InterPore2025

Review of Chaotic Advection in Porous Media

May 19, 2025, 2:20 PM

15m

Oral Presentation (MS08) Mixing, dispersion and reaction processes across scales in heterogeneous and fractured media MS08

Speaker

Prof. David Mays (University of Colorado Denver)

Description

Garrison Sposito’s “Chaotic Solute Advection by Unsteady Groundwater Flow” (Water Resources Research, 42, W06D03, https://doi.org/10.1029/2005WR004518, 2006) was the first in a growing body of literature exploring chaotic advection in porous media. In the nearly two decades since, this literature has provided new insights into solute transport, mixing, and reaction across multiple scales, from the micrometer scale of pores to the 10-meter scale of groundwater remediation field sites, in two-dimensional (2D) and 3D geometries, including both natural and engineered flows, with contributions from groups in Australia, Canada, Germany, India, Spain, and the United States. In this presentation, we introduce this literature under the three headings of fundamentals, applications, and prospects. Starting with fundamentals, chaos refers to a deterministic system manifesting sensitive dependence on initial conditions, popularly known as the butterfly effect. This unpredictability results, not from inertial terms in the Navier-Stokes equations nor from random heterogeneity in the porous media, but from the nonlinear structure of the dynamic system itself. Chaotic advection refers to chaos in laminar flows, that is, flows at low Reynolds numbers that could result from high viscosity (for example in mixing paint or lava flows) or from small scales or low velocities (for example in micromachines). Chaotic advection in porous media generally includes small scales and low velocities but importantly, because porous media flows are generally irrotational, they exclude the mechanical stirrers employed in much of the broader literature on chaotic advection. Instead, chaotic advection in porous media refers to flows in which solute plumes are stretched and folded, popularly known as the baker's transformation. The analysis of such flows depends on Lagrangian analysis including Lyapunov exponents to quantify the butterfly effect and Poincaré sections to visualize the flow morphology. The literature features three principal applications to date, namely (1) ubiquitous chaotic advection at the pore scale, (2) naturally occurring chaotic advection at the Darcy scale, and (3) engineered chaotic advection, a subset of engineered injection and extraction (EIE). Among these applications, EIE has attracted the most attention so far, including theoretical developments, laboratory experiments, and one field test. Under prospects, these contributions lay the groundwork for future work under a broad conceptual framework in which porous media, both natural and engineered, serve as mixers and reactors despite the constraint of laminar flows. While the most popular application thus far has been groundwater remediation, chaotic advection in porous media also suggests promising applications for understanding natural processes, such as carbon and nutrient cycling, and engineered processes, such as in situ leach mining. In sum, if one begins with the premise that the rich complexity of biogeochemistry is often transport-limited, then chaotic advection offers a conceptual framework to rethink flow as a knob that might be adjusted to overcome that limitation.