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.Key words. dynamics of locomotion, low-Reynolds swimming, dynamic stability AMS subject classifications. 37J15, 37J25, 76M60DOI. 10.1137/1008087451. Introduction. The locomotion of microorganisms, as well as of futuristic miniature robotic swimmers for biomedical applications, is governed by low-Reynolds-number hydrodynamics [30,40,60]. Reynolds number, which encompasses the ratio of inertial forces to viscous forces, is defined as Re = V L/ν, where V is a characteristic velocity, L is a characteristic length scale, and ν is the kinematic viscosity of the fluid. For example, a typical Reynolds number for a human swimmer who is governed by inertial effects is on the order of 10 4 , whereas microorganisms typically have Re ≈ 10 −4 and swim by harnessing viscous effects. The theory of low-Re locomotion of microorganisms and motile cells in nature has been widely studied in the physics, fluid mechanics, and biology literature, e.g., [12,46,58]. In the context of nanotechnology and engineering, some efforts to develop miniaturized swimmers, primarily for biomedical applications, were reported in [4,21,26,42,70]. While a vast majority of the theoretical works use the simplifying assumption of unbounded fluid domain, in realistic scenarios microswimmers often move in confined environments and interact with the boundaries. The presence of solid boundaries has profound effects on the dynamics and motion trajectories of low-Re swimmers, as confirmed by numerical simulations [23,28,61,72] and observed in several laboratory experiments with swimming microorganisms [14,25,45].

The motion of microorganisms as well as of tiny robotic swimmers for biomedical applications is governed by low Reynolds number (Re) hydrodynamics, where viscous effects dominate and inertial effects are negligible. This paper presents experimental results that verify theoretical predictions of our recent work which analyzed the dynamics and stability of a low-Re swimmer near a plane wall. The experimental setup uses macro-scale swimmer prototypes which are propelled by rotating cylinders in highly viscous silicone oil. The motion is recorded by a video camera and position measurements are taken by an optical tracking system. The results show good qualitative agreement with our recent theoretical predictions.