Hydrodynamic synchronization of externally driven colloids

The collective dynamics of externally driven $N_{\rm p}$-colloidal systems ($1\le N_{\rm p}\le 4$) in a confined viscous fluid have been investigated using three-dimensional direct numerical simulations with fully resolved hydrodynamics. The dynamical modes of collective particle motion are studied by changing the particle Reynolds number {as determined by the strength of the external driving force} and the confining wall distance. For a system with $N_{\rm p}= 3$, we found that at a critical Reynolds number, a dynamical mode transition occurs from the doublet-singlet mode to the triplet mode, which has not been reported experimentally. The dynamical mode transition was analyzed in detail from the following two viewpoints: (1) spectrum analysis of the time evolution of a tagged particle velocity and (2) the relative acceleration of the doublet cluster with respect to the singlet particle. For a system with $N_{\rm p}=4$, we found similar dynamical mode transitions from the doublet-singlet-singlet mode to the triplet-singlet mode and further to the quartet mode.