Role of flexibility in the water repellency of water strider legs: Theory and experiment

Abstract

Water striders enjoy an intriguing ability to stand and walk freely on water surfaces, which is mainly attributed to the superior water repellency of their slender legs. In previous theoretical analyses, the legs are usually treated as rigid beams and the results show that a tremendously deep dimple and a large supporting force can be achieved when the leg descends into water. In this paper, the effect of the flexibility of water strider legs on their water-repellent ability is investigated, both theoretically and experimentally. We analyze a hydrophobic and flexible leg pressing obliquely on water. The leg may undergo a large deformation and assume different geometric configurations. It is shown that the flexible leg can float easily on a water surface, inducing only a shallow water puddle and a moderate supporting force as observed in real water striders. When the long leg is sufficiently compliant, the water surface will never be pierced and the leg will never sink. The findings are experimentally testified by using flexible fibers to represent water strider legs pressing on water.

Floating Versus Sinking

“…These models show that the force that may be supported by such objects is larger than the corresponding force for a rigid sheet because the middle portion of the beam is able to reach greater depths (and hence higher hydrostatic pressures) than its ends can. Ji et al (2012) also showed that if the beam is sufficiently long, then it is so deformed by the hydrostatic pressure and surface tension forces that its far end bends upward and actually never reaches the criterion for piercing the interface: Within the limitations of this model, these beams never pierce the surface. Here, the term long means long compared to the elastocapillary length, which is the length scale above which an object becomes floppy to capillary forces (see, e.g., Roman & Bico 2010).…”

“…In the first approach, the leg is effectively modeled as a two-dimensional beam that is inclined at an angle to the horizontal direction and then lowered into a bath of liquid ( Ji et al 2012, Park & Kim 2008) (see Figure 4a). Because the bath is two dimensional, the beam is deflected by the hydrostatic pressure in the liquid, acting along its length, together with a line force from surface tension acting at its end.…”

A glimpse of superb tribological designs in nature

“…The mechanism is similar to that of lotus leaf. Additionally, the adaptive-deformation of the leg is regarded as another factor for its walking-on-water property (102,103). The compound eyes of the mosquito (Culex pipiens) have hundreds of microscale hemispheres (i.e., ommatidia), which also lead to extraordinary super-hydrophobic property to prevent itself from being covered with water in high-humidity environment (104).…”

Biomimetic mechanics behaviors of the strider leg vertically pressing water

“…3 A plethora of theoretical models have been proposed, where the strider leg has normally been modeled as a cylindrical rod horizontally or obliquely pressing into water, and then the expressions of the critical sinking condition and the buoyant force are given. [4][5][6][7][8] In conclusion, the current viewpoints on the origin of the superior buoyant force of the strider leg mainly deal with the following factors: (i) The capillary effect of the slender leg due to the contribution of the surface tension; 9 (ii) The hierarchical micro/nano-structures of its leg rendering a large contact angle to enhance the superhydrophobicity; 2,8 (iii) The hollow cross section of the leg producing a bigger ejected water volume compared with the solid leg for the given material; 8 (iv) The elastic deformations of the setae on the leg surface and the whole compliant leg; 8,10 and (v) The joints linking the leg segments self-adaptive to the liquid/vapor interface. 11 Although much effort has been performed on disclosing the secret of water strider walking on water, there is a nonnegligible fact that the strider leg can take the posture of vertically pressing into water.…”