Hydrodynamic Self-assembly in Suspensions of Microrollers: a Dynamical System Insight

Hydrodynamic self-assembly has been observed in suspensions of colloidal microrollers [Driscoll, M., Delmotte, B., Youssef, M., Sacanna, S., Donev, A. and Chaikin, P. (2017). Nature Physics, 13(4), 375]. Microrollers rotate about an axis parallel to the floor and generate strong, slowly decaying, advective flows. Here we show that pairs of microrollers can exhibit various hydrodynamic bound states whose nature depends on a dimensionless number, denoted $B$, that compares the relative strength of gravitational forces and external torques. Using a dynamical system framework we characterize these various states in phase space. We analyze the various bifurcations of the system as $B$ varies. In particular, we show that there is a critical value of $B$ for the existence of stable motile orbiting trajectories, reminiscent of the ``colloidal creatures" observed by Driscoll \textit{et al}. These results help us understand the hydrodynamic mechanisms that lead to spontaneous self-assembly and to envision particle transport using microroller suspensions.