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Abstract:
We investigate analytically a simple microfluidic device consisting of a tube with non-uniform but spatially periodic diameter (a contraction-expansion array). The fluid is driven back and forth by a pump and carries colloidal particles. Although the net flow of the fluid is zero, the particles move preferentially in one direction due to ratchet mechanism, which occurs by simultaneous effect of inertial hydrodynamics and Brownian motion. Analytical treatment of the underlying advection-diffusion problem is done using Fick-Jacobs mapping on effective one-dimensional system. We investigate separately the regime where diffusion is dominant and the regime where diffusion is infinitesimally weak. We show that in both regimes the average current is strongly sensitive to particle size, thus facilitating colloidal particle sorting.