Confinement induced three-dimensional trajectories of microswimmers in rectangular channels

Abstract

We study the trajectories of a model microorganism inside three-dimensional channels with square and rectangular cross sections. Using (1) numerical simulations based on the lattice-Boltzmann method and (2) analytical expressions using far-field hydrodynamic approximations and the method of images we systematically investigate the role of the strength and finite-size of the squirmer, confinement dimensions, and initial conditions in determining the three-dimensional trajectories of microswimmers. Our results indicate that the hydrodynamic interactions with the confining walls of the channel significantly affect the swimming speed and trajectory of the model microswimmer. Specifically, pullers always display sliding motion inside the channel: weak pullers slide through the channel center line, while strong pullers slide through a path close to any of the walls. Pushers generally follow helical motion in a square channel. Unlike pullers and pushers, the trajectories of neutral swimmers are not easy to generalize and are sensitive to the initial conditions. Despite this diversity in the trajectories, the far-field expressions capture the essential features of channel-confined swimmers. Finally, we propose a method based on the principle of superposition to understand the origin of the three-dimensional trajectories of channel confined swimmers. Such construction allows us to predict and justify the origin of apparently complex three-dimensional trajectories generated by different types of swimmers in channels with square and rectangular cross sections.