State diagram of a three-sphere microswimmer in a channel

Daddi-Moussa-Ider, Abdallah; Lisicki, Maciej; Mathijssen, Arnold J. T. M.; Hoell, Christian; Goh, Segun; Bławzdziewicz, Jerzy; Menzel, Andreas M. and Löwen, Hartmut (2018). State diagram of a three-sphere microswimmer in a channel. Journal of Physics: Condensed Matter, 30, article no. 254004.

DOI: https://doi.org/10.1088/1361-648X/aac470

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.