  The stochastic transport of suspended particles through a periodic pattern of
obstacles in microfluidic devices is investigated by means of the Fokker-Planck
equation. Asymmetric arrays of obstacles have been shown to induce the
continuous separation of DNA molecules of different length. The analysis
presented here of the asymptotic distribution of particles in a unit cell of
these systems shows that separation is only possible in the presence of a
driving force with a non-vanishing normal component at the surface of the solid
obstacles. In addition, vector separation, in which different species move, in
average, in different directions within the device, is driven by differences on
the force acting on the various particles and not by differences in the
diffusion coefficient. Monte-Carlo simulations performed for different
particles and force fields agree with the numerical solutions of the
Fokker-Planck equation in the periodic system.
