Particle-obstacle interaction and reversibility in Stokes flows

Neutrally buoyant, force-free particles in Stokes flow have a strong tendency to passively follow streamlines. When encountering an obstacle, steric requirements force a particle to deviate from its initial streamline, but if the flow geometry is fore-aft symmetric reversibility necessitates the particle's return to the initial streamline. However, in scenarios that lack this symmetry particles may be irreversibly displaced. We investigate when such permanent displacement can be expected, using prototypical vortical flow fields as well as transport flows to assess the relevant conditions for such particle manipulation at zero Reynolds number. As theory predicts that the particle motion relative to the fluid is governed by gradients and curvatures of the flow field, counterintuitive particle trajectories can result if the flow is chosen judiciously. This may open up new possibilities for particle manipulation and a deeper understanding of deterministic lateral displacement.