Closed Formula for Transport across Constrictions

In the last decade, the Fick-Jacobs approximation has been exploited to capture transport across constrictions. Here, we review the derivation of the Fick-Jacobs equation with particular emphasis on its linear response regime. We show that, for fore-aft symmetric channels, the flux of noninteracting systems is fully captured by its linear response regime. For this case, we derive a very simple formula that captures the correct trends and can be exploited as a simple tool to design experiments or simulations. Lastly, we show that higher-order corrections in the flux may appear for nonsymmetric channels.

Automated summary

In the past decade, the Fick-Jacobs approximation has been used to study transport across constrictions. This paper reviews the derivation of the Fick-Jacobs equation with a focus on its linear response regime. It is found that for fore-aft symmetric channels, the flux of noninteracting systems can be fully captured by the linear response regime. A simple formula is derived for this case, which accurately captures the trends and can be used as a tool for experiment design and simulations. Furthermore, it is shown that higher-order corrections in the flux may arise for nonsymmetric channels.