Abstract
I will present recent numerical experimental and theoretical results about the mixing potential of flows in granular porous media. While these flows are observed in many natural contexts (96% of the fresh water resource is underground), their dispersive and reactive dynamics are poorly constrained. As an example, no universal relationship has yet been able to relate the effective macroscopic dispersion coefficients to the porous media structure and flow properties. Based on numerical simulations in ordered granular porous media, we show that the deformation to which the fluid is subjected increases exponential in time, except for very particular directions of the global flow. This chaotic behavior of deformation is associated to a folding of material lines. We explain it from the interactions between stable and unstable flow manifolds which originate from the beads. Furthermore, using an experimental setup based on the optical matching of the fluid to the solid phase, we decipher the mechanisms generating chaotic streamlines at the pore scale. We propose a general model capable of predicting Lyapunov exponents for a large range of porous media. We show that granular porous media generally leads to stronger chaos than continuous porous media and that it is possible to tune the media properties (in terms of volume fraction and coordination number) to achieve a target mixing rate. More generally, we show how the lamellar description of mixing together with the chaotic properties of porous flow may partly explain the evolution of solute concentrations and gradients, preparing the grounds for reactive model formulations based on the physics of pore-scale mixing.
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