At finite Reynolds numbers, $Re$, particles migrate across laminar flow streamlines to their equilibrium positions in microchannels. This migration is attributed to a lift force, and the balance between this lift and gravity determines the location of particles in channels. Here we demonstrate that velocity of finite-size particles located near a channel wall differs significantly from that of an undisturbed flow, and that their equilibrium position depends on this, referred to as slip velocity, difference. We then present theoretical arguments, which allow us to generalize expressions for a lift force, originally suggested for some limiting cases and $Re\ll 1$, to finite-size particles in a channel flow at $Re\leqslant 20$. Our theoretical model, validated by lattice Boltzmann simulations, provides considerable insight into inertial migration of finite-size particles in a microchannel and suggests some novel microfluidic approaches to separate them by size or density at a moderate $Re$.
Analysis of non-physical slip velocity in lattice Boltzmann simulations using the bounce-back scheme
