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We study biased, diffusive transport of Brownian particles through narrow,spatially periodic structures in which the motion is constrained in lateraldirections. The problem is analyzed under the perspective of the Fick-Jacobsequation which accounts for the effect of the lateral confinement byintroducing an entropic barrier in a one dimensional diffusion. The validity ofthis approximation, being based on the assumption of an instantaneousequilibration of the particle distribution in the cross-section of thestructure, is analyzed by comparing the different time scales that characterizethe problem. A validity criterion is established in terms of the shape of thestructure and of the applied force. It is analytically corroborated andverified by numerical simulations that the critical value of the force up towhich this description holds true scales as the square of the periodicity ofthe structure. The criterion can be visualized by means of a diagramrepresenting the regions where the Fick-Jacobs description becomes inaccuratein terms of the scaled force versus the periodicity of the structure.Comment: 20 pages, 7 figure

Biased diffusion in confined media: Test of the Fick-Jacobs approximation and validity criteria