The study of dynamic force acted on water strider leg departing from water surface

The hierarchical structure^1–5 on legs helps water striders walk on the water surface easily as shown in Fig. 1. Super hydrophobicity may make it very easy to detach legs from the surface, as insects need to jump and skate on the surface. Many estimates and experiments show that the adhesion force and the energy required to depart a leg from water surface decrease dramatically as the contact angle approaches 180.⁴ The adhesion force (pull-off) of water strider legs was measured by Pal Jen Wei, which was found to be 2 dyn.⁵ Keh-chih Hwang stated that nano to micro structural hierarchy is crucial for stable super hydrophobic and water-repellent surface and the second level structure results in dramatic reduction in the contact area and minimizing adhesion between water and the solid surface.⁶ Keh-chih Hwang established a 2D model to analyze the process of legs that detach from the water surface. The model shows that the super hydrophobicity of the legs’ surface is critically important for reducing the detaching force and detaching energy.⁷ 

However, only quasi-static experiment is reported by former researchers.^5,7 In this paper, the adhesion force acted on the leg when departing from the water surface at different speeds was investigated. This results may help to understand the function of super hydrophobicity in the dynamic process when skating on water surface.

Scanning electron microscope (SEM) observations clearly revealed that legs of water striders are covered with a large number of tiny setae,^8–12 as shown in Fig. 1(b). A high-resolution SEM image shows that setae are long and softly serrated, and they are about 100 μm in length and less than 5 μm in diameter in the root and 0.2 μm in diameter in the apex. There are nano grooves on each seta, which is shown in Fig. 1(c). From the SEM image, the seta are not compactly arranged, but are well spaced out with a longitudinal space of 20 μm and a lateral space of 10 μm. The number of seta would not be too small, or the epidermis of legs would be wetted when pressed down.

To check the adhesion force acted on the leg when departing from the water surface, an in situ dynamic force measurement system^13–17 which is schematically shown in Fig. 2, was used to record force data and photographs during the whole process. In this study, a back leg was used to investigate the adhesion force and mounted on the fast stage. The vertical force of a leg against a water surface was measured by a dynamic force measurement sensor (DFMS) made of Polyvinylidene Fluoride (PVDF) moving a water strider leg by a stage. A water drop (5 uL) was placed on the surface of DFMS. To monitor the deformation of the water surface, an optical microscope lens and a camera system are used to record the departing process.

The leg was moved to contact with water surface. As shown in Fig. 3(a), the water did not spread on this leg indicated that the hydrophobicity was well.^18–21 The force acted on the leg departing from water surface at lifting speed from 0.02 m/s to 0.4 m/s was measured by DFMS at the sampling rate of 10000 Hz as shown in Fig. 3(b).

Fig. 4 shows the relationship between the lifting speed and force for water striders’ leg. The adhesion force decreased from 0.12 μN to 0.03 μN with the increase of speed, U, from 0.02 m/s to 0.4 m/s. The low adhesion force would help water strider jumping upward easily. The function of setae on departing from water surface may result from the needle shape, the model of energy detaching from water surface for a needle shape seta was built, and the reason for the decrease of adhesive force with the increase of lifting speed was explained.

The needle-shape seta had the thin apex which is about 0.2 μm. The root of seta links to the epidermis of legs which is extremely thick. The stiffness of setae varies a lot along to the length of seta, as shown in Fig. 5. The stiffness could be calculated using Eq. (1) and (2). In this way, the thickness of the root ensured that the epidermis could not be wetted when pressed down the water surface, as shown in Fig. 5.

where L refers to the length which is about 100 μm, E is the elastic modulus and d(x) is the diameter of setae.

When the leg pulling up, the seta on each leg would be bent by the adhesion force as shown in Fig. 6. Water would be peeled from the needle shape seta.^22–24 The seta would be made vertical to the water surface. The bending of seta would reduce the perimeter to the diameter of seta which is about 0.2 μm. The relation between the force F and the diameter D as F_s ≈ π·D· γ = 45 nN. The adhesion work of the seta and water surface E_det is

where, γ is surface tension coefficient, 72 mJ/m². The bent seta could reduce the contact area significantly, and thereby decrease the work detaching from the water surface. So the needle-shape setae would help water strider to jump upward or forward with small energy.

Now, we will discuss the relationship between the lifting speed and adhesion force. As shown in Fig. 4, the adhesion force decreases significantly with the increase of lifting speed. The water surface would be lifted up by seta. The departing condition is that the energy acted on the water, E, is equal to E_det. The lifting water, whose mass is m, would obtain potential work E_p = mgh and kinetic energy E_k = 0.5·m·U². For all lifting speeds, the total work detaching from water surface is constant which is determined by the hydrophobicity of leg. Higher lifting speed leads to large kinetic energy and small potential work. As for slow lifting speed, E_k is very small, and E_p would be very large. The adhesion force F_s = mg, which is proportional to E_p. In this case, higher lifting speed would lead to small adhesion force, while slower lifting speed could bring about large adhesion force. The adhesion force on water strider leg would dramatically decrease under the condition of high lifting speed with the help of needle shape setae.

In summary, in this paper, the dynamic force measurement setup is built to support dynamical studies on super hydrophobic surfaces for a better understanding of setae’s function on water strider leg. The function of super hydrophobicity and the hierarchical structure was investigated by measuring the adhesion force of legs when departing from the water surface at different speeds. The results show that the needle shape setae on legs of water striders can help them save energy. Our force measurement device could also be adopted to other water walking insects such as water spiders and water treaders, whose setae on the leg are different from water striders. In the next step, the function of water spiders and water treaders’ setae would be investigated.

When measuring the force acted on the leg of water striders by DFMS, the procedure is recommended as follows:

Step 1. Calibrate DFMS using electrostatic force proposed in Ref. 15, 16.

Step 2. Move the leg to the water drop placed on the surface of DFMS by the highly accurate stage. Observe the output of DFMS to check whether the leg and the drop remain touching or not.

Step 3. Move the leg down to 0.1 mm.

Step 4. After 10 s, move the leg upward to depart from the drop. This process was monitored by a camera. During this period, the force acted on the leg is measured.

Step 5. Repeat step 4 for different lifting speeds.

The authors thank the National Key Technology Research and Development Program of the Ministry of Science and Technology of China (No. 2011BAK15B06) for their support.

The authors declare no conflict of interest.