Purcell swimmer near a wall

TL;DR

This paper investigates how a three-link swimmer's movement is affected by a nearby wall in low Reynolds number conditions, revealing controllability and displacement behaviors through theoretical and numerical analysis.

Contribution

It derives equations of motion for the Purcell swimmer near a wall and demonstrates controllability and displacement effects using geometric control theory.

Findings

Controllability near a wall for nearly parallel configurations

Net displacement observed in tilted configurations

Numerical experiments support analytical results

Abstract

We study the effects of hydrodynamic interactions between a wall and the Purcell three-link swimmer in the two-dimensional case. After deriving the equations of motion in a low Reynolds number regime using Resistive Force Theory with suitably modified drag coefficients, we show, by means of criteria from Geometric Control Theory, that the system is controllable at configurations that are nearly parallel to the wall. Furthermore, we study configurations that are tilted, and we show net displacement with respect to the initial orientation. Some numerical experiments illustrate the analytical results.