PoreLab lecture on chaotic advection/mixing in 3D granular porous media

PoreLab is pleased to announce the PoreLab Lecture this Wednesday at 13:00 (Central Europe)on Zoom. To join, please follow the link below the abstract or add this event to your calendar by opening the attached calendar ics-file.

When: Wednesday 21 April at 13:00 (Central Europe Time)

Where: online, see below

Title: Chaotic advection/mixing in 3D granular porous media

Speaker: Yves Méheust

Affiliation: Assistant Professor, Geosciences Rennes, Université Rennes 1


The transport and mixing of solutes in porous media is central to many subsurface phenomena, because it controls effective reactive rates in the subsurface [1]. Hence, it plays an important role in geochemical cycles of the critical zone (the zone extending from aquifers to the Earth surface-atmosphere interface) and in contaminant transfers from the surface to aquifers, as well as in many subsurface applications such as soil/aquifer remediation, CO2 storage or the storage of radioactive contaminants. Solute mixing is crucially impacted by the stretching of the solute-advecting fluid, which tends to increase concentration gradients and thus competes with the homogenizing molecular diffusion [2]. Theoretical studies on three-dimensional (3D) random continuous porous media (i.e., consisting of connected channels within a continuous solid phase) have provided evidence that permanent Stokes flow in such geometries is chaotic, which means that fluid deformation grows exponentially in time [3]. This constitutes a change of paradigm with respect to two-dimensional (2D) geometries, since permanent 2D flows cannot be chaotic. I will present numerical and experimental studies demonstrating that permanent Stokes flow in 3D granular porous media is also intrinsically chaotic, and showing how the value of the associated Lypaunov exponent (i.e., its logarithmic stretching rate) can be predicted from the geometry.

We first studied Stokes flow through a regular (cubic-centered) packing of monodisperse beads for various orientations of the flow. As soon as the flow direction is not perpendicular to a reflection symmetry plane of the lattice, the flow is chaotic. This can be explained by the transverse intersection of flow separation/reattachment surfaces, termed manifolds, that originate from the surface of solid grains [4,5]. A geometric model relating the intersection of these manifolds to the mean flow orientation allows predicting the dependence of the Lyapunov exponent associated to the chaotic flow on that orientation [4,5]. We then investigated permanent Stokes flow in random granular packings experimentally, using a combination of refractive index matching between the fluid and the solid phase, and laser-induced fluorescence, to record the 3D concentration field of a permanent solute plume with a very small molecular diffusion coefficient. The length of the filament backbone of 2D cuts of the concentration field transverse to the macroscopic flow orientation grows exponentially, which provides the Lyapunov exponent [6]. Repeated folding of the filament, which is necessary for exponential growth of its length in a finite space, is shown to result from the passing of the manifolds at the contact between solid grains. A theoretical model accounting for this phenomenology allows predicting the measured Lyapunov exponent from the mean pore size, grain size, porosity, and coordination number of the packing [6]. This model is also successful at predicting the Lyapunov associated to the numerically-studied ordered geometry. Another experiment, where the velocity field, rather than the concentration, is measured, and fluid stretching is computed numerically in the experimental velocity field, confirms the intrinsically chaotic nature of permanent Stokes flow in 3D granular porous media [7].

[1] P. de Anna, J. Jimenez-Martinez, H. Tabuteau, R. Turuban, T. Le Borgne, M. Derrien & Y. Méheust (2014), Mixing and reaction kinetics in porous media: an experimental pore scale quantification, Environ. Sci. Tech. 48, 508-516.

[2] T. Le Borgne, M. Dentz, E. Villermaux (2015), The lamellar description of mixing in porous media, J. Fluid Mech. 770, 458-498.

[3] D. R. Lester, G. Metcalfe, & M. G. Trefry (2013), Is chaotic advection inherent to porous media flow ?, Phys. Rev. Lett. 111, 174101.

[4] R. Turuban, D. R. Lester, T. Le Borgne & Y. Méheust (2018), Space-Group Symmetries Generate Chaotic Fluid Advection in Crystalline Granular Media, Phys. Rev. Lett., 120, 024501.

[5] R. Turuban, D. R. Lester, H. Heyman, T. Le Borgne & Y. Méheust (2019), Chaotic Mixing in Crystalline Granular Media, J. Fluid Mech. 871, 562-594.

[6] J. Heyman, D. R. Lester, R. Turuban, Y. Méheust, & T. Le Borgne (2020), Stretching and folding sustain microscale chemical gradients in porous media., Proc. Nat. Acad. Sci. 117 (24), 13359-13365.

[7] M. Souzy., H. Lhuissier, Y. Méheust, T. Le Borgne & B. Metzger (2020), Velocity distributions, dispersion and stretching in three-dimensional porous media, J. Fluid Mech 891, A16.

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Meeting link: https://uio.zoom.us/j/67356471922
Meeting ID: 673 5647 1922

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Meeting ID: 673 5647 1922