Confined squirmers: interactions, contacts and clusters.

The hydrodynamic squirmer model has been used as a proxy to understand the dynamics of microswimmers with diverse propulsion mechanisms, ranging from the beating of biological cilia to artificial chemical or phoretic actuation. When confined, a suspension of such swimmers exhibits collective properties, e.g. the clustering of Marangoni droplets above a wall. Here, we investigate the extent to which hydrodynamics, as opposed to other mechanisms, control these interactions. We first consider theoretically the symmetric boundary-mediated encounters of model microswimmers under gravity through the far-field interaction of a pair of weak squirmers. The behaviour of the swimmers is set by their orientation, itself controlled by the squirming parameters, which distinguishes pullers from pushers. We find that close to walls, contacts are unavoidable and that the interactions are then dominated by the dynamics after contact. We therefore focus on the near-field stability of groups of squirmers. Considering for simplicity a circular assembly, we can determine analytically the stability conditions for the clusters. Our simplified approach to active clustering enables us to highlight the hydrodynamic contribution to the dynamics, which can be otherwise hard to isolate in large-scale suspension simulations.