Elegant Shadow Making Tiny Force Visible for Water-Walking

Article pubs.acs.org/Langmuir

Elegant Shadow Making Tiny Force Visible for Water-Walking Arthropods and Updated Archimedes’ Principle Yelong Zheng,† Hongyu Lu,† Wei Yin,† Dashuai Tao, Lichun Shi, and Yu Tian* State Key Laboratory of Tribology, Tsinghua University, Beijing 100084, People’s Republic of China S Supporting Information *

ABSTRACT: Forces acted on legs of water-walking arthropods with weights in dynes are of great interest for entomologist, physicists, and engineers. While their floating mechanism has been recognized, the in vivo leg forces stationary have not yet been simultaneously achieved. In this study, their elegant bright-edged leg shadows are used to make the tiny forces visible and measurable based on the updated Archimedes’ principle. The force was approximately proportional to the shadow area with a resolution from nanonewton to piconewton/pixel. The sum of leg forces agreed well with the body weight measured with an accurate electronic balance, which verified updated Archimedes’ principle at the arthropod level. The slight changes of vertical body weight focus position and the body pitch angle have also been revealed for the first time. The visualization of tiny force by shadow is cost-effective and very sensitive and could be used in many other applications.

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on legs1,4,7,18,27 as Mg = Fb + Fc, where Fb is the hydrostatic pressure force acted on the leg area in contact with water and Fc is the vertical component of the surface tension, σ sin θ, along the contact perimeter.4 Therefore, parameters of pressed depth, contact area, and contact angle of legs with water need to be in vivo simultaneously and accurately measured to achieve the floating force, which is technically rather difficult as a result of the slim leg/water contact geometry. Another approach is relying on updated Archimedes’ principle.11,28,29 An ex vivo measurement with an electronic balance showed that the maximum floating force of one water strider leg could be up to 152 dyn, several times its body weight.7 A recent study recorded the side view of legs pressed into the water surface to estimate the floating force of hind legs of water striders.28 However, an in vivo measurement floating force of all of the legs of an arthropod has not yet been accomplished. To verify updated Archimedes’ principle at the level of a waterwalking arthropod and explore the in vivo floating forces to obtain a more profound comprehension of the locomotion principles of water-walking arthropods, in this study, we make the tiny floating forces visible using their leg shadows that well overcomes the challenge.

INTRODUCTION In situ measuring forces acted on individual legs of animals and insects in a natural state is difficult but important for disclosing their locomotion principles and to guide the design of advanced biomimetic robotics. Among them, the exceptional waterwalking capabilities of certain arthropods, such as water striders, with tiny weights in dynes1−3 have received great interests from scientists and engineers.4−10 More than 2000 years ago, the ancient Greek scientist Archimedes found that any floating object displaces fluid of its own weight, later called Archimedes’ principle and recently updated.11−14 In the Three Kingdoms period of China, Chong Cao also proposed a similar method of using the buoyancy principle to weigh an elephant.15 The classic floating mechanism has supported the invention of many modern water- or air-floating vehicles, such as ship, submarine, and dirigible. For water-walking arthropods, the water is not really displaced by immersing legs into it but is expelled by the hairy superhydrophobic legs by distorting the water surface and mainly supported with surface tension. Updated Archimedes’ principle predicts that the weight of the expelled volume of water equals the floating force.11−14 Therefore, along with the development of micro-/nanomanufacturing technologies to reduce the size of actuators and sensors,16,17 there is a lot of interest in studying water-walking arthropods and their biomimetic robots.7−11,15−23 However, because the weight of a water-walking arthropod is usually in dynes (1 dyn = 10 μN), its leg force is almost impossible to be in vivo measured with traditional weak force measurement technologies, such as atomic force microscopy (AFM)24−26 or various small force sensors. Instead, former studies considered that the weight of water striders was supported by water pressure and surface tension forces acted © 2016 American Chemical Society

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EXPERIMENTAL SECTION

Preparation of Water Strider and Shadow Image Recording. Water striders were captured from the lotus pond of Approaching Spring Garden at Tsinghua University, Beijing, China, and raised in an acrylic aquarium in the laboratory at room temperature (25 °C). It was taken for experiment when needed. In the experiment, an acrylic Received: August 5, 2016 Revised: September 25, 2016 Published: September 26, 2016 10522

