Inertial migration in pressure-driven channel flow: beyond the Segre-Silberberg pinch

TL;DR

This paper theoretically investigates how finite particle size affects inertial migration in pressure-driven channel flow, revealing new equilibrium positions and implications for microfluidic particle sorting.

Contribution

It introduces a finite size correction to classical inertial migration theory, showing new stable equilibria and migration behaviors not captured by point-particle models.

Findings

Finite size alters inertial lift profiles at high Reynolds numbers.

New stable equilibria are found closer to the channel centerline.

Results align with recent experiments and simulations.

Abstract

We examine theoretically the inertial migration of a neutrally buoyant rigid sphere in pressure-driven channel flow, accounting for its finite size relative to the channel width (the confinement ratio). For sufficiently large channel Reynolds numbers\,($Re_c$), a small but finite confinement ratio qualitatively alters the inertial lift velocity profiles obtained using a point-particle formulation. Finite size effects are shown to lead to new equilibria, in addition to the well known Segre-Silberberg pinch locations. Consequently, a sphere can migrate to either the near-wall Segre-Silberberg equilibria, or the new stable equilibria located closer to the channel centerline, depending on $Re_c$ and its initial position. Our findings are in accord with recent experiments and simulations, and have implications for passive sorting of particles based on size, shape and other physical characteristics, in microfluidic applications.