How pore-scale disorder controls fluid stretching in porous media

TL;DR

This study explores how the microstructure disorder in porous media influences fluid stretching, combining experiments, simulations, and analytical models to quantify the impact on mixing processes.

Contribution

It provides the first quantitative link between pore-scale disorder and fluid stretching statistics, advancing understanding of mixing in heterogeneous porous structures.

Findings

Fluid deformation is localized near solid boundaries across disorder levels.

Mean stretching grows linearly in ordered media and quadratically in disordered media.

Stretching distributions are approximately log-normal.

Abstract

Fluid stretching in porous media governs the mixing of reactants, contaminants, and nutrients, yet how the solid microstructure controls the stretching statistics remains poorly understood. We investigate how porous-medium heterogeneity controls stretching using (i) particle-tracking velocimetry experiments in 3D-printed millifluidic cells, (ii) numerical simulations of solute-plume deformation in the measured flow fields, and (iii) analytical calculations of fluid stretching. The cells contain arrays of cylindrical rods with systematically-varying disorder levels, from ordered to random. Velocity and shear-rate measurements reveal that fluid deformation is strongly localized near solid boundaries for all disorder levels, suggesting that near-wall flow is the main driver of stretching. The mean stretching grows linearly in time for ordered media and quadratically for disordered media, while the stretching distributions are approximately log-normal. We analytically describe the stretching produced by flow around an isolated cylinder and embed this description in a random-walk model that reproduces the observed stretching statistics in random media. These results provide the first quantitative connection between porous-medium structure and fluid-stretching statistics, revealing the extent to which disordered media accelerate mixing relative to ordered media and enabling progress beyond the common mean-field description of stretching in two-dimensional media as a simple shear flow.