Water striders have three pairs of legs: one pair of forelegs for grabbing and support, and two pairs of long appendages for locomotion. The distal segments of each leg are composed of a femur, tibia, and tarsus, as shown in Figure 5A. The leg is covered by uniformly tilted bristles (Figure 5B), which contain grooves on each (Figure 5C). There are two types of bristles distinguished by their size: i.e., thick and sparse bristles (thorns) used as grooming combs (Finet et al., 2018) and thin and dense bristles that render the legs superhydrophobic (Gao & Jiang, 2004), with their tips bent inward to avoid piercing the water surface. Both types are innervated bristles that can act as mechanoreceptors to sense fluctuations on the water surface (Finet et al., 2018).
In early studies, it was generally believed that secreted wax and hair piles render the insect’s body and legs non-wetting (Caponigro & Eriksen, 1976; Dickinson, 2003; Hu et al., 2003; Spence et al., 1980; Thorpe, 1950; Thorpe & Crisp, 1947, 1949). In 2004, however, Gao & Jiang (2004) pointed out that the water CA of wax on water strider legs is 105°, an angle characteristic of insect cuticle wax (Holdgate, 1955), which is not sufficient for superhydrophobicity. They thus proposed that the hierarchical structure of the water strider legs (i.e., presence of dense bristles and grooves) is more significant for a superhydrophobic state. Modelling bristles and grooves as infinitely long rigid cylinders, Feng et al. (2007) demonstrated that the theoretical analysis agrees well with the measured value of the CA, thus suggesting that grooves are essential in generating the superhydrophobicity of water strider legs.
These remarkable works have inspired a new wave of in-depth biomechanical study on the hierarchical structure of water strider legs. The features of legs, bristles, and grooves can be classified into four aspects (Table 1), namely (a) deformation, (b) orientation, (c) dimensions, and (d) spacing. Current topics mainly focus on their roles in maximizing propelling forces and minimizing resistant forces.
Morphological trait Value Main finding Function Reference Deformation Legs Young’s modulus: ~10 GPa Adaptive deformation at three joints increases supporting force. Maximizing propelling forces Zheng et al., 2009 Flexibility of each segment increases supporting force. Maximizing propelling forces Ji et al., 2012 Bristles Young’s modulus: ~10 GPa Microscale droplets between bristles can be expelled out due to elastic deformation of bristles. Minimizing resistant forces Wang et al., 2015 Bristle deformation during lift-up of legs reduces contact area with water, thus reducing detach force. Minimizing resistant forces Sun et al., 2018 Orientation Legs Unfixed Supporting force decreases as stepping angle increases. Penetration occurs at 28°. Maximizing propelling forces Feng et al., 2007 Midleg experiences larger stroking force as they extend perpendicularly to direction of motion. Maximizing propelling forces Prakash & Bush, 2011 Hindleg experiences less drag force as they extend along direction of motion. Minimizing resistant forces Prakash & Bush, 2011 Bristles Tilt angle: 30°–50° Droplets advance more easily toward leg tip, which is linked to a peeling mode during lift-up of legs. Minimizing resistant forces Prakash & Bush, 2011 Grooves Tilt angle: ~10° Flow slips more easily in direction of grooves. Minimizing resistant forces Choi et al., 2006 Dimensions Legs Length: 1.3–1.7 μm (midleg)
Width: 90–110 μm
Critical leg aspect ratio l/r (l: wetted length; r: radius of leg) at which supporting force reaches a plateau. Maximizing propelling forces Vella, 2008 Bristles Length: 20–40 μm
Width: 1.5–2 μm
Grooves Depth: ~200 nm
Width: ~400 nm
Spacing Legs Coxa spacing:
Foreleg-midleg: ~5 mm
Midleg-hindleg: ~2 mm
Bristles 6–8 μm Critical bristle spacing at which supporting force reaches a maximum. Maximizing propelling forces Xue et al., 2014 Upper limit to maintain Cassie state, and lower limit to prevent bristle collision. Minimizing resistant forces Su et al., 2010 Grooves Closely packed Data gathered from our scanning electron microscope (SEM) study, Hinton (1976), and Hu & Bush (2010).
Table 1. Morphological traits of adult Aquarius remigis and related functions
For Aquarius remigis, the maximum vertical propelling force per leg without piercing the water surface is ~1.52 mN (15 times body weight), indicating an extraordinary load-bearing capacity (Feng et al., 2007; Gao & Jiang, 2004). In locomotion, the lateral propelling force on one midleg is estimated to be ~0.18 mN (Uesugi et al., 2017). Early calculations treated the leg as an infinitely long rigid cylinder that horizontally resides on the water surface and gave a theoretical vertical propelling force slightly lower than the experimental result (Liu et al., 2007; Vella et al., 2006), suggesting other unconsidered factors at play.
The effect of deformation was not considered until later. Water strider legs are mostly hollow, which results in great flexibility (Wei et al., 2009b). Zheng et al. (2009) and Ji et al. (2012) discovered that the adaptive bending at three joints and elastic deformation of each segment play prominent roles in enhancing vertical propelling force. The flexibility can help the leg adjust to the inclined meniscus (Wei et al., 2009b), thus preventing the tip from piercing the surface (Ji et al., 2012; Koh et al., 2015).
