Optimal control of colloidal trajectories in inertial microfluidics using the Saffman effect

TL;DR

This paper develops an optimal control method to precisely steer colloidal particles in inertial microfluidic channels using the Saffman effect, enabling efficient particle separation and targeted delivery.

Contribution

It introduces a novel optimal control approach for particle steering in microfluidics, considering particle size and channel length effects, improving over constant-force methods.

Findings

Optimal control reduces energy cost compared to constant force.

Particles can be accurately guided to target positions.

Different particle sizes can be effectively separated.

Abstract

In inertial microfluidics colloidal particles in a Poiseuille flow experience the Segr\'e-Silberberg lift force, which drives them to specific positions in the channel cross section. Due to the Saffman effect an external force applied along the microchannel induces a cross-streamline migration to a new equilibrium position. We apply optimal control theory to design the time protocol of the axial control force in order to steer a single particle as precisely as possible from a channel inlet to an outlet at a chosen target position. We discuss the influence of particle radius and channel length and show that optimal steering is cheaper than using a constant control force. Using a single optimized control-force protocol, we demonstrate that even a pulse of particles spread along the channel axis can be steered to a target and that particles of different radii can be separarted most efficiently.