New explicit formula for inertial lift in confined flows

Abstract

Inertial migration has proven effective for high-throughput manipulation of tiny particles in confined flows. However, complex and even controversial relationships between hydrodynamic forces and flow conditions hinder the development of an explicit formula for inertial lift acting on finite-sized particles at Reynolds numbers in the hundreds. Herein, we reveal the different scaling laws for shear gradient-induced inertial lift and wall-induced inertial lift by separating the contributions of pressure stress and viscous stress. A direct result of this treatment is a new explicit formula for the total inertial lift, valid for Reynolds numbers up to 400 and particle blockage ratios up to 0.25. This study provides an alternative way to understand inertial lift, thereby greatly facilitating the prediction of particle migration in practical microfluidic applications.