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

TL;DR

This paper studies how overdamped particles move and can be separated in a two-dimensional periodic energy landscape under a uniform external force, revealing phase-locking and Devil's staircase behavior.

Contribution

It provides exact analytical results for deterministic transport in a square lattice of obstacles and links phase-locking phenomena to particle separation mechanisms.

Findings

Particles exhibit phase-locking and Devil's staircase in migration angles.

Transition points correspond to tangent bifurcations analyzed via Poincare maps.

Separation depends on particle properties and obstacle interactions.

Abstract

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.