Inertial focusing of neutrally buoyant spherical particle in shallow microchannels

TL;DR

This paper develops an explicit formula to predict the lift force on neutrally buoyant spherical particles in shallow microchannels at low Reynolds numbers, validated against experimental data.

Contribution

It introduces a new explicit model for lift force prediction applicable to larger particles up to a/H=0.35 in shallow microchannels at Re_p ≤ 1.

Findings

The model accurately predicts lift forces for particles up to a/H=0.35.

Increased slip length reduces near-wall lift force and shifts equilibrium position.

Predicted particle trajectories agree well with experimental data.

Abstract

This study investigates the lift force acting on a finite-size, neutrally buoyant spherical particle suspended in a liquid while flowing through a shallow channel at low Reynolds numbers. Using an immersed boundary method, we calculate the lift force for particle radius-to-channel height ratios spanning \(0.03 \leq a/H \leq 0.35\) in 2D planar Poiseuille flows. We propose an explicit formula that accurately predicts the lift force for particles as large as \(a/H = 0.35\) and remains valid for particle Reynolds number \(Re_p \leq 1\), despite a reduction in near-wall lift force at higher \(Re_p\). The influence of slip boundary conditions is also explored, demonstrating that increased slip length reduces near-wall lift force and shifts the particle equilibrium position closer to the wall. Predictions of the particle trajectory from the derived model are in good agreement to the published experimental data. These findings offer a practical framework for estimating the migration of large particles in microfluidic devices.(This article has been accepted for publication in Physics of Fluids. After publication, it will be available via the AIP Publishing website.)