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      Solute transport and reaction in porous electrodes at high Schmidt numbers

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          Abstract

          We present lattice Boltzmann pore-scale numerical simulations of solute transport and reaction in porous electrodes at a high Schmidt number, $Sc=10^{2}$ . The three-dimensional geometry of real materials is reconstructed via X-ray computed tomography. We apply a volume-averaging upscaling procedure to characterise the microstructural terms contributing to the homogenised description of the macroscopic advection–reaction–dispersion equation. We firstly focus our analysis on its asymptotic solution, while varying the rate of reaction. The results confirm the presence of two working states of the electrodes: a reaction-limited regime, governed by advective transport, and a mass-transfer-limited regime, where dispersive mechanisms play a pivotal role. For all materials, these regimes depend on a single parameter, the product of the Damköhler number and a microstructural aspect ratio. The macroscopic dispersion is determined by the spatial correlation between solute concentration and flow velocity at the pore scale. This mechanism sustains reaction in the mass-transfer-limited regime due to the spatial rearrangement of the solute transport from low-velocity to high-velocity pores. We then compare the results of pre-asymptotic transport with a macroscopic model based on effective dispersion parameters. Interestingly, the model correctly represents the transport at short characteristic times. At longer times, high reaction rates mitigate the mechanisms of heterogeneous solute transport. In the mass-transfer-limited regime, the significant yet homogeneous dispersion can thus be modelled via an effective dispersion. Finally, we formulate guidelines for the design of porous electrodes based on the microstructural aspect ratio.

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          Most cited references10

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          Discrete lattice effects on the forcing term in the lattice Boltzmann method

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            Pore-scale simulation of fluid flow and solute dispersion in three-dimensional porous media

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              Transport in ordered and disordered porous media II: Generalized volume averaging

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                Author and article information

                Contributors
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                Journal
                Journal of Fluid Mechanics
                J. Fluid Mech.
                Cambridge University Press (CUP)
                0022-1120
                1469-7645
                August 10 2020
                May 29 2020
                August 10 2020
                : 896
                Article
                10.1017/jfm.2020.344
                299f9b20-f95c-4bb9-9194-f6bc4fc546f1
                © 2020

                http://creativecommons.org/licenses/by-nc-sa/4.0/

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