Stretching and folding sustain microscale chemical gradients in porous media

Abstract

<jats:p>Fluid flow in porous media drives the transport, mixing, and reaction of molecules, particles, and microorganisms across a wide spectrum of natural and industrial processes. Current macroscopic models that average pore-scale fluctuations into an effective dispersion coefficient have shown significant limitations in the prediction of many important chemical and biological processes. Yet, it is unclear how three-dimensional flow in porous structures govern the microscale chemical gradients controlling these processes. Here, we obtain high-resolution experimental images of microscale mixing patterns in three-dimensional porous media and uncover an unexpected and general mixing mechanism that strongly enhances concentration gradients at pore-scale. Our experiments reveal that systematic stretching and folding of fluid elements are produced in the pore space by grain contacts, through a mechanism that leads to efficient microscale chaotic mixing. These insights form the basis for a general kinematic model linking chaotic-mixing rates in the fluid phase to the generic structural properties of granular matter. The model successfully predicts the resulting enhancement of pore-scale chemical gradients, which appear to be orders of magnitude larger than predicted by dispersive approaches. These findings offer perspectives for predicting and controlling the vast diversity of reactive transport processes in natural and synthetic porous materials, beyond the current dispersion paradigm.</jats:p>

The Lagrangian kinematics of three-dimensional Darcy flow

“…Recent studies (Lester et al 2016b;Turuban et al 2018Turuban et al , 2019Souzy et al 2020) have established that chaotic advection is inherent to steady 3-D Stokes flow at the pore-scale, even in a medium that is homogeneous at the pore scale, providing a decisive link between pore-scale structural properties and the Lagrangian kinematics of porous media (Heyman et al 2020;Heyman, Lester & Le Borgne 2021). This result is not surprising as the Poincaré-Bendixson theorem states that only continuous systems with three or more degrees-of-freedom (DOFs) can admit a chaotic dynamics, hence, chaos is possible in three dimensions but not 2-D steady pore-scale flow.…”

A Closer Look: High-Resolution Pore-Scale Simulations of Solute Transport and Mixing Through Porous Media Columns

“…While these experimental data are tremendously valuable, they have some important limitations, regarding both ( ) control over experimental conditions, and ( ) scale, frequency and accuracy of observations. Recent advances have allowed researchers to physically reproduce and measure pore-scale flows with high resolution (e.g., Souzy et al, 2020;Heyman et al, 2020). These notable works investigate hydrodynamic deformation and spreading within relatively small domains in the (virtual) absence of diffusion, but do not provide the full picture for the evolution of mixing and reactions.…”

Plume deformation, mixing, and reaction kinetics: An analysis of interacting helical flows in three-dimensional porous media

“…Most studies of mixing in heterogeneous porous media have been performed in two-dimensional (2D) setups including quasi two-dimensional flow-through experiments and detailed 2D numerical simulations [12,[29][30][31][32][33], whereas fewer contributions have investigated mixing in fully three-dimensional (3D) systems [34][35][36][37][38][39][40][41][42][43][44]. Complex flows can develop in fully three-dimensional anisotropic porous media, entailing whirling and twisting streamlines [35,[45][46][47][48][49][50][51][52]. Such 3D flow fields can cause significant deformation of dissolved solute plumes and ultimately result in considerable mixing enhancement.…”