Separation of suspended particles in microfluidic systems by directional-locking in periodic fields

We investigate the transport and separation of overdamped particles under the action of a uniform external force in a two-dimensional periodic energy landscape. Exact results are obtained for the deterministic transport in a square lattice of parabolic, repulsive centers that correspond to a piecewise-continuous linear-force model. The trajectories are periodic and commensurate with the obstacle lattice and exhibit phase-locking behavior in that the particle moves at the same average migration angle for a range of orientation of the external force. The migration angle as a function of the orientation of the external force has a Devil's staircase structure. The first transition in the migration angle was analyzed in terms of a Poincare map, showing that it corresponds to a tangent bifurcation. Numerical results show that the limiting behavior for impenetrable obstacles is equivalent to the high Peclet number limit in the case of transport of particles in a periodic pattern of solid obstacles. Finally, we show how separation occurs in these systems depending on the properties of the particles.