes.
larger than the body weight,7 and the stroke force in the horizontal direction is around 10 times its body weight.11 However, the velocities in the experiments are much smaller than
Langmuir 2009, 25(12), 7006–7009
Wetting is advantageous to propulsion but disadvantageous to floating and drag. To prevent the other side from becoming wetted, a water strider lifts the driving legs from the water surface when it recovers its initial posture. The tiny friction after a stroke benefits from not only its nonwetted legs but also the posture by which its legs remain parallel to the direction of movement. For movement against forward flow, the superhydrophobic contact angle was effectively found to reduce fluidic drag.19 The large thrust from the lateral flow stroke and the tiny friction from the forward flow posture are useful to water striders moving quickly on the water. Acknowledgment. This work was supported by the Center for Frontier Materials and Micro/Nano Science and the Technology Center, National Cheng Kung University, Taiwan (D97-2700). (19) Shi, F.; Niu, J.; Liu, J. L.; Liu, F.; Wang, Z. Q.; Feng, X. Q.; Zhang, X. Adv. Mater. 2007, 19, 2257.
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