An effective advection induced by oscillating microstructure in a diffusion equation

TL;DR

This paper investigates how oscillating microstructures in a porous medium induce a novel, locally varying advection in the homogenized diffusion equation, revealing new ways to control flow in such media.

Contribution

It introduces a homogenization framework for diffusion in media with oscillating microstructures, showing how microstructure oscillations generate controllable advection fields.

Findings

Oscillating microstructures induce a new advection term in homogenized equations.

The advection velocity can be arbitrarily controlled by microstructure oscillations.

The method allows for locally varying advection fields in porous media.

Abstract

We consider the homogenisation of a diffusion equation in a porous medium. The microstructure is time-dependent and oscillating on a small time scale. This oscillation causes a novel advection in the homogenised equations. Allowing for a locally varying geometry, the oscillating microstructure demonstrates the ability to generate arbitrary and locally varying advection velocity fields.