Feedback control of inertial microfluidics using axial control forces.

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 determined the 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 demonstrated how an axial control force, which slows down the particles and shifts the stable equilibrium position towards the channel center. Ultimately, the particles then stay on the centerline for forces exceeding the threshold value. This effect is sensitive to the 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 the particle throughput.