Instability of particle inertial migration in shear flow

TL;DR

This paper shows that inertial particles in shear flow can experience unstable equilibrium positions due to the Saffman lift force, explaining previously observed phenomena through theoretical analysis and simulations.

Contribution

It introduces a theoretical criterion for the instability of inertial particle equilibrium positions in shear flow, validated by simulations.

Findings

Inertial particles can have unstable equilibrium positions in shear flow.

The critical Stokes number determines the onset of instability.

Simulations confirm the theoretical predictions.

Abstract

In a shear flow particles migrate to their equilibrium positions in the microchannel. Here we demonstrate theoretically that if particles are inertial, this equilibrium can become unstable due to the Saffman lift force. We derive an expression for the critical Stokes number that determines the onset of instable equilibrium. We also present results of lattice Boltzmann simulations for spherical particles and prolate spheroids to validate the analysis. Our work provides a simple explanation of several unusual phenomena observed in earlier experiments and computer simulations, but never interpreted before in terms of the unstable equilibrium.