RESUMEN
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.
RESUMEN
We propose a new experimental set up to characterize mixing and reactive transport in porous media with a high spatial resolution at the pore scale. The analogous porous medium consists of a Hele-Shaw cell containing a single layer of cylindrical solid grains built by soft lithography. On the one hand, the measurement of the local, intrapore, conservative concentration field is done using a fluorescent tracer. On the other hand, considering a fast bimolecular reaction A + B â C occurring as A displaces B, we quantify the rate of product formation from the spatially resolved measurement of the pore scale reaction rate, using a chemiluminescent reaction. The setup provides a dynamical measurement of the local concentration field over 3 orders of magnitude and allows investigating a wide range of Péclet and Damköhler numbers by varying the flow rate within the cell and the local reaction rate. We use it to study the kinetics of the reaction front between A and B. While the advection-dispersion (Fickian) theory, applied at the continuum scale, predicts a scaling of the cumulative mass of product C as MC â ât, the experiments exhibit two distinct regimes in which the produced mass MC evolves faster than the Fickian behavior. In both regimes the front rate of product formation is controlled by the geometry of the mixing interface between the reactants. Initially, the invading solute is organized in stretched lamellae and the reaction is limited by mass transfer across the lamella boundaries. At longer times the front evolves into a second regime where lamellae coalesce and form a mixing zone whose temporal evolution controls the rate of product formation. In this second regime, the produced mass of C is directly proportional to the volume of the mixing zone defined from conservative species. This interesting property is indeed verified from a comparison of the reactive and conservative data. Hence, for both regimes, the direct measurement of the spatial distribution of the pore scale reaction rate and conservative component concentration is shown to be crucial to understanding the departure from the Fickian scaling as well as quantifying the basic mechanisms that govern the mixing and reaction dynamics at the pore scale.