A Comment on the Scale Length Validity of the Position Dependent Diffusion Coefficient Representation of Structural Heterogeneity

TL;DR

This paper investigates the validity of using a position-dependent diffusion coefficient to describe particle motion in heterogeneous colloid suspensions, challenging previous assumptions and proposing a delocalized force interpretation.

Contribution

It introduces a delocalized force perspective based on local equilibrium to reconcile experimental MSD data with theoretical predictions in inhomogeneous systems.

Findings

Experimental MSD data do not match predictions assuming point forces.

A delocalized force model explains the observed discrepancies.

Implications for modeling mass transport in heterogeneous media.

Abstract

Experimental studies of the variation of the mean square displacement (MSD) of a particle in a confined colloid suspension that exhibits density variations on the scale length of the particle diameter are not in agreement with the prediction that the spatial variation in MSD should mimic the spatial variation in density. The predicted behavior is derived from the expectation that the MSD of a particle depends on the system density and the assumption that the force acting on a particle is a point function of position. The experimental data come from studies of the MSDs of particles in narrow ribbon channels and between narrowly spaced parallel plates, and from new data, reported herein, of the radial and azimuthal MSDs of a colloid particle in a dense colloid suspension confined to a small circular cavity. In each of these geometries a dense colloid suspension exhibits pronounced density oscillations with spacing of a particle diameter. We remove the discrepancy between prediction and experiment using the Fisher-Methfessel interpretation of how local equilibrium in an inhomogeneous system is maintained to argue that the force acting on a particle is delocalized over a volume with radius equal to a particle diameter. Our interpretation has relevance to the relationship between the scale of inhomogeneity and the utility of translation of the particle MSD into a position dependent diffusion coefficient, and to the use of a spatially dependent diffusion coefficient to describe mass transport in a heterogeneous system.