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