Mosquitoes possess a remarkable ability to stand effortlessly and walk freely on water surfaces because their six legs provide a large force to support the body weight. This study is focused on the role of the tarsus (the distal segment of the mosquito leg) because it was observed that normally only the tarsi make contact with water. The maximum value of the supporting force of the tarsus (6 mm long) in contact with water is estimated as 492 ± 5 μN, nearly 20 times the body weight of the mosquito, whereas the value for the whole leg (11 mm) is about 23 times the body weight. We demonstrate that the huge force provided by the tarsus originates from its flexibility, which ensures that the leg does not easily pierce the water. Adjustment of the initial stepping angle of the tarsus assists the mosquito to control the supporting force. These findings help to illustrate how mosquitoes stand or walk on water with only their tarsi in nearly horizontal contact with the water surface. Besides enhancing our understanding of mechanisms underlying “walking on water” by semi-aquatic insects, these investigations could provide inspiration for the biomimetic design of miniature robotics.
Small arthropods such as water striders, water spiders, fire ants and mosquitoes capture the striking feature of superior weight-bearing ability; as we often observe, they can walk or jump freely on the water surfaces of ponds, rivers, and even open oceans.1–4 This kind of insects, like water striders and mosquitoes, typically possess six slender legs, each of which is composed of three elongated sections: the femur, the tibia and the tarsus. Besides this, their legs are often covered with hairs to remain nonwetted by water.5–8 It was reported that the maximal supporting force of a water strider’s single intact leg can attain to the value 15 times of its body weight.8 Wu et al.9 declared that a single leg of another insect, mosquito can even provide a water supporting force which is about 23 times as large as the body weight. These remarkable water-walking behaviors could have great potential in engineering applications, such as the design of miniature aquatic devices and fabrication of non-wetting materials.10–12
In recent decades, much attention has been attracted on the extremely large water supporting force of these insects, which is directed towards disclosing their locomotion mechanism on water.13–18 For example, Gao and Jiang8 observed the micro-structures of the water strider leg, which are coated with a cuticular wax secretion. Rough, hydrophobic hairs that form a stable air cushion at the leg/water interface, are believed to be responsible for the superior water-repellence of the water strider’s limbs.15–17 Similarly, Wu et al. noticed that numerous grid-like scales endow the mosquito leg with a super-hydrophobic property, associated with a macroscopic contact angle up to 153°.9 Feng et al.19 proposed that a hierarchy of micro- and nano-structures on the strider leg play an important role in its super-hydrophobicity, ensuring that the leg creates a deep dimple without piercing the water surface. Liu et al.20 further built a two-dimensional model of the water-strider leg to analyze the basis of its motion, taking account of the buoyant force of the volume of water displaced by the leg. They stressed that the surface tension, the super-hydrophobicity and cross-sectional shape of the leg, and the self-adaptive property to water surface on the setae are main reasons for the production of such a large force.
Besides the above factors, the flexibility of the insect leg may be important for generating the large buoyant force. Experimental observations15–17 have shown that the legs of these semi-aquatic insects are not rigid and their flex can conform to the shape of the water surface. This flexibility appears to be beneficial for attaining a higher buoyant force. Zheng et al.21 fabricated an artificial leg from wax-coated steel wire and measured the maximum buoyant force. They emphasized that the real strider leg is able to conform to the liquid/vapor interface because it has three flexible joints, creating a larger buoyant force than the artificial leg without joints. In addition, Shi et al.22 depressed the water surface with a rigid gold rod and found that the maximum force supported is not a monotonic function with respect to the diameter of the rod. Vella,23 Park and Kim,24 and Bush et al.25 established theoretical models for the contact of a slender rod with a water surface and showed that a flexible rod produces a different buoyant force from that of a rigid rod. More recently, Ji et al.26 used a flexible hydrophobic fiber to form a large deformation when pressed obliquely onto the water, mimicking a water-strider leg. They demonstrated that if the leg is sufficiently compliant, the water surface will never be pierced, and thus the leg cannot sink.
Previous measurements of the ability of water surfaces to support insects have mainly focused on single whole legs.8,9,21,26 However, close observation indicates that these insects rarely use all three main sections of the leg to tread a V-shaped puddle, but only utilize the distal portion of their tarsus to almost horizontally reside on the water surface (see Fig. 1(a)). It is also evident that the initial stepping angle of the tarsus (as shown in Fig. 2) could be adjusted by the joints of the leg (femur/tibia and tibia/tarsus). Therefore, the role played by the tarsus in producing a force that supports the whole mosquito’s body should be further clarified. By selecting the mosquito leg for these experiments, our goal is to explore the functions of the tarsus, which has been largely ignored in previous work.
