Biological organisms swimming at low-Reynolds number are often influenced by the presence of rigid boundaries and soft interfaces. In this paper, we present an analysis of locomotion near a free surface with surface tension. Using a simplified two-dimensional singularity model and combining a complex variable approach with conformal mapping techniques, we demonstrate that the deformation of a free surface can be harnessed to produce steady locomotion parallel to the interface. The crucial physical ingredient lies in the nonlinear hydrodynamic coupling between the disturbance flow created by the swimmer and the free boundary problem at the fluid surface.
Bibliographical noteFunding Information:
This work was funded in part by the US National Science Foundation through grants CTS-0624830 (EL and AEH) and CBET-0746285 (EL). D.C. acknowledges the support of an EPSRC Advanced Research Fellowship as well as the hospitality of the Department of Mathematics at MIT where this work was initiated. O.S. also acknowledges support from an EPSRC studentship.
- interfacial flows (free surface)
- low-Reynolds number flows
- low-dimensional models