Measurement of FLux Fluctuations in Diffusion in the Small-Numbers Limit

TL;DR

This study investigates flux fluctuations in microscopic diffusion using microfluidics, confirming Gaussian flux distributions, Fick's Law validity at small particle numbers, and introducing a Flux Fluctuation Theorem.

Contribution

It provides experimental validation of diffusion laws and fluctuation theorems at the microscale with very few particles, extending classical diffusion understanding.

Findings

Flux distribution is Gaussian.

Fick's Law holds at minimal particle gradients.

Flux variance scales with particle number.

Abstract

Using a microfluidics device filled with a colloidal suspension of microspheres, we test the laws of diffusion in the limit of small particle numbers. Our focus is not just on average properties such as the mean flux, but rather on the features of the entire distribution of allowed microscopic trajectories that are possible during diffusive dynamics. The experiments show that: (1) the flux distribution is Gaussian; (2) Fick's Law --- that the average flux is proportional to the particle gradient --- holds even for particle gradients down to one or zero particles; (3) the variance in the flux is proportional to the sum of the particle numbers; and (4) there are backwards flows, where particles flow up a concentration gradient, rather than down it, and their numbers are well-predicted by theory and consistent with a new Flux Fluctuation Theorem.