Mechanics of jumping on water

Invited

Mechanics of jumping on water

Ho-Young Kim, Juliette Amauger, Han-Bi Jeong, Duck-Gyu Lee, Eunjin Yang, and Piotr G. Jablonski

Phys. Rev. Fluids 2, 100505 – Published 17 October 2017

An article within the collection: 2017 Invited Papers

Abstract

Some species of semiaquatic arthropods including water striders and springtails can jump from the water surface to avoid sudden dangers like predator attacks. It was reported recently that the jump of medium-sized water striders is a result of surface-tension-dominated interaction of thin cylindrical legs and water, with the leg movement speed nearly optimized to achieve the maximum takeoff velocity. Here we describe the mathematical theories to analyze this exquisite feat of nature by combining the review of existing models for floating and jumping and the introduction of the hitherto neglected capillary forces at the cylinder tips. The theoretically predicted dependence of body height on time is shown to match the observations of the jumps of the water striders and springtails regardless of the length of locomotory appendages. The theoretical framework can be used to understand the design principle of small jumping animals living on water and to develop biomimetic locomotion technology in semiaquatic environments.

Received 16 July 2017

DOI:https://doi.org/10.1103/PhysRevFluids.2.100505

Physics Subject Headings (PhySH)

Biological fluid dynamics Locomotion Surface tension effects

Fluid Dynamics

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This article appears in the following collection:

2017 Invited Papers

Physical Review Fluids publishes a collection of papers associated with the invited talks presented at the 69th Annual Meeting of the APS Division of Fluid Dynamics.

Authors & Affiliations

Ho-Young Kim^1,2,*, Juliette Amauger³, Han-Bi Jeong¹, Duck-Gyu Lee⁴, Eunjin Yang⁵, and Piotr G. Jablonski^6,7

¹Department of Mechanical and Aerospace Engineering, Seoul National University, Seoul 08826, Korea
²Urban Data Science Lab, SNU BDI, Seoul 06324, Korea
³Département de Physique, Ecole Normale Supérieure, PSL Research University, 24 rue Lhomond, 75005, Paris, France
⁴Department of Nature-Inspired Nanoconvergence Systems, Korea Institute of Machinery and Materials, Daejeon 34103, Korea
⁵Korea Institute of Science and Technology Evaluation and Planning, Seoul 06775, Korea
⁶School of Biological Sciences, Seoul National University, Seoul 08826, Korea
⁷Institute and Museum of Zoology, Polish Academy of Sciences, Wilcza 64, 00-679 Warsaw, Poland

^*hyk@snu.ac.kr

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Vol. 2, Iss. 10 — October 2017

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Images

Figure 1
(a) The front view of a water strider jumping off the water surface taken by a high-speed camera. (b) The side view of a water strider during its jump with length parameters used in the modeling. Adapted from Ref. [11].
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Figure 2
(a) Forces acting on a cylinder floating on water. (b) The shape of a long flexible cylinder which is supported by the deformed interface. (c) The profile of meniscus extending from an end of a cylinder at depth $h = 0.6$ mm to the undisturbed free surface of water. The three-dimensional Laplace-Young equation was solved assuming that $η$ at $z = 0$ is given by the two-dimensional Laplace-Young equation solved for the cylinder side. Only half the depressed surface (positive $x$ ) is shown for clarity. (d) The scaled volume, $\hat{Ω} = Ω / (l_{c}^{2} h)$ , displaced by the meniscus vs the scaled depth of the cylinder end, $h / l_{c}$ . The circles are the computational results and the line is from the best-fitting formula.
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Figure 3
(a) The height of body center of jumping water striders vs time. Circles and triangles correspond to the experimental results and lines correspond to the theoretical predictions. Black symbols correspond to the jump of a male Aquarius paludum with $m = 37$ mg, $r = 130 μ m, l_{l} = 22.6$ mm, $l_{w} = 13$ mm, and $ω = 60$ rad $s^{- 1}$ . Red symbols correspond to the jump of a male Gerris paludum with $m = 31$ mg, $r = 130$ $μ m, l_{l} = 15.9$ mm, $l_{w} = 7.7$ mm, and $ω = 77$ rad $s^{- 1}$ . (b) The force acting on a leg of a water strider vs time corresponding to the black symbols in panel (a).
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Figure 4
(a) The effects of the leg rotation speed in the penetration of water surface. When the leg rotation rate $ω$ is too high, the legs pierce the water surface, thereby failing to use the capillary force. (b) The role of leg rotation in prolonging the interaction between the leg and water surface. In the upper case where the leg pushes down the water surface without rotation, the leg is disengaged from the water surface too early. In the lower case where the leg rotates, the interaction time of leg and water surface increases.
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Figure 5
(a) Micrograph of a springtail with the body length of 1.7 mm. (b) Time series of jumping of the springtail on the water surface. The time interval between the adjacent images is 0.2 ms. (c) The height of the body center vs time. The circles correspond to the measurement result of Ref. [5] and the line is our theoretical prediction. (d) The temporal evolution of the total capillary force $F$ consisting of the forces on the side ( $F_{s}$ ) and the end ( $F_{e}$ ) of the furcula. Panels (a) and (b) reprinted with permission from Sudo et al. [5], copyright 2015 by the Japanese Society for Experimental Mechanics.
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