Control of Microparticles Through Hydrodynamic Interactions

TL;DR

This paper demonstrates how a single actively controlled microparticle can manipulate passive particles in a viscous fluid using hydrodynamic interactions, with theoretical and numerical validation of control strategies.

Contribution

It introduces a geometric control framework for manipulating passive microparticles via a single active particle in viscous flow, supported by theoretical and numerical analysis.

Findings

Active particle can control one or two passive particles.

Theoretical predictions closely match numerical simulations.

Potential for complex micromanipulation with minimal control inputs.

Abstract

The controllability of passive microparticles that are advected with the fluid flow generated by an actively controlled one is studied. The particles are assumed to be suspended in a viscous fluid and well separated so that the far-field Stokes flow solutions may be used to describe their interactions. Applying concepts from geometric control theory, explicit moves characterized by a small amplitude parameter $\varepsilon$ are devised to prove that the active particle can control one or two passive particles. The leading-order (in $\varepsilon$) theoretical predictions of the particle displacements are compared with those obtained numerically and it is found that the discrepancy is small even when $\varepsilon\approx 1$. These results demonstrate the potential for a single actuated particle to perform complex micromanipulations of passive particles in a suspension.