On the Flow-Induced Control of Particles and Complex Structures in Three Dimensions

Abstract

The precise manipulation of microscale particles and polymer chains in three dimensions remains a central challenge in soft matter engineering and microfluidic control. In this work, a computational framework is developed that extends the hydrodynamic trapping paradigm of the Stokes trap to three dimensions, enabling flow based manipulation of particles and polymer chains. Control inputs are determined through Model Predictive Control (MPC), with the flow field modeled using a Green's function solution to the incompressible Stokes equations. Polymer dynamics are represented by a bead--spring model with finitely extensible nonlinear elastic bonds and steric repulsion. A key feature of the framework is the use of a simplified predictor within the MPC optimization that accounts only for the imposed flow field and neglects interparticle forces. This introduces a systematic model mismatch between the predicted and true dynamics. Despite this discrepancy, the controller successfully achieves target configurations across a range of tasks, including single particle transport, coordinated multi--particle motion, and the formation of structured polymer geometries such as letters and helices. The results suggest that accurate control does not require a high fidelity model of the underlying physics. Instead, performance is governed by the ability of the receding horizon architecture to correct prediction errors through repeated feedback. However, as particles approach contact and strong repulsive interactions dominate, the simplified predictor cannot capture sufficient dynamics for convergence. More broadly, these findings indicate that model fidelity can be traded for frequent feedback, provided prediction errors remain bounded over short time intervals. This establishes a scalable extension of the Stokes trap framework to three-dimensional, multi particle, and polymer systems, and identifies the regimes in which simplified predictive models remain effective.