A two-dimensional model of low-Reynolds number swimming beneath a free surface

TL;DR

This paper presents a two-dimensional model showing how low-Reynolds number swimmers can achieve steady locomotion near a free surface by exploiting surface deformation and nonlinear hydrodynamic coupling.

Contribution

It introduces a simplified singularity model combined with conformal mapping to analyze swimming near a free surface with surface tension, highlighting the role of surface deformation.

Findings

Surface deformation enables steady swimming parallel to the free surface.

Nonlinear hydrodynamic coupling is key to propulsion near interfaces.

Model demonstrates potential for controlled locomotion near free surfaces.

Abstract

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.