# Hydrodynamic and entropic effects on colloidal diffusion in corrugated channels

## TL;DR

This study experimentally investigates colloidal diffusion in corrugated microchannels, revealing that hydrodynamic effects significantly influence transport times and must be incorporated into models for accurate predictions.

## Contribution

It provides the first experimental validation of hydrodynamic effects on colloidal diffusion in corrugated channels and demonstrates how to incorporate measured diffusivity into Fick-Jacobs theory.

## Key findings

- Hydrodynamic effects cause a 40% underestimation of diffusion times when neglected.
- Fick-Jacobs theory aligns with experiments when reformulated with measured diffusivity.
- Hydrodynamic effects vary spatially within the channels.

## Abstract

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-Jakobs theory can be restored by reformulating it in terms of the experimentally measured diffusivity. Our work thus demonstrates that hydrodynamic effects play a key role in diffusive transport through narrow channels and should be included in theoretical and numerical models.