  Inertial microfluidics is a promising tool for many lab-on-a-chip
applications. Particles in channel flows with Reynolds numbers above one
undergo cross-streamline migration to a discrete set of equilibrium positions
in square and rectangular channel cross sections. This effect has been used
extensively for particle sorting and the analysis of particle properties. Using
the lattice Boltzmann method, we determine equilibrium positions in square and
rectangular cross sections and classify their types of stability for different
Reynolds numbers, particle sizes, and channel aspect ratios. Our findings
thereby help to design microfluidic channels for particle sorting. Furthermore,
we demonstrate how an axial control force, which slows down the particles,
shifts the stable equilibrium position towards the channel center. Ultimately,
the particles then stay on the centerline for forces exceeding a threshold
value. This effect is sensitive to particle size and channel Reynolds number
and therefore suggests an efficient method for particle separation. In
combination with a hysteretic feedback scheme, we can even increase particle
throughput.
