  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<<1, to
finite-size particles in a channel flow at Re < 20. Our theoretical model,
validated by lattice Boltzmann simulations, provides considerable insight into
inertial migration of finite-size particles in microchannel and suggests some
novel microfluidic approaches to separate them by size or density at a moderate
Re.