The orientation of legs can be easily related to propelling forces. Feng et al. (2007) revealed that vertical propelling force decreases as the leg stepping angle increases to 28° before penetrating the water surface. Bristles can also contribute to the propelling force in an unexpected way. As demonstrated in Figure 5B, bristles protrude toward the leg tip. This topography leads to a unidirectional adhesion property: i.e., droplets roll off the bristles more easily parallel to the leg than perpendicular to the leg (Prakash & Bush, 2011). Similarly, in regard to orientation of the grooves, liquid flowing perpendicular to the grooves will experience more drag (Choi et al., 2006). As a result, by posing the midleg perpendicular to the direction of motion, the midleg will experience larger drag force when stroking backward, thus in turn generating a larger thrust forward.
The dimensions of the leg have intrigued researchers in terms of leg length. As surface tension is proportional to wetted length, one may expect that the tibia and tarsus should be as long as possible (Su et al., 2010). However, theoretical analysis shows that there is a critical leg aspect ratio l/r (l: wetted length; r: radius of leg) at which vertical propelling force reaches a plateau, whereby the leg will bend greatly to extend above the water surface, leaving the tip unattached to the water (Song et al., 2006; Vella, 2008). Vella (2008) examined several species from the genus Gerris and Aquarius and found that the aspect ratios of their midlegs are below but close to the critical value.
Similarly, calculation with a flat surface model reveals a critical value of bristle spacing when maximizing vertical propelling force, with bristle spacing of Aquarius remigis below but remarkably close to this critical value (Xue et al., 2014).
The first attempts to minimize resistant forces arose from the fact that superhydrophobicity may be unnecessary in generating propelling forces. Analyses conducted by Liu et al. (2007), Zheng et al. (2009), and Su et al. (2010) demonstrated that maximum force increases insignificantly with the increase in CA, given that CA is higher than 100°. Shi et al. (2007) used coated gold threads to confirm this finding. For dynamic processes, numerical analysis by Gao & Feng (2011) demonstrated that the propulsive force, as in the static case, is also insensitive to the CA if the surface is hydrophobic.
However, the focus here may not be propelling forces but rather resistant forces. The rigid cylinder model indicated that a larger CA is essential for reducing the vertical resistant force of a leg detaching from the water surface (Lee & Kim, 2009; Su et al., 2010). This was confirmed by Watson et al. (2010), who found that a bristle without grooves exhibits much greater adhesion and weaker resistance to water penetration. Shi et al. (2007) examined fluidic drag on a gold thread surrounded by a layer of oxygen gas and concluded that the air cushion formed by the hierarchical structure reduces fluidic drag on water strider legs. Under a quasi-static process, Wei et al. (2009a, 2009b) measured the force to lift an Aquarius remigis leg from the water surface to be ~20 μN. The detachment force on the water surface is much smaller with a magnitude of ~0.1 μN and can be further reduced to ~0.01 μN with increased lift-up velocity (Sun et al., 2018).
The deformation of bristles plays a crucial part in maintaining the Cassie state, thus reducing resistant forces. Microscale droplets that migrate between bristles can be expelled due to the elastic deformation of bristles, thus preventing transition to the Wenzel state in a humid environment (Wang et al., 2015). Deformation of bristles during leg lift-up can also reduce the water contact area, thus decreasing the detachment force (Sun et al., 2018).
The orientations of legs, bristles, and grooves play vital roles in minimizing resistant forces. For large droplets, the uniform tilt angle of bristles results in a unidirectional adhesion property: i.e., droplets advance more easily toward the leg tip than backward, as the deformation of bristles will resist the backward motion of droplets (Prakash & Bush, 2011; Xu et al., 2012). Similarly, liquid will flow more easily in the direction of grooves (Choi et al., 2006). Consequently, in locomotion, the hindlegs will experience less drag force as they extend along the direction of motion. Additionally, a peeling mode has been observed in water striders when they lift-up their legs, which is directly linked to this unidirectional adhesion property (Prakash & Bush, 2011).
One may assume that there is a critical bristle spacing to minimize resistant force, with small spacing making it easier to form a capillary bridge that sticks adjacent bristles together (Bush et al., 2007). Through sheer calculations, Su et al. (2010) stated that there should be an upper limit of bristle spacing so that a transition to the Cassie state does not occur under medium pressure, as well as a lower limit beyond which the bristles will easily bend so as to contact with adjacent bristles. They claimed that biological surfaces in nature fall into their predicted range.
Interfacial phenomena of water striders on water surfaces: a review from biology to biomechanics
- Received Date: 2019-12-06
- Accepted Date: 2020-03-20
- Available Online: 2020-03-20
- Publish Date: 2020-05-01
Abstract: Water striders have intrigued researchers for centuries from the viewpoints of biology to biomechanics. In this review, we introduce the basic theories and techniques of physics and force measurement for biomechanical research into water striders. Morphological and behavioral traits of water striders are summarized and discussed from biomechanical perspectives, along with comparative study. This integrated review also highlights potential directions for studies on water-walking arthropods, which might inspire future biological and biomechanical research.
|Citation:||Jing-Ze Ma, Hong-Yu Lu, Xiao-Song Li, Yu Tian. Interfacial phenomena of water striders on water surfaces: a review from biology to biomechanics[J]. Zoological Research, 2020, 41(3): 231-246. doi: 10.24272/j.issn.2095-8137.2020.029|