Structural order and pair formation in a two-dimensional colony of hydrodynamically interacting pushers

We consider a system of hydrodynamically interacting spheroidal pushers bound to move in a two-dimensional sheet embedded into a three-dimensional fluid. Previously developed mean-field kinetic theory predicts that a spatially homogeneous and isotropic distribution of prolate spheroidal pushers exhibits the orientational instability that sets in above a critical density at a smallest length scale available. Here we use particle-based approach to describe the structural properties of the system depending on the average and degree of elongation of pusher's body. We show that a structure with well-defined positional and orientational order emerges below the critical density predicted by the mean field theory. The emerging order is associated with the existence of stable bonding pairs that correspond to rotational attractors in the system of two hydrodynamically interacting prolate spheroidal pushers. As a result, sharp peaks are formed in the angular position-orientation pair distribution function at low number densities. The characteristic size of the bonding pairs approximately coincides with the distance away from pusher's body, at which the angle-averaged dipolar flow velocity coincides with the self-propulsion speed. Inclusion of steric repulsion between pushers does not eliminate orientational order as long as the effective exclusion separation distance is much smaller than bonding pair size.