A Unified Theory for Chaotic Mixing in Porous Media: from Pore Networks to Granular Systems

TL;DR

This paper develops a unified theory explaining chaotic mixing in various porous media, highlighting the roles of stretching, folding, and cutting/shuffling mechanisms, and their dependence on the medium's topology.

Contribution

It introduces a comprehensive framework linking chaotic mixing mechanisms across discrete and continuous porous systems, unifying previous disparate theories.

Findings

Mixing rate governed by stretching in continuous media

Discrete media involve only stretching motions

Unified theory connects pore-scale chaos to medium topology

Abstract

Recent studies have revealed the central role of chaotic stretching and folding at the pore scale in controlling mixing within porous media, whether the solid phase is discrete (as in granular and packed media) or continuous (as in vascular networks and open porous structures). Despite its widespread occurrence, a unified theory of chaotic mixing across these diverse systems remains to be developed. Furthermore, previous studies have focused on fluid stretching mechanisms but the folding mechanisms are largely unknown. We address these shortcomings by presenting a unified theory of mixing in porous media. We thus show that fluid stretching and folding (SF) arise through the same fundamental kinematics driven by the topological complexity of the medium. We find that mixing in continuous porous media manifests as discontinuous mixing through a combination of SF and cutting and shuffling (CS) actions, but the rate of mixing is governed by SF only. Conversely, discrete porous media involves SF motions only. We unify these diverse systems and mechanisms by showing that continuous media represents an analog of discrete media with finite-sized grain contacts. This unified theory provides insights into the generation of pore-scale chaotic mixing and points to design of novel porous architectures with tuneable mixing and transport properties.