State diagram of a three-sphere microswimmer in a channel

TL;DR

This paper investigates the dynamics of a three-sphere microswimmer in a channel, revealing how confinement influences swimming behavior, stability, and bifurcations, with analytical descriptions for velocity and rotation rate.

Contribution

It provides a detailed state diagram of microswimmer behavior under confinement, including bifurcation analysis and analytical modeling using hydrodynamic images.

Findings

Pushers are trapped at channel walls.

Neutral swimmers and pullers can glide and navigate stably.

A supercritical pitchfork bifurcation occurs with increasing channel height.

Abstract

Geometric confinements are frequently encountered in soft matter systems and in particular significantly alter the dynamics of swimming microorganisms in viscous media. Surface-related effects on the motility of microswimmers can lead to important consequences in a large number of biological systems, such as biofilm formation, bacterial adhesion and microbial activity. On the basis of low-Reynolds-number hydrodynamics, we explore the state diagram of a three-sphere microswimmer under channel confinement in a slit geometry and fully characterize the swimming behavior and trajectories for neutral swimmers, puller- and pusher-type swimmers. While pushers always end up trapped at the channel walls, neutral swimmers and pullers may further perform a gliding motion and maintain a stable navigation along the channel. We find that the resulting dynamical system exhibits a supercritical pitchfork bifurcation in which swimming in the mid-plane becomes unstable beyond a transition channel height while two new stable limit cycles or fixed points that are symmetrically disposed with respect to the channel mid-height emerge. Additionally, we show that an accurate description of the averaged swimming velocity and rotation rate in a channel can be captured analytically using the method of hydrodynamic images, provided that the swimmer size is much smaller than the channel height.