Abstract
We study biased, diffusive transport of Brownian particles through narrow, spatially periodic structures in which the motion is constrained in lateral directions. The problem is analyzed using the Fick‐Jacobs equation in which the effect of the lateral confinement is replaced by an entropic barrier. The validity of this approximation, being based on the assumption of an instantaneous equilibration of the particle distribution in the cross‐section of the structure, is analyzed by comparing the different time scales that characterize the problem. A validity criterion is established in terms of the shape of the structure and of the applied force. It is analytically corroborated and verified by numerical simulations that the critical value of the force up to which this description holds true scales as the square of the periodicity of the structure. The criterion can be visualized by means of a diagram representing the regions where the Fick‐Jacobs description becomes inaccurate in terms of the scaled force versus the periodicity of the structure.
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