Colloid particles in microfluidic inertial hydrodynamic ratchet at moderate Reynolds number

The movement of spherical Brownian particle carried by an alternating fluid flow in a tube of periodically variable diameter is investigated. On the basis of our previous results [Phys. Rev. E 99, 012604 (2019)10.1103/PhysRevE.99.012604] on the hydrodynamics of the problem, we look at the competition of hydrodynamics and diffusion. We use the method of Fick-Jacobs mapping on an effective one-dimensional problem. We calculate the ratchet current and show that is is strictly related to finite size of the particles. The ratchet current grows quadratically with particle radius. We also show that the dominant contribution to the ratchet current is due to inertial hydrodynamic effects. This means that Reynolds number must be at least of order one. We discuss the possible use for separation of particles by size and perspectives of optimization of the tube shape.