DOI: 10.1021/acs.langmuir.6b02922 Langmuir 2016, 32, 10522−10528

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Figure 1. Shadows of hydrophobic slim poles under point light illumination. (a) Shadow of a water strider in a lotus pond (Approaching Spring Garden of Tsinghua University). (b) Typical shadow of a water strider achieved in the laboratory. (c) Micromorphology of a hairy hydrophobic water strider leg with nanosized grooves on each hair (inset). (d) Sketch of the shadow-taken principle in the laboratory. [poly(methyl methacrylate) (PMMA)] vessel (10 × 15 × 20 cm3) with a wall thickness of 5 mm, a water depth of 50 mm, and a white paper at the bottom of the vessel acting as a screen was used. A film ruler (transparent plastic ruler with a thickness of 0.1 mm) was also placed above the screen. A white point light source (3 W, ZHPLHP803, Beijing Hezhong HangXun Sci. Tech. Corp., China) was placed 1000 mm right above the water surface. A Canon camera (EOS650D, maximum size of 5184 × 3456 pixels) was placed about 150 mm below the screen. Pictures or videos were recorded when the needed shadow of water striders came into the central area of screen. The video mode is a full high-definition (HD) recording with 1920 × 1080 pixels and 25 frames per second (fps). The pictures or videos were read in the MATLAB program and processed in single pictures. Leg Shadow Area Selection and Tilt Angle Correction. A typical leg shadow has a bright region outside the dark shadow. In the shadow selection, a critical threshold of the gray was used to define the boundary of the dark leg shadow area and transform the image into a binary image for a later process. Manual selection of the top and bottom points of leg shadows (shadow edges at both ends of the legs) was carried out to calculate the tilt angle of the leg shadow. Then, the leg shadow was tilted into 0° through the function [B = IMROTATE(A,ANGLE,METHOD)] in MATLAB software to simplify the later floating force calculation of each leg. Vertical Weight Focus Position Change Calculation. The vertical displacement of weight focus of water striders, Δhweight focus, was estimated by Δhweight focus = [d1(hmax,S2 + hmax,S3)/2 + hmax,S1d2]/(d1 + d2), where hmax,S1, hmax,S2, and hmax,S3 were maximum pressed depths of legs S1, S2, and S3 and maximum widths of the shadow, d1 and d2 were the distances from weight focus to the center of leg S1 and the center of connection between legs S2 and S3, respectively, with d1 = 11.2 mm and d2 = 19.5 mm.

Hair/Polydimethylsiloxane (PDMS) Contact Force Measurement. The tested hair (diameter, 60 μm; length, 50 mm) was glued on a one-dimensional translation stage. At the beginning, the end of the hair was put about 0.5 mm above the PDMS surface. Then, it was pressed down to contact the upper PDMS disc surface, holding for a period of time, increased from 30 to 90 s at the same external load of 4 μN, and finally separated at a driving speed of 0.05 mm/s.

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RESULTS AND DISCUSSION Basic Principle of the Shadow Method. On the bottom of a clean pond under sunshine, water striders usually left rounded or ellipsoidal leg shadows with bright edges, as shown in Figure 1a. The elegant shadows could be ascribed to the light refraction as a result of the distorted water surfaces, which could be readily achieved in vivo in the laboratory, as shown in Figure 1b. It is realized by irradiating a point light on water striders and their hairy superhydrophobic legs (Figure 1c) with an apparatus as sketched in Figure 1d. Because the shadow represented the water surface curvature, therefore, the expelled water volume and the corresponding floating force according to updated Archimedes’ principle could be calculated from the leg shadows. Thus, the elegant shadows can make the tiny floating force acted on hydrophobic water strider legs visible and measurable. While there is no full description accounting the surface tension, fluid momentum, viscosity, and pressure of a moving dimple, former studies have disclosed that the distorted water surface curvature by a hydrophobic water strider leg is dominated by the pressed water depth and the surface tension of the water surface.4−8,30−33 With treatment of a water strider leg as a rigid 10523

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Figure 2. Floating force measurement from shadows of water strider legs according to updated Archimedes’ principle. (a) Typical water strider leg shadow. (b) Typical distorted water surface profile section by a hydrophobic slim pole and a comparison between its experimental and theoretical results of the relative light intensity. (c) Relationships among the pressed depth, shadow width, and floating force strength of a slim pole. By integration of the floating force at each section f n along the y direction, the floating force represented by the whole leg shadow Fn could be calculated. (d) Verification of the shadow method with an electronic balance by simultaneously measuring the vertical force acted on a water strider leg at different pressed depths and its corresponding shadow formed at the bottom surface of the vessel, which agreed very well with each other.

