Diffusion in a Curved Tube

TL;DR

This paper derives a quasi-one-dimensional diffusion equation for particles in a curved, winding tube, highlighting how geometric properties influence diffusion in biological and porous media.

Contribution

It introduces a novel diffusion model accounting for curvature and torsion effects in thin, winding tubes, extending previous flat or straight tube analyses.

Findings

Geometric quantities modify the diffusion equation

Curvature and torsion influence particle transport

Applicable to biological and porous media systems

Abstract

The diffusion of particles in confining walls forming a tube is discussed. Such a transport phenomenon is observed in biological cells and porous media. We consider the case in which the tube is winding with curvature and torsion, and the thickness of the tube is sufficiently small compared with its curvature radius. We discuss how geomerical quantities appear in a quasi-one-dimensional diffusion equation.