The article is organized as follows. In Section II, we introduce the design of the experimental setup, which provides a convenient means of measuring the water supporting force of mosquito leg. In Section III, we first compare the supporting forces generated by leg segments with different lengths and show that the tarsus is the most efficient section for generating this force. The mechanism of the superior aquatic load-bearing ability of the tarsus is then analyzed in relation to its flexibility. In succession, the influence of the initial stepping angle between the tarsus and the water surface on the supporting force is discussed. Finally the conclusions follow up.
II. EXPERIMENTAL SECTION
Mosquitoes (Culex pipiens pallens) captured in the city of Jinzhou and Shenyang (northeastern of China) were fed and maintained in the laboratory. The weight of individual mosquitoes is about 25 μN. As shown in Fig. 1(a), the mosquito has six long, thin legs. The hind legs are about 11 mm long in average (Fig. 1(b)). From proximal to distal, each leg is divided into three major elongated sections, i.e. the femur, the tibia and the tarsus. The tarsus of the hind leg is about 6 mm long, and the tibia and femur are each about 2.5 mm long. The three portions of the leg are characterized by different stiffness. The tarsus is the thinnest and most flexible region, while the tibia and femur are much thicker and stiffer than the tarsus. The main tarso-tibial and tibio-femoral joints are here referred to as joint 1 and joint 2, respectively (Fig. 1(b)).
An in situ measurement system, shown schematically in Fig. 2, was used to record the force data and for photography during the experiment. A live tarsus was attached to a fine steel needle, which could be used to conveniently adjust the initial stepping angle θ (the angle between the horizontal water surface and the tarsus before the tarsus presses on the water, as previously defined.19,21). The steel needle was then fixed to a special indenter column controlled by a manipulation device. The indenter column could be operated to move vertically up and down at specific constant speeds, causing the tarsus to depress and detach from the water surface in a steady state. A water vessel was placed on a micro-force sensor that has a precision of 0.1 μN (Sartorius model BT230, Germany). The tarsus was first moved away from the water surface and the measured force adjusted to zero to compensate for the weight of the vessel. As soon as the tarsus contacted the water surface, the force sensor automatically commenced recording a force-distance curve. To monitor the deformation of the tarsus and the water surface, an optical microscope and CCD camera were applied to record video at 30 frame/s.
III. RESULTS AND DISCUSSION
A. Supporting force achieved by leg sections of different lengths
We first investigate the load-bearing ability of the region of the tarsus that normally contacts the water. Typically, only the distal half of the tarsus makes contact with the water surface; we therefore selected a distal portion of the tarsus from a hind leg of a living mosquito, with an average length of 3 mm. This segment was then pressed onto the water surface to measure its supporting force using the test system as shown in Fig. 2. The initial stepping angle θ of the tarsus in contact with the water surface was adjusted within the range of 0–20°, which corresponds to the observed postural angle of the mosquito leg standing or walking on water (see Fig. 1(a)). Because live mosquito legs gradually become stiffer after their removal, all test samples were taken from living mosquitoes just before the experiments commenced.
A typical force-distance curve of a terminal section of the tarsus depressing the water surface is displayed in Fig. 3. Before the tarsus contacted water, the force was set as zero. Between points 1 and 3, as the displacement of the fixed end of the tarsus increases, the force generated on the water by the tarsal section gradually increases, reaching a maximal value (point 3) of 248 ± 5 μN. That is, approximately one half of the tarsus of a single leg is able to generate a force of nearly 10 times the insect’s body weight without piercing the water surface. Previously it was reported that a single whole hind leg could support a force of about 23 times the body weight of a mosquito.9 We have therefore introduce a new parameter to characterize the efficiency of the leg section in generating a force at the water surface. We define the force per unit length of the leg section:
where L is the length of the leg used in the experiment, and F is the measured maximum water supporting force achieved.
To further investigate the supporting efficiency of different sections of the leg, we selected a number of mosquito hind legs of approximately similar total length (approximately 11 mm), from which the leg fragments with total lengths ranging from 1–11 mm were produced by removing portions from the proximal end. As the length of the tarsus is about 6 mm and the tibia and femur are both about 2.5 mm long, these leg fragments consist of: 0–6 mm, tarsus only; 6–8.5 mm, tibia/tarsus; and 8.5–11 mm, femur/tibia/tarsus. The dependence of the maximum supporting force on length is shown in Fig. 4(a). Thus the function of the maximum supporting force with respect to the leg length is fitted by the linear equations:
and its curve with respect to the leg length is displayed in Fig. 4(b).
