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

Area of Science:

• Biophysics
• Statistical Mechanics

Background:

• Random walk analysis is crucial for understanding particle movement in complex media.
• Heterogeneous environments often exhibit exponential step-size distributions, differing from Brownian motion's Gaussian model.

Purpose of the Study:

• To develop a theoretical framework for passive tracer motion in environments with varying viscosity.
• To derive an analytical expression for particle step-size distribution in a multi-viscosity system.

Main Methods:

• Theoretical modeling of passive tracer movement across diverse viscosity sub-environments.
• Experimental validation using glycerol-water mixtures with systematically varied glycerol concentrations.

Main Results:

• An exact analytical expression for particle step-size distribution was derived in the limit of many equi-distributed sub-environments.
• The derived distribution approaches an exponential form for small step sizes.
• Experimental results validated the theoretical framework.

Conclusions:

• The assumption of exponential step-size distributions may overestimate large steps in heterogeneous systems.
• Findings have significant implications for analyzing biophysical processes like pathogen transport and drug delivery.