a1 Department of Chemical and Biological Engineering, University of British Columbia, Vancouver, BC V6T 1Z3, Canada
a2 Department of Mathematics, University of British Columbia, Vancouver, BC V6T 1Z2, Canada
This paper presents a finite-element simulation of the interfacial flow during propulsion of water walkers such as fishing spiders and water striders. The unsteady stroke of the driving leg is represented by a two-dimensional cylinder moving on a specified trajectory. The interface and the moving contact lines are handled by a diffuse-interface model. We explore the mechanism of thrust generation in terms of the interfacial morphology and flow structures. Results show that the most important component of the thrust is the curvature force related to the deformation of the menisci and the asymmetry of the dimple. For water walkers with thick legs, the pressure force due to the inertia of the water being displaced by the leg is also important. The viscous force is negligible. An extensive parametric study is performed on the effect of leg velocity, stroke depth, leg diameter and surface wettability. The propulsive force is insensitive to the contact angle on the leg. However, the hydrophobicity of the leg helps it detach from the surface during the recovery stroke and thus decreases the resistance. It is also important for averting or delaying penetration of the interface at large rowing velocity and depth. In two dimensions, surface waves are more efficient than vortices in transferring the momentum imparted by the leg to the water.
(Received February 08 2010)
(Revised September 06 2010)
(Accepted September 12 2010)
(Online publication November 30 2010)