Self-organization of clusters of spheroidal squirmers

In previous work, we found that oblate-shaped squirmers with non-axisymmetric interfacial actuation can form stable bound pairs (Poehnl and Uspal, Phys. Rev. Fluids, 2023). Here, we generalize our work by considering the possibility of obtaining n-particle clusters. Analytically, building on the Saintillian-Shelley kinetic theory of microswimmers, we develop an approximate “point-particle” approach that truncates hydrodynamic interactions at the level of the active stresslet. This framework captures the effect of particle shape and the extent of axisymmetry breaking in the slip profile. Numerically, we use the boundary element method, which can account for the particles’ finite size and near-field hydrodynamic interactions. We show that particles can self-organize into immotile clusters. In a cluster, the particles are positioned on the vertices of a regular polygon, and the particle axes are oriented towards the polygon's centroid. Finally, we consider how this tendency to form clusters leads to dynamical arrest and ordered structures on larger length scales for monolayers of active particles.