Confinement induced trajectory of a squirmer in a two dimensional channel

Abstract

Micro-swimmers in confinement are encountered in a variety of scenarios such as locomotion of sperm cells in female reproductive tract, targeted drug delivery and biofilm formation. Using a squirmer, a surface actuating model, we simulate the trajectory of swimmers in a two-dimensional channel confinement. Exploiting the simplicity of squirmer model and performing the study in two dimensions we restrict the analysis to minimum number of parameters and isolate and analyze the confinement induced swimmer trajectories. Using exact solutions of two dimensional disk squirmers we first show that they behave qualitatively similar to three dimensional spherical squirmers near a repulsive, planar wall. In a channel, fully resolved flow and thus hydrodynamic interaction between the squirmer and the channel walls are obtained using the lattice Boltzmann method. We find that strong pullers and pushers slide along the channel walls, a behavior determined by single wall. In contrast, swimmers with weak force dipoles break the symmetry in behavior between pushers and pullers, and this behavior is determined by both walls of the channel. Weak pullers stay at the channel center and weak pushers execute an oscillatory trajectory spanning the channel width. Straight line trajectories can be solely characterized by a fixed point on a phase plane spanned by its orientation angle and the distance from the channel centerline whereas oscillatory trajectories can be solely characterized using its escape angle from the wall. The nature of the trajectories is found to be robust to the details of higher modes and the size of the confinement.