'The Japan Society for Industrial and Applied Mathematics'
Doi
Abstract
The locomotion of microorganisms and tiny artificial swimmers is governed by low-Reynolds-number
hydrodynamics, where viscous effects dominate and inertial effects are negligible. While the theory
of low-Reynolds-number locomotion is well studied for unbounded fluid domains, the presence of a
boundary has a significant influence on the swimmer’s trajectories and poses problems of dynamic
stability of its motion. In this paper we consider a simple theoretical model of a microswimmer near
a wall, study its dynamics, and analyze the stability of its motion. We highlight the underlying
geometric structure of the dynamics, and establish a relation between the reversing symmetry of
the system and existence and stability of periodic and steady solutions of motion near the wall.
The results are demonstrated by numerical simulations and validated by motion experiments with
macroscale robotic swimmer prototypes
