  Trapping and manipulation of small particles underlies many scientific and
technological applications. Recently, the precise manipulation of multiple
small particles was demonstrated using a Stokes trap that relies only on fluid
flow without the need for optical or electric fields. Active flow control
generates complex flow topologies around suspended particles during the
trapping process, yet the relationship between the control algorithm and flow
structure is not well understood. In this work, we characterize the flow
topology during active control of particle trajectories using a Stokes trap.
Our results show that optimal control of two particles unexpectedly relies on
flow patterns with zero or one stagnation points, as opposed to positioning two
particles using two distinct stagnation points. We characterize the sensitivity
of the system with respect to the parameters in the control objective function,
thereby providing a systematic understanding of the trapping process. Overall,
these results will be useful in guiding applications involving the controlled
manipulation of multiple colloidal particles and the precise deformation of
soft particles in defined flow fields.
