Chaotic Mixing in Three Dimensional Porous Media

TL;DR

This paper investigates how chaotic advection and complex topology in 3D porous media enhance scalar mixing, developing a novel model that aligns well with simulations and reveals exponential mixing scaling.

Contribution

It introduces a new stretching CTRW model for pore-scale mixing in 3D porous media, capturing the effects of chaotic advection and transit time distributions.

Findings

Chaotic advection causes exponential scalar mixing with advection.

2D porous media limit mixing to algebraic scaling.

The model aligns well with direct numerical simulations.

Abstract

Under steady flow conditions, the topological complexity inherent to all random 3D porous media imparts complicated flow and transport dynamics. It has been established that this complexity generates persistent chaotic advection via a three-dimensional (3D) fluid mechanical analogue of the baker's map which rapidly accelerates scalar mixing in the presence of molecular diffusion. Hence pore-scale fluid mixing is governed by the interplay between chaotic advection, molecular diffusion and the broad (power-law) distribution of fluid particle travel times which arise from the non-slip condition at pore walls. To understand and quantify mixing in 3D porous media, we consider these processes in a model 3D open porous network and develop a novel stretching continuous time random walk (CTRW) which provides analytic estimates of pore-scale mixing which compare well with direct numerical simulations. We find that chaotic advection inherent to 3D porous media imparts scalar mixing which scales exponentially with longitudinal advection, whereas the topological constraints associated with 2D porous media limits mixing to scale algebraically. These results decipher the role of wide transit time distributions and complex topologies on porous media mixing dynamics, and provide the building blocks for macroscopic models of dilution and mixing which resolve these mechanisms.