# Flow topology during multiplexed particle manipulation using a Stokes Trap

## TL;DR

This paper investigates the flow structures involved in multiplexed particle manipulation using a Stokes trap, revealing that optimal control depends on flow patterns with minimal stagnation points, which aids in precise particle control.

## Contribution

It provides a detailed characterization of flow topologies during active particle control in a Stokes trap, highlighting the relationship between control algorithms and flow structures.

## Key findings

- Optimal control relies on flow patterns with zero or one stagnation point.
- System sensitivity analysis clarifies the influence of control parameters.
- Results guide applications in colloidal particle manipulation and soft particle deformation.

## Abstract

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.