Figure 3. In situ floating force measurement of individual legs of water striders at rest. (a) Shadows of five water striders and some typical results of floating force, shadow area, and maximum pressed depth of water strider V. (b) Comparison between the weights achieved from their shadows and the weights measured with an electronic balance. (c) Fitted linear relationship between the supporting force and the leg shadow area.

and superhydrophobic slim cylinder, the water surface profile governing equations are as follows:33 h(x , Φ, θ ) = B(Φ, θ )e−1/ cx

B(Φ, θ ) = −ce(1/ cR sin Φ) tan(θ + Φ − π )

(2)

(1) 10524

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Figure 4. In vivo floating force measurement of individual legs of a water strider during its leg refreshing. (a) Shadow images of a water strider before, during, and after its middle-left leg (indicated by the red circle) refreshing. (b) In vivo floating forces acted on legs versus time during the leg refreshing. (c) Sum of leg floating forces and the vertical displacement of its body weight focus.

c=

σ 1 ρg (1 + s 2)3/2

shadows could visualize the tiny forces acted on individual legs of water striders with a high accuracy. Weighing Water Striders. Weights of seven water striders with different sizes have been achieved and compared to the results measured with an electronic balance (Movie S1 of the Supporting Information). Results are shown in Figure 3. Typical floating force, shadow area, and maximum pressed depths of two legs of water strider V were shown in Figure 3a with a force resolution of about 10 nN/pixel. If one leg shadow corresponding to a floating force of 50 μN occupies one-third area of a 30 million pixel image (such as Nikon D810 camera), the force resolution could be up to 5 pN/pixel, approaching the level of a single molecular force.24,25 The calculated weight focuses of the water striders indicated by red dots are right on the body center of water striders, showing the well balanced forces and torques of their legs. Results also indicated that the floating forces could be significantly different for the same water strider leg with similar maximum pressed depth but different hydrophobicities with different shadow geometries and areas (Figure S3 of the Supporting Information). The sum of the floating forces of six legs of each water strider at a static state agreed well with that weighted with an electronic balance, as shown in Figure 3b. A continuous shadow recording of water striders at rest showed very stable values with a standard deviation of less than 0.5% (Table S1 of the Supporting Information). Interestingly, Figure 3c shows that the floating force acted on legs is approximately linearly proportional to the shadow area. Therefore, the results in Figure 3 experimentally verified updated Archimedes’ principle at the level of arthropods by visualizing those tiny floating forces by leg shadows.

(3)

where θ is the contact angle between leg and water, Φ is the submerge angle, σ is the surface tension of water (0.072 N/m), B is the area representing the surface tension force, R is the radius of a cylinder, ρ is the density of water, g is the acceleration of gravity, x is the position on the x axis, and s is a constant. A typical water strider leg shadow is shown in Figure 2a. According to the calculated distorted water surface profile according to the above equations, a typical relative brightness of leg shadow was calculated with a linear-optical analysis software ZEMAX agreeing well with measured results, as shown in Figure 2b (Figures S1 of the Supporting Information). Each pressed depth h0 also corresponds to a shadow width S with a repelled water surface section area B, as shown in Figure 2b. According to updated Archimedes’ principle, the floating force strength could be calculated by f n = ρgB, which showed an approximately linear relationship, as shown in Figure 2c, in agreement with previous studies.5,29 The floating force Fn acted on the leg could be achieved by integrating all of the shadow sections along the y direction as Fn = ∫ L0 f n dy. Further calculation showed that the leg radius of water striders has little effect on the floating force strength (Figure S2 of the Supporting Information). To verify the effectiveness of the floating force measured from the leg shadow, an electronic balance (ME235S, Sartorius Corp., with a resolution of 0.01 mg) was used to simultaneously measure the vertical force acted on a strider leg pressed into a water surface while recording the leg shadow. As shown in Figure 2d, the measured forces with electronic balance agreed very well with the results achieved from leg shadows. Therefore, the 10525

