On the transport of interacting particles in a chain of cavities: Description through a modified Fick-Jacobs equation

TL;DR

This paper develops a modified Fick-Jacobs equation to model the transport of interacting Brownian particles in a varying cross-section tube, validated by Monte Carlo simulations showing good agreement.

Contribution

It introduces a new modified Fick-Jacobs equation accounting for particle interactions and solves it numerically for different cavity geometries.

Findings

Good agreement between theory and Monte Carlo simulations.

Effective modeling of particle concentration in asymmetric cavities.

Validation of the modified equation for various geometries.

Abstract

We study the transport process of interacting Brownian particles in a tube of varying cross section. To describe this process we introduce a modified Fick-Jacobs equation, considering particles that interact through a hard-core potential. We were able to solve the equation with numerical methods for the case of symmetric and asymmetric cavities. We focused in the concentration of particles along the direction of the tube. We also preformed Monte Carlo simulations to evaluate the accuracy of the results, obtaining good agreement between theory and simulations.