Sorting of very small particles dispersed in a fluid is a crucial problem of microfluidics and nanofluidics. A small pump pushing the fluid back and forth keeps the system very far from equilibrium. We show that combined action of inertial hydrodynamic effects plus Brownian motion leads to rectification of particle flow. We computed the average particle velocity analytically. This velocity is strongly sensitive to particle size, which promises high eficiency of sorting.
Microchannels of periodically varying diameter may serve as a ratchet device, rectyfying the movment of tiny colloidal particles immersed in the fluid. The fluid is pumped back and forth, the average flow being zero. Despite of that, the particles move in a specific direction determined by the mirror-asymmetric variation of the tube diameter. This was proved by several recent experiments. In our work we compute analytically the particle flow and show that the decisive mechanism behind the rectification is the inertial effect of the fluid flow, combined with the Brownian motion of the colloidal particle. The ratchet current depends very strongly on particle diameter, thus making such setup an ideal device for sorting of micron- and submicton-sized particles.
  Left panel: Sketch of particle flowing in tube of periodically varying diameter. Right panel: streamlines of the flow of particles. Note the "half-vortices", responsible for the ratchet effect. |