Stability of interlocked self-propelled dumbbell clusters

Combining experimental observations of Quincke roller clusters with computer simulations and a stability analysis, we explore the formation and stability of two interlocked self-propelled dumbbells. For large self-propulsion and significant geometric interlocking, there is a stable joint spinning motion of two dumbbells. The spinning frequency can be tuned by the self-propulsion speed of a single dumbbell, which is controlled by an external electric field for the experiments. For typical experimental parameters the rotating pair is stable with respect to thermal fluctuations but hydrodynamic interactions due to the rolling motion of neighboring dumbbells leads to a break-up of the pair. Our results provide a general insight into the stability of spinning active colloidal molecules which are geometrically locked.