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The deformation of fluid elements plays a central role in solute by steepening concentration gradients, increasing interfacial area for diffusive mass transfer, and enhancing encounter rates between solutes and reactive surfaces (e.g. Borgman et al. 2023, Izumoto et al. 2023, Aquino et al. 2023, Le Borgne and Heyman 2025). In three-dimensional porous media, fluid deformation at the pore scale arises from repeated stretching and folding of fluid elements, leading to chaotic mixing (Heyman et al., 2020; Souzy et al., 2020; Lester et al., 2025). While this induces an exponential elongation of fluid elements, confinement in the pore space and interaction with diffusion after the mixing time may limit the impact of pore scale chaotic stretching on Darcy-scale mixing and reaction.
Here we present experiments of mixing and reaction in bead packs (Fig. 1), linking 3D pore scale imaging of conservative and reactive solute concentrations (Sanquer et al. 2024) to Darcy scale measurement of reaction rates in mixing fronts (Izumoto et al. 2025). We show that the effect of pore scale chaotic mixing persists beyond the mixing time and leads to a distinct scaling of the Darcy scale reaction kinetics with time and Peclet number, diverging from the macrodispersion prediction. We propose a mechanism that captures these observations and links pore-scale chaotic mixing to Darcy scale reaction kinetics. Based on this theoretical framework, we discuss the range of temporal and spatial scales, as well as Peclet and Damkohler numbers, over which pore scale chaotic mixing should influence Darcy scale reaction kinetics.
| References | Le Borgne, T. and J. Heyman (2025) Fluid Deformation and Mixing in Porous Media as Drivers for Chemical and Biological Processes, Annual Review of Fluid Mechanics, 58. Izumoto, S., Rousseau, G., Le Borgne, T., & Heyman, J. (2025). Effective reaction kinetics of steady mixing fronts in porous media. Journal of Fluid Mechanics, 1013, A4. Lester, D. R., Heyman, J., Méheust, Y., & Le Borgne, T. (2025). A unified theory of pore-scale chaotic advection. Journal of Fluid Mechanics, 1017, A13. Sanquer, H., Heyman, J., Hanna, K., & Le Borgne, T. (2024). Microscale chaotic mixing as a driver for chemical reactions in porous media. Environmental Science & Technology, 58(20), 8899-8908. Izumoto, S., Heyman, J., Huisman, J. A., De Vriendt, K., Soulaine, C., Gomez, F., ... & Le Borgne, T. (2023). Enhanced mixing and reaction in converging flows: Theory and pore‐scale imaging. Water Resources Research, 59(8), e2023WR034749. Borgman, O., Turuban, R., Géraud, B., Le Borgne, T., & Méheust, Y. (2023). Solute front shear and coalescence control concentration gradient dynamics in porous micromodel. Geophysical Research Letters, 50(5), e2022GL101407. Aquino, T., Le Borgne, T., & Heyman, J. (2023). Fluid–solid reaction in porous media as a chaotic restart process. Physical Review Letters, 130(26), 264001. Heyman, J., Lester, D. R., Turuban, R., Méheust, Y., & Le Borgne, T. (2020). Stretching and folding sustain microscale chemical gradients in porous media. Proceedings of the National Academy of Sciences, 117(24), 13359-13365. Souzy, M., Lhuissier, H., Méheust, Y., Le Borgne, T., & Metzger, B. (2020). Velocity distributions, dispersion and stretching in three-dimensional porous media. Journal of Fluid Mechanics, 891, A16. |
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| Country | France |
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