Issue 45, 2022

Distributed medium viscosity yields quasi-exponential step-size probability distributions in heterogeneous media

Abstract

The analysis of the statistics of random walks undertaken by passive particles in complex media has important implications in a number of areas including pathogen transport and drug delivery. In several systems in which heterogeneity is important, the distribution of particle step-sizes has been found to be exponential in nature, as opposed to the Gaussian distribution associated with Brownian motion. Here, we first develop a theoretical framework to study a simplified version of this problem: the motion of passive tracers in a range of sub-environments with different viscosity. We show that in the limit of a large number of equi-distributed sub-environments spanning a broad viscosity range, an exact analytical expression for the underlying particle step-size distribution can be derived, which approaches an exponential distribution when step sizes are small. We then validate this using a simple experimental system of glycerol–water mixtures, in which the volume fraction of glycerol is systematically varied. Overall, the assumption of exponentially distributed step sizes may substantially over-estimate the incidence of large steps in heterogeneous systems, with important implications in the analysis of various biophysical processes.

Graphical abstract: Distributed medium viscosity yields quasi-exponential step-size probability distributions in heterogeneous media

Article information

Article type
Paper
Submitted
17 Jul 2022
Accepted
11 Oct 2022
First published
14 Nov 2022
This article is Open Access
Creative Commons BY-NC license

Soft Matter, 2022,18, 8572-8581

Distributed medium viscosity yields quasi-exponential step-size probability distributions in heterogeneous media

N. A. Bustos, C. M. Saad-Roy, A. G. Cherstvy and C. E. Wagner, Soft Matter, 2022, 18, 8572 DOI: 10.1039/D2SM00952H

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