Non-Gaussian diffusion near surfaces

TL;DR

This paper investigates non-Gaussian diffusion of particles near surfaces, deriving theoretical predictions for displacement distributions and validating them with experiments and simulations, revealing Gaussian tails contrary to some models.

Contribution

It provides a theoretical framework linking non-Gaussian diffusion near surfaces with displacement cumulants and validates it through experiments and simulations.

Findings

Displacement parallel to walls is Brownian with non-Gaussian features.

The fourth cumulant and distribution tails are accurately predicted by the theory.

Tails of the displacement distribution are Gaussian, not exponential.

Abstract

We study the diffusion of particles confined close to a single wall and in double-wall planar channel geometries where the local diffusivities depend on the distance to the boundaries. Displacement parallel to the walls is Brownian as characterized by its variance, but it is non-Gaussian having a non-zero fourth cumulant. Establishing a link with Taylor dispersion, we calculate the fourth cumulant and the tails of the displacement distribution for general diffusivity tensors along with potentials generated by either the walls or externally, for instance gravity. Experimental and numerical studies of the motion of a colloid in the direction parallel to the wall give measured fourth cumulants which are correctly predicted by our theory. Interestingly, contrary to models of Brownian-yet-non-Gaussian diffusion, the tails of the displacement distribution are shown to be Gaussian rather than exponential. All together, our results provide additional tests and constraints for the inference of force maps and local transport properties near surfaces.