Fig. 4 shows that these curves are divided into three sections. For L = 0–6 mm, the absolute value of the maximum force is smallest but has the greatest slope. As a consequence, the force per unit length, Funit, is the highest, indicating that the tarsal section is the most efficient in producing the supporting force. The maximum value of the supporting force generated by the whole tarsus (L = 6 mm) is about 492 ± 5 μN, nearly 20 times the body weight of a single mosquito. This high supporting ability of the tarsus would permit the mosquito to stand and walk safely without sinking with just its tarsus in contact with the water, and would also provide sufficient dynamic reaction force for it to freely take off and land on the water surface. The second section of the curve for the maximum force (between 6–8.5 mm) has a lower slope than that of the first segment, i.e., its capacity to create an effective supporting force is weaker. Finally, the third section of the maximum force curve (between 8.5–11 mm) nearly approaches a plateau, and the parameter Funit has the lowest value. These observations confirm that it is reasonable for the mosquito not to use its whole leg and that it is sufficient for just the tarsus to contact the water.
Another advantage of maintaining only the tarsus in contact with the water is that it would assist takeoff from the water surface. It has been shown that the wet adhesion forces between the leg and water is proportional to the contacting length, i.e., Fadhesion ∝ L.27 As a smart creature, the mosquito is able to adjust the contact length of its leg on water, enabling it to reduce the wet adhesion force and energy dissipation during takeoff. Therefore, this behavior is an optimizing strategy for the mosquito that realizes a huge supporting force and reduces the adhesion force for takeoff.
B. Effect of tarsal flexibility on the supporting force
How the tarsus is able to achieve such a large supporting force per unit length remains puzzling. To further explore the origin of this force, we recorded the deformation of the tarsus and the water surface during the contact process using a synchronized CCD camera system, as shown in Fig. 2. Figs. 5(a)–5(c) shows typical images corresponding to the terminal half of the tarsus progressively pressing on the water surface. An obvious dimple was observed around the footprint of the tarsus (Fig. 5(b)), which increases in volume as the displacement of the fixed end of the tarsus increases. At the peak of the force curve (point 3 in Fig. 3), the depth of the dimple is greatest, and at this point, the tarsus pierces the surface and plunges into the water (Fig. 5(c)). Fig. 5(b) shows that the tarsus is sufficiently flexible to deform into a curve that conforms to the free surface of the water. As a comparison, several views of the whole hind leg pressing onto the water surface are shown in Figs. 5(d)–5(f). In this case, the whole leg forms a V-shape as joint 1 flexes. Clearly, the angle of joint 1 represents a singularity in the force distribution, i.e., a concentration of stress. As a consequence, the water surface is apt to be pierced at this point, and the leg is no longer able to support the body weight. In contrast to the flexing of the whole hind leg, the tarsus deforms continuously (Fig. 5(b)), which ensures that the depth of the dimple in the surface of the water is maximized before piercing occurrs.
To further explore the importance of tarsal flexibility, we analyzed the supporting force achieved by tarsi of different stiffness. As mentioned earlier, the leg becomes progressively stiffer after its isolation from the body of a living mosquito. First, we carefully cut off one half of the tarsus from the hind leg of a living mosquito. To maintain its freshness and natural flexibility, the force measurement experiment was completed as soon as possible. We then left this tarsal section in the air for several hours while periodically measuring the supporting force. The dependence of the maximum supporting force on the time in air is demonstrated in Fig. 6. It reveals that with the time increasing, the tarsus becomes stiffer and accompanied with a smaller water supporting force. After 12 hours, the maximum supporting force decreased by nearly fifty percent to 128 ± 5 μN. After several days in air, it became quite dry and fragile. It then rapidly collapsed in contact with water and was unable to generate a supporting force.
The efficient water-supporting ability of the tarsus can be further rationalized as follows. According to the generalized Archimedes’ law,20,28–34 the force supported by water is equivalent to the volume of water displaced by the dimple V in contact with the leg:
where ρ is the mass density of the water, and g is the gravitational acceleration. The scaling law for the volume is V = V(L, h, E, R, γ), where h is the characteristic length of the dimple, such as its maximum depth. The radius R (0.07–0.1 mm) of the leg cross section is considered as a constant, and γ is the surface tension of water. The experiment shows that the flexible tarsus repelles more water than the rigid tarsus, and createsa larger force. The coupling between the leg’s elasticity and its capillary effect is the so-called elastocapillarity phenomenon. Our experimental results are in excellent agreement with previous theoretical analyses24 which indicates that in the hydrophobic case, a compliant sheet is able to produce a larger buoyant force than a stiff one.
