Introductory Remarks

We theoretically quantify the pairwise hydrodynamic interactions between self-propelled colloidal bodies, "microswimmers," that are pinned to an interface. The microswimmers are modeled as steady spherical squirmers with a general swimming stroke that allows for simultaneous self translation and self rotation. For simplicity, we assume that the two fluids forming the interface have equal viscosities. We compute the flow via a simultaneous Stokes multipole expansion about each squirmer. This method is especially convenient because it naturally splits the flow into components associated with interfacial forces and the self-translation/rotation of each swimmer. Modes associated with self translation and interfacial pinning are relatively long-ranged, and they dominate hydrodynamic interaction of the swimmers when they are well separated. However, the shorter-ranged self-rotational modes become important at smaller separation distances, and may result in large deflections of swimmers which approach one another by within a distance comparable to the diameter of the squirmer. Our work has interesting applications in predicting the behavior of suspensions of bacteria and colloids on interfaces. In particular, we show qualitative agreement between our theoretical model and an experimental system of bacteria attached to colloids at interfaces.