Two Coupled Mechanisms Produce Fickian, yet non-Gaussian Diffusion in Heterogeneous Media

TL;DR

This study reveals that non-Gaussian yet Fickian diffusion in heterogeneous media results from coupled effects of spatially varying particle diffusivities and their distribution, explained through a superstatistical model, applicable to biological and soft matter systems.

Contribution

It identifies two coupled mechanisms causing non-Gaussian Fickian diffusion and validates this with a simple mathematical superstatistical model, advancing understanding of diffusion in heterogeneous environments.

Findings

Non-Gaussianity arises from spatially dependent diffusivities.

Coupled mechanisms lead to non-Gaussian Fickian diffusion.

A superstatistical model explains the observed behavior.

Abstract

Fickian yet non-Gaussian diffusion is observed in several biological and soft matter systems, yet the underlying mechanisms behind the emergence of non-Gaussianity while retaining a linear mean square displacement remain speculative. Here, we characterize quantitatively the effect of spatial heterogeneities on the appearance of non-Gaussianity in Fickian diffusion. We study the diffusion of fluorescent colloidal particles in a matrix of micropillars having a range of structural configurations: from completely ordered to completely random. We show that non-Gaussianity emerges as a direct consequence of two coupled factors; individual particle diffusivities become spatially dependent in a heterogeneous randomly structured environment, and the spatial distribution of the particles varies significantly in such environments, further influencing the diffusivity of a single particle. The coupled mechanisms lead to a considerable non-Gaussian nature even due to weak disorder in the arrangement of the micropillars. A simple mathematical model validates our hypothesis that non-Gaussian yet Fickian diffusion in our system arises from the superstatistical behavior of the ensemble in a structurally heterogeneous environment. The two mechanisms identified here are relevant for many systems of crowded heterogeneous environments where non-Gaussian diffusion is frequently observed, for example in biological systems, polymers, gels and porous materials.