From Eqs. (2) and (4), we can infer the relationship V/E = Lmh (m = 0 or 1), and especially when the leg segment is in the range of 8.5 ≤ L ≤ 11 mm (femur), the quantity V/E is a constant. In fact, this relationship has already been demonstrated by the experimental results; it was observed that with the flexion of joint 1, the water volume extruded by the whole leg does not change much. Thus it is necessary to introduce a new parameter h/L, which represents the ability to extrude water volume per unit length of the leg. For example, the measured maximum depth of the dimple around half tarsi ranges from 1.1 mm to 1.5 mm (average 1.3 mm) and a whole hind leg of that length creates a maximum dimple depth of 2.6–3 mm. Although the maximum depth of the dimple induced by the tarsus is less than that of the whole leg, the value of h/L for the tarsus (0.43) is greater than that for the leg (0.24). This again emphasizes that the tarsus more efficiently extrudes a water volume than the whole leg does.
C. Initial stepping angle of the tarsus on the water surface
Besides the flexibility of the tarsus, the posture of the mosquito leg in contact with water is an important factor that affects the supporting force. It was observed that the mosquito can freely adjust the initial stepping angle θ between the tarsus and the water surface, particularly during walking, taking off and landing on the water surface. In practice, the initial stepping angle usually lays in the range 0–20°, which prompts us to study its effect on the supporting force. We carried out a series of experiments to measure the supporting force of a fresh tarsus section at different initial stepping angles. The force–angle curve is shown in Fig. 7. With increasing the initial stepping angle, the maximum supporting force of the tarsus decreases sharply. The largest force appeares in the range of 0–20°, which represents the normal posture of a leg standing on water. In addition, it was noted that in this range the force variation is very small among different angles, which agrees well with earlier reports.9,19 When θ is greater than 68°, the tip of the tarsus is found to pierce the water surface when it begins to contact water, and at this critical state, the maximum value of the water supporting force is just a few micronewtons. This is also in accordance with the theoretical work of Liu et al. and Su et al.,35,36 who investigated a cylindrical fiber vertically piercing a water surface.
In life, the optimal initial stepping angle can be realized by adjusting the flexion of the femur. It can be seen that, this remarkable insect is able to freely regulate the body posture by adjusting the motion of the femur and tibia, consequently changing the stepping angle and then the contact length of the leg with the water. For example, in order to survive in some special situations, e.g. in gusty wind conditions, the mosquito can greatly improve the stability of standing on water by slightly decreasing the initial stepping angle of the tarsus with the water surface. Although the tarsus is the most efficient part of the leg for creating the supporting force, the other two parts also contribute to the impressive abilities of mosquitoes to move across a water surface. For instance, as shown in Fig. 4(b), the tibia provides a moderate supporting force per unit length, although with a value lower than that of the tarsus. During stormy weather, the tibia may be used to increase the supporting force, as the contact length of the leg with the water is increased. The femur is unable to generate a supporting force, but in flexing it exerts a strong control on the postures of the tibia and tarsus. That is, the sophisticated components of the mosquito leg including the tarsus, tibia and femur possess different rigidities and biological functions. These exquisite structures achieve comprehensive regulation of its posture on water and help the mosquito to adapt to various living conditions.
In conclusion, the role of the mosquito tarsus in producing an extremely large supporting force was re-emphasized in this study. Using a self-designed measurement device, we obtained the maximum supporting force of mosquito legs of different lengths and found that the tarsus is the most capable of bearing the external load on the water surface. The maximal supporting force of a half tarsus was estimated as 248 ± 5 μN, about 10 times the total body weight of this insect (the maximum force produced by the whole total tarsus was 492 ± 5 μN). The origin of this force can be attributed to two factors. The first is the flexibility of the tarsus, which was verified by synchronized observations during depression of the water surface and by changes in force and stiffness over time. The second reason is that as a smart creature, the mosquito can use the comprehensive regulation of the tarsus, tibia and femur to realize an optimal initial stepping angle to approach the most efficient way of residing on water and reducing the wet adhesion force.
These findings illustrate why the mosquito normally uses only the tarsus rather than the whole leg to contact water when it is standing or walking, and why the tarsus presses on the water almost horizontally (the initial stepping angle is 0–20°). However, there remain some unsolved questions, including the anisotropy of the leg surface microstructures, the wet adhesion force of the leg, and the dynamic behavior of the leg, which should be further explored. Nevertheless, the current analyses deepen our understanding of the mechanisms of water-walking of these aquatic insects, and may help in the design of biomimetic structures, super-hydrophobic devices, aquatic robotics, or small boats.
We thank the National Natural Science Foundation of China (11302093, 11302094 & 11272357) and Liaoning Province Ministry of Education Scientific Study Project (L2013253) for financial support.