Force-induced dispersion in heterogeneous media

TL;DR

This paper investigates how external forces like electric or gravitational fields influence the dispersion of Brownian particles in media with spatially varying diffusivity, revealing potential for controlling dispersion properties.

Contribution

It introduces a Kubo formula to analyze force-induced dispersion in periodic heterogeneous media, highlighting how external forces can modulate dispersive behavior.

Findings

External forces significantly enhance dispersion along the force direction.

Dispersion perpendicular to the force can be non-monotonic and less affected.

The Kubo formula applies to any periodic advection-diffusion system in any dimension.

Abstract

The effect of a constant applied external force, induced for instance by an electric or gravitational field, on the dispersion of Brownian particles in periodic media with spatially varying diffusivity, and thus mobility, is studied. We show that external forces can greatly enhance dispersion in the direction of the applied force and also modify, to a lesser extent and in some cases non-monotonically, dispersion perpendicular to the applied force. Our results thus open up the intriguing possibility of modulating the dispersive properties of heterogeneous media by using externally applied force fields. These results are obtained via a Kubo formula which can be applied to any periodic advection diffusion system in any spatial dimension.