Modeling of the Propulsion Hydrodynamics for the Water Strider Locomotion on Water Surface

Modeling of the propulsion hydrodynamics of water striders, which was rare performed in previous studies, was developed in this paper. First, kinematical mechanism of the production of dipolar vortex in the wake of striders was illustrated by investigating the dependencies between the velocities on trajectories of the leg and velocity distribution in vortices. Subsequently, topological similarities between the hemispherical vortex and dipolar vortex was demonstrated by comparing their geometries and velocity distributions. Afterwards, velocity dependencies between the leg and flow in vortex further revealed that the translational speed of vortex is roughly determined by leg speed and that peak leg speed is about 2.5 times of the mean leg speed. Hence, the acceleration was formulized based on the peak and mean speeds of the leg. According to Theorem of Momentum and equivalence between the momentums of the water strider and fluid, mean propulsion force was then formulized, which is correlated with the leg acceleration and volume of vortex. It was found that the strider should produce bigger ‘water balls’ (enclosed in vortices) and push them backward with a larger acceleration so that to obtain a greater reaction force for propelling. For the same strider, further derived scaling law tells propulsion force is linearly dependent on leg speed and is parabolic with respective to Weber number. An incisive analysis on experimental data indicated the radius of dipolar vortex is comparable to the length of leg's second tarsal on water. Finally, Young-Laplace equation was yielded for the balance of pressures on upside and underside of water surface. Accordance between reported measurements and predicted values indicates the validity and reasonability of the model.