Bound states of spheroidal squirmers

The “squirmer model” is a classical hydrodynamic model for the motion of interfacially-driven microswimmers, such as self-phoretic colloids or volvocine green algae. To date, most studies using the squirmer model have considered spherical particles. Recently, we generalized the squirmer model to particles with spheroidal shape and axisymmetric distribution of the surface slip. Additionally, in a recent collaboration, we predicted that discoidal particles moving by induced-charged electrophoresis can form “head-to-head” bound pairs. Here, we develop a general approach to the pairing and scattering dynamics of two spheroidal squirmers. We assume that the direction of motion of the squirmers is restricted to a plane, which is approximately realized in many experimental systems. In the framework of an analytically tractable kinetic model, we predict that, for identical squirmers, a “head-to-head” configuration is stable only when the particles have oblate shape and a non-axisymmetric distribution of surface slip. We also obtain conditions for stability of a “head-to-tail” configuration: for instance, the two particles must have unequal self-propulsion velocities. Our analytical predictions are compared against detailed numerical calculations obtained using the boundary element method.