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Hydrodynamic and entropic effects on colloidal diffusion in corrugated channels

Xiang Yang,Chang Liu,Yunyun Li,F. Marchesoni,P. Hänggi,Hepeng Zhang

Published 2017 in Proceedings of the National Academy of Sciences of the United States of America

ABSTRACT

Significance When a particle diffuses in a corrugated channel, the channel’s boundaries have a twofold effect of limiting the configuration space accessible to the particle and increasing its hydrodynamic drag. Analytical and numerical approaches well-reproduce the former (entropic) effect, while ignoring the latter (hydrodynamic) effect. Here, we experimentally investigate nonadvective colloidal diffusion in channels with periodically varying width. While validating the current theory for channels much wider than the particle radius, we show that, in narrow channels, hydrodynamic and entropic effects can be equally strong and that hydrodynamic effects can be incorporated into existing descriptions by using an experimentally measured diffusivity. These results significantly advance our understanding of diffusive transport in confined geometries, such as in ionic channels and nanopores. In the absence of advection, confined diffusion characterizes transport in many natural and artificial devices, such as ionic channels, zeolites, and nanopores. While extensive theoretical and numerical studies on this subject have produced many important predictions, experimental verifications of the predictions are rare. Here, we experimentally measure colloidal diffusion times in microchannels with periodically varying width and contrast results with predictions from the Fick–Jacobs theory and Brownian dynamics simulation. While the theory and simulation correctly predict the entropic effect of the varying channel width, they fail to account for hydrodynamic effects, which include both an overall decrease and a spatial variation of diffusivity in channels. Neglecting such hydrodynamic effects, the theory and simulation underestimate the mean and standard deviation of first passage times by 40% in channels with a neck width twice the particle diameter. We further show that the validity of the Fick–Jacobs theory can be restored by reformulating it in terms of the experimentally measured diffusivity. Our work thus shows that hydrodynamic effects play a key role in diffusive transport through narrow channels and should be included in theoretical and numerical models.

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