Hydrodynamics of active particles confined in a periodically tapered channel

Active particles in diverse circumstances encounter confined channels with asymmetric bounding walls. In the present work, employing the squirmer model, we analyze the trajectory of a single and a pair of active particles in a two-dimensional periodically tapered channel with asymmetric bounding walls through a combined analytical-numerical approach. Assuming Stokes equations for the flow inside the channel, both puller and pusher types of squirmers are treated. We illustrate through phase diagrams how for different projection angles of the squirmer the associated swimming trajectories are non-trivially altered for various tapering angles of the channel. The phase diagram characterizes the trajectory of the squirmer as trapped or escaped depending on these angles. It is observed that for a fixed projection angle, the swimmer exhibits a transition in the swimming state at a critical tapering of the channel. Correspondingly, the combination of the projection and tapering angles may serve as a control mechanism guiding the swimmer for relevant applications in micro-fluidic systems. We further investigate the stability of the individual squirmer trajectory in the presence of a second squirmer, which hints at the development of parallel or coordinated swimming motion inside the channel. The results indicate that the tapering of the channel acts as a decisive parameter in the mutual attraction or repulsion and navigates the collective swimming state of the squirmers.