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Langmuir Floating Force during Leg Refreshing. Besides water striders being weighted with the visualization of tiny floating forces by leg shadows, their states in certain actions could also be revealed with the shadows. Occasionally, water strider would lift up its two forelegs to rub them around their mouth and then rub one of them with their target middle or hind legs (Movie S2 of the Supporting Information). Before the rubbing, the leg shadow usually is not so smooth, indicating the change of hydrophobicity of legs. After rubbing, the leg shadow became smoother, showing a recovery of the leg hydrophobicity. A typical rubbing process is shown in Figure 4a. During rubbing, the body weight focus (red dots) slightly shifted to the right side. Considering the rubbing was started from their mouth, some oily hydrophobic materials rather than waxy materials might be secreted from their mouth and transferred to target legs to recover the hydrophobicity. This rubbing is called leg refreshing in this study, which has not been reported in former studies. During leg refreshing, the floating forces acted on individual legs S1−S5 during leg refreshing were shown in Figure 4b. The force on leg S5 was about 0.37−7.40 μN in its subtle dipping, which was mainly compensated by the force on leg S1 on the same side of its body, which was in the range of 100.57−94.94 μN. Additionally, the sum of floating force acted on the water strider legs slightly changed between 224.65 and 228.59 μN, as shown in Figure 4c and Figure S4 of the Supporting Information. According to the maximum pressed depth of individual legs, the change of vertical position of its body weight focus was in the range from −5 to 10 μm with a resolution of 2 μm/pixel, as shown in Figure 4c, which is rather difficult to be disclosed with other methods. Shadow Method Based on Different Liquids. As described by the theoretical model,33 the visualization could use liquids with different surface tensions and densities. With the addition of a small amount of ethanol in water, the surface tension and density of the solution could be slightly changed but the water strider could still reside above the solution surface. As shown in Figure 5a, with different surface tensions of the ethanol solution, the measured weight (Figure S5 and Table S2 of the Supporting Information) reasonably agreed with that of pure water by considering the change of the surface tension and density during the calculation. On the weak force measured with a hydrophobic polytetrafluoroethylene (PTFE) circular plate, the relationship between the additional force and the additional shadow area could be readily calibrated, as shown in Figure 5b, which could also be directly achieved from theoretical predictions (Table S3 of the Supporting Information). Weak Force Measurement Device. The shadow-visualized tiny force measurement could also be developed into a universal weak force measurement instrument. As an example, using a hydrophobic circular PTFE plate (diameter, 12 mm; thickness, 0.2 mm) with a thin PDMS surface on the top (diameter, 5 mm; thickness, 3 mm) (Figure 6 and Movie S3 of the Supporting Information), the relationship between additional forces (putting weight above) and the change of the shadow area (Figure S6 of the Supporting Information) could be obtained, which showed a force resolution of about 0.3 nN/pixel. As an application of this measurement method, the aging effect on the adhesion force of a human hair/PDMS surface contact was investigated as a simulation of a hair/human skin contact.34 The adhesion force (the negative value in separation) was successfully measured, showing a significant increase from about 6 to 10 μN with the increase of the holding time, similar to the aging of the static friction force in amorphous SiO2 contacts.35

Figure 5. Verification of the universality of the proposed shadow method for liquids with different surface tensions and densities. (a) Water strider weight measured on ethanol solutions with different concentrations, surface tensions, and densities. (b) Basic curves of added force versus added shadow pixel for weak force measured with a thin hydrophobic PTFE circular plate floating on liquids with different surface tensions and densities.

Figure 6. Force−time curves of adhesion tests of a hair/PDMS surface contact supported on a thin hydrophobic PTFE circular plate at different holding times of 30, 60, and 90 s.

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CONCLUSION In summary, this study has provided direct evidence that, through the shadows of hydrophobic objects floating on liquid, the equivalent floating force with a resolution down from nanonewton to piconewton/pixel could be visualized and accurately measured. Notably, this shadow-visualized tiny force method has led to the novel design of an apparatus for weak interfacial interactions measured widely existing in nature and industry. This shadow visualization has broader impacts in biomechanics and biomimetic design of various robots, weak force measurement, etc.

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.langmuir.6b02922. Experimental apparatus in the laboratory for shadow recording (Figure S1), effect of leg radius R on the 10526

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calculated shadow width at different pressed depths (Figure S2), floating forces acted on the same leg (Figure S3), vertical position change of weight focus from the vertical displacement of S1, S2, and S3 (Figure S4), shadow for measured weights and surface tension coefficients under different concentrations of aqueous ethanol (Figure S5), relationship between the floating force and shadow area of a PTFE circular plate floating on the water surface (Figure S6), weight of seven different water striders measured with an electronic balance and the shadow method (Table S1), ethanol solutions with different concentrations, surface tensions, and densities in a water strider weight measurement (Table S2), and different surface tension coefficients and densities for weak force measurement with a thin hydrophobic PTFE circular plate floating on liquids (Table S3) (PDF) Movie clip of a static water strider on the water surface (Movie S1) (MOV) Movie clip of a water strider refreshing its feet (Movie S2) (MOV) Movie clip of the adhesion force measurement between a single hair and a PDMS surface with a hydrophobic PTFE circular plate floating on the water surface (Movie S3) (MOV)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Author Contributions †

Yelong Zheng, Hongyu Lu, and Wei Yin contributed equally to this work. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work is supported by the National Natural Science Foundation of China (Grants 51425502 and 51323006). REFERENCES

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