Optimal Control of Colloidal Trajectories in Inertial Microfluidics Using the Saffman Effect.

Felix Rühle,Christian Schaaf,Holger Stark

doi:10.3390/mi11060592

Abstract

In inertial microfluidics colloidal particles in a Poiseuille flow experience the Segré-Silberberg lift force, which drives them to specific positions in the channel cross section. An external force applied along the microchannel induces a cross-streamline migration to a new equilibrium position because of the Saffman effect. 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.

Highlights

The field of microfluidics is of utmost importance for numerous technological, biochemical, and biomedical applications, especially for inexpensive lab-on-a-chip applications and parallelized or automized studies [1,2,3,4]
One important characteristic of the regime of intermediate Reynolds numbers, where flow is still laminar, is the breaking of Stokes reversibility. This leads to self-assembly, such as the famous Segré-Silberberg effect discovered by its namesakes in 1961 [7], where colloids travel to distinct lateral positions in the channel cross section that are driven by inertial lift forces
Exploiting the Saffman effect, the easiest approach to steer a particle to a target position is to use constant axial control forces

Summary

Introduction

The field of microfluidics is of utmost importance for numerous technological, biochemical, and biomedical applications, especially for inexpensive lab-on-a-chip applications and parallelized or automized studies [1,2,3,4]. One important characteristic of the regime of intermediate Reynolds numbers, where flow is still laminar, is the breaking of Stokes reversibility. This leads to self-assembly, such as the famous Segré-Silberberg effect discovered by its namesakes in 1961 [7], where colloids travel to distinct lateral positions in the channel cross section that are driven by inertial lift forces. The particles’ lateral positions in the cross section of a microchannel can be manipulated with axial external forces, which drive the particles, e.g., via electrophoresis [16,17,18]

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