Predicting the enhancement of mixing-driven reactions in nonuniform flows using measures of flow topology

The Role of High-Permeability Inclusion on Solute Transport in a 3D-Printed Fractured Porous Medium: An LIF–PIV Integrated Study

It is well-known that the presence of geometry heterogeneity in porous media enhances solute mass mixing due to fluid velocity heterogeneity. However, laboratory measurements are still sparse on characterization of the role of high-permeability inclusions on solute transport, in particularly concerning fractured porous media. In this study, the transport of solutes is quantified after a pulse-like injection of soluble fluorescent dye into a 3D-printed fractured porous medium with distinct high-permeability (H-k) inclusions. The solute concentration and the pore-scale fluid velocity are determined using laser-induced fluorescence and particle image velocimetry techniques. The migration of solute is delineated with its breakthrough curve (BC), temporal and spatial moments, and mixing metrics (including the scalar dissipation rate, the volumetric dilution index, and the flux-related dilution index) in different regions of the medium. With the same H-k inclusions, compared to a H-k matrix, the low-permeability (L-k) matrix displays a higher peak in its BC, less solute mass retention, a higher peak solute velocity, a smaller peak dispersion coefficient, a lower mixing rate, and a smaller pore volume being occupied by the solute. The flux-related dilution index clearly captures the striated solute plume tails following the streamlines along dead-end fractures and along the interface between the H-k and L-k matrices. We propose a normalization of the scalar dissipation rate and the volumetric dilution index with respect to the maximum regional total solute mass, which offers a generalized examination of solute mixing for an open region with a varying total solute mass. Our study presents insights into the interplay between the geometric features of the fractured porous medium and the solute transport behaviors at the pore scale.

Linking mixing and flow topology in porous media: An experimental proof

Transport processes in porous media are controlled by the characteristics of the flow field which are determined by the porous material properties and the boundary conditions of the system. This work provides experimental evidence of the relation between mixing and flow field topology in porous media at the continuum scale. The setup consists of a homogeneously packed quasi-two-dimensional flow-through chamber in which transient flow conditions, dynamically controlled by two external reservoirs, impact the transport of a dissolved tracer. The experiments were performed at two different flow velocities, corresponding to Péclet numbers of 191 and 565, respectively. The model-based interpretation of the experimental results shows that high values of the effective Okubo-Weiss parameter, driven by the changes of the boundary conditions, lead to high rates of increase of the Shannon entropy of the tracer distribution and, thus, to enhanced mixing. The comparison between a hydrodynamic dispersion model and an equivalent pore diffusion model demonstrates that despite the spatial and temporal variability in the hydrodynamic dispersion coefficients, the Shannon entropy remains almost unchanged because it is controlled by the Okubo-Weiss parameter. Overall, our work demonstrates that under highly transient boundary conditions, mixing dynamics in homogeneous porous media can also display complex patterns and is controlled by the flow topology.

Reactive particle-tracking solutions to a benchmark problem on heavy metal cycling in lake sediments

Geochemical systems are known to exhibit highly variable spatiotemporal behavior. This may be observed both in non-smooth concentration curves in space for a single sampling time and also in variability between samples taken from the same location at different times. However, most models that are designed to simulate these systems provide only single-solution smooth curves and fail to capture the noise and variability seen in the data. We apply a recently developed reactive particle-tracking method to a system that displays highly complex geochemical behavior. When the method is made to most closely resemble a corresponding Eulerian method, in its unperturbed form, we see near-exact match between solutions of the two models. More importantly, we consider two approaches for perturbing the model and find that the spatially-perturbed condition is able to capture a greater degree of the variability present in the data. This method of perturbation is a task to which particle methods are uniquely suited and Eulerian models are not well-suited. Additionally, because of the nature of the algorithm, noisy spatial gradients can be highly resolved by a large number of mobile particles, and this incurs negligible computational cost, as compared to expensive chemistry calculations.

Three-Dimensional Vortex-Induced Reaction Hot Spots at Flow Intersections

We show the emergence of reaction hot spots induced by three-dimensional (3D) vortices with a simple A+B→C reaction. We conduct microfluidics experiments to visualize the spatial map of the reaction rate with a chemiluminescence reaction and cross validate the results with direct numerical simulations. 3D vortices form at spiral-saddle-type stagnation points, and the 3D vortex flow topology is essential for initiating reaction hot spots. The effect of vortices on mixing and reaction becomes more vigorous for rough-walled channels, and our findings are valid over wide ranges of channel dimensions and Damköhler numbers.

Upscaling Mixing in Highly Heterogeneous Porous Media via a Spatial Markov Model

In this work, we develop a novel Lagrangian model able to predict solute mixing in heterogeneous porous media. The Spatial Markov model has previously been used to predict effective mean conservative transport in flows through heterogeneous porous media. In predicting effective measures of mixing on larger scales, knowledge of only the mean transport is insufficient. Mixing is a small scale process driven by diffusion and the deformation of a plume by a non-uniform flow. In order to capture these small scale processes that are associated with mixing, the upscaled Spatial Markov model must be extended in such a way that it can adequately represent fluctuations in concentration. To address this problem, we develop downscaling procedures within the upscaled model to predict measures of mixing and dilution of a solute moving through an idealized heterogeneous porous medium. The upscaled model results are compared to measurements from a fully resolved simulation and found to be in good agreement.

Coupled continuous-time random walks for fluid stretching in two-dimensional heterogeneous media

We study the relation between flow structure and fluid deformation in steady flows through two-dimensional heterogeneous media, which are characterized by a broad spectrum of stretching behaviors, ranging from sub- to superlinear. We analyze these behaviors from first principles, which uncovers intermittent shear events to be at the origin of subexponential stretching. We derive explicit expressions for Lagrangian deformation and demonstrate that stretching obeys a coupled continuous-time random walk, which for broad distributions of flow velocities becomes a Lévy walk. The derived model provides a direct link between the flow and deformation statistics, and a natural way to quantify the impact of intermittent shear events on the stretching behavior.