Two-dimensional point singularity model of a low-Reynolds-number swimmer near a wall

Abstract

This paper studies a simple two-dimensional model of a swimmer at low-Reynolds-number near a no-slip wall by utilizing methods of complex analysis. The swimmer is propelled by purely tangential surface deformations and is modeled by moving point singularities. The nonlinear dynamics of the swimmer is formulated explicitly, and its motion near the wall is fully characterized. The results show qualitative agreement with predictions of three-dimensional models and with motion experiments on a robotic swimmer. The success and simplicity of the model suggest that it will provide a simple way to study the dynamics of low-Reynolds-number swimmers in more complicated geometries.