Dynamics of a microswimmer near a curved wall: guided and trapped locomotions

We propose a combined analytical-numerical strategy to predict the dynamics and trajectory of a microswimmer next to a curved spherical obstacle. The microswimmer is actuated by a slip velocity on its surface and a uniformly valid solution is provided by utilizing the Reynolds reciprocal theorem in conjunction with the exact hydrodynamic solution of translation/rotation of a sphere in an arbitrary direction next to a stationary obstacle. This approach permits the hydrodynamic interaction of the microswimmer and the obstacle to be consistently and accurately calculated in both far and near fields. Based on the analysis, it was shown that while the "point-singularity solution" is valid when the microswimmer is far from the obstacle, it fails to predict the correct dynamics when the swimmer is close to the obstacle (i.e. gap size is approximately twice the characteristic length of the microswimmer). Two different paradigms for propulsion, so-called "squirmer" and "phoretic" models, were examined and for each type of microswimmer, various types of trajectories are highlighted and discussed under which circumstances the swimmer can be hydrodynamically trapped or guided by the obstacle. The analysis indicates that it is always easier to capture a microswimmer in a closed circular orbit with a large sized obstacle ($\sim 20$-$40$ times larger than the microswimmer size) as in this case the magnitude of rotational velocity can be sufficiently large that the swimmer can adjust its distance and orientation vector with the obstacle.