# The hydrodynamics of water strider locomotion

By Sung Hoon Kang

Title: The hydrodynamics of water strider locomotion

Reference: David L. Hu, Brian Chan and John W. M. Bush, *Nature* 424, 663 (2003).

## Contents

## Soft matter keywords

surface tension, hydrophobic, capillary

## Abstract from the original paper

Water striders Gerridae are insects of characteristic length 1 cm and weight 10 dynes that reside on the surface of ponds, rivers, and the open ocean. Their weight is supported by the surface tension force generated by curvature of the free surface, and they propel themselves by driving their central pair of hydrophobic legs in a sculling motion. Previous investigators have assumed that the hydrodynamic propulsion of the water strider relies on momentum transfer by surface waves. This assumption leads to Denny’s paradox: infant water striders, whose legs are too slow to generate waves, should be incapable of propelling themselves along the surface. We here resolve this paradox through reporting the results of high-speed video and particle tracking studies. Experiments reveal that the strider transfers momentum to the underlying fluid not primarily through capillary waves, but rather through hemispherical vortices shed by its driving legs. This insight guided us in constructing a self-contained mechanical water strider whose means of propulsion is analogous to that of its natural counterpart.

## Soft matter example

Hydronamics of the surface locomotion of semiaquatic insects is an interesting subject which is not well understood. In general, there are two ways of walking on water depending on the relative magnitudes of the body weight (Mg) and the maximum curvature force (σP), where M is the body mass, g is the gravitational acceleration,σ is the surface tension and the P is the contract perimeter of the water-walker [1].

Water-walkers with M_{c} = Mg/σP > 1, such as the basilisk lizard, uses the force generated by their feet slapping the surface and propelling water downward, whereas creatures with M_{c} = Mg/σP < 1, such as the wter strider rely on the curvature force by distortion of the free surface as shown in Fig. 1. They have non-wetting body and legs covered by thousands of hairs [2-3].

The force balance on a stationary water strider can be written as Mg = F_{b} + F_{c}, where F_{b} is the buoyancy force and F_{c} is the curvature force. F_{b} is obtained by integrating the hydrostatic pressure over the body area in contact with the water, while F_{c} is deduced by integrating the curvature pressure over this area, or equivalently the vetical component of the surface tension, σ sin θ, along the contact perimeter (Fig. 1b). For a long thin water-strider leg, this ratio is F_{b}/F_{c} ~ w/L_{c} <<1, where the leg radius, w ~ 40 um, the capillary length, L_{c} = (σ/ρg)^{1/2} ~ 2 mm, and ρ, the density of water. The strider's weight is supported almost by surface tension.

## References

[1] Vogel, S. Life in Moving Fluids (Princeton Univ. Press, Princeton, NJ, 1994).

[2] Andersen, N. M. A comparative study of locomotion on the water surface in semiaquatic bugs (Insecta, Hemiptera, Gerromorpha). Vidensk. Meddr. Dansk. Naturh. Foren. 139, 337–396 (1976).

[3] de Gennes, P.-G., Brochard-Wyart, F. & Quere, D. Gouttes, Boules, Perles et Ondes (Belin, Collection Echelles, Paris, 2002).