Inertial focusing of neutrally buoyant spherical particle in shallow microchannels

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≤a/H≤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 Rep≤1, despite a reduction in near-wall lift force at higher Rep. 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 with the published experimental data. These findings offer a practical framework for estimating the migration of large particles in microfluidic devices.