Deterministic transport of particles in a micro-pump

We study the drift of suspended micro-particles in a viscous liquid pumped back and forth through a periodic lattice of pores (drift ratchet). In order to explain the particle drift observed in such an experiment, we present an one-dimensional deterministic model of Stokes' drag. We show that the stability of oscillations of particle is related to their amplitude. Under appropriate conditions, particles may drift and two mechanisms of transport are pointed out. The first one is due to an spatio-temporal synchronization between the fluid and particle motions. As results the velocity is locked by the ratio of the space periodicity over the time periodicity. The direction of the transport may switch by tuning the parameters. Noteworthy, its emergence is related to a lattice of 2-periodic orbits but not necessary to chaotic dynamics. The second mechanism is due to an intermittent bifurcation and leads to a slow transport composed by long time oscillations following by a relative short transport to the next pore. Both steps repeat in a quasi-periodic manner. The direction of this last transport is strongly dependent on the pore geometry.