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1. Multiscale modelling of diffusion and enzymatic reaction in porous electrodes in Direct Electron Transfer mode

Author

Cristina Carucci, Didier Lasseux, Sébastien Gounel, Alexander Kuhn, Tatjana Šafarik, Lin Zhang, Sabrina Bichon, Tien Dung Le, Francesca Lorenzutti, Nicolas Mano, Institut de Mécanique et d'Ingénierie (I2M), Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM), Laboratoire Énergies et Mécanique Théorique et Appliquée (LEMTA ), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Institut des Sciences Moléculaires (ISM), Université Montesquieu - Bordeaux 4-Université Sciences et Technologies - Bordeaux 1-École Nationale Supérieure de Chimie et de Physique de Bordeaux (ENSCPB)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS), Centre de Recherche Paul Pascal (CRPP), Université de Bordeaux (UB)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS), ANR-10-LABX-0042,AMADEus,Advanced Materials by Design(2010), ANR-10-IDEX-0003,IDEX BORDEAUX,Initiative d'excellence de l'Université de Bordeaux(2010), ANR-17-CE08-0005,MOMA,Modélisation d'électrodes poreuses pour leur conception optimisée(2017), ANR-16-CE19-0001,BIO3,Electrodes poreuses biocompatibles et biofonctionnelles pour des biopiles enzymatiques miniaturisées(2016), European Project: 8813006(1988), HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM), and Université Montesquieu - Bordeaux 4-Université Sciences et Technologies - Bordeaux 1 (UB)-École Nationale Supérieure de Chimie et de Physique de Bordeaux (ENSCPB)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Work (thermodynamics), Materials science, General Chemical Engineering, Volume averaging method, Thermodynamics, 02 engineering and technology, engineering.material, 010402 general chemistry, 01 natural sciences, Industrial and Manufacturing Engineering, Electron transfer, [CHIM.GENI]Chemical Sciences/Chemical engineering, Coating, Diffusion reaction, Direct Electron Transfer, [SPI.GPROC]Engineering Sciences [physics]/Chemical and Process Engineering, Diffusion (business), Porosity, Bilirubin oxidase, Voltammetry, Bilirubin Oxidase, Applied Mathematics, [SPI.FLUID]Engineering Sciences [physics]/Reactive fluid environment, Porous electrode, General Chemistry, [CHIM.CATA]Chemical Sciences/Catalysis, 021001 nanoscience & nanotechnology, 0104 chemical sciences, [CHIM.THEO]Chemical Sciences/Theoretical and/or physical chemistry, Electrode, engineering, 0210 nano-technology
Abstract

This work is dedicated to a multi-scale modelling of coupled diffusion and reaction in a porous microelectrode operating in the Direct Electron Transfer mode. The pore-scale physico-electrochemical unsteady model is developed considering the oxygen reduction, catalyzed by an enzyme coating the pores of the electrode, coupled to the diffusion of oxygen and mass balance of enzymes. This model is formally upscaled to obtain an original closed unsteady macroscopic model operating at the electrode scale, together with the associated closure providing the effective diffusivity tensor. A validation of this model is carried out from a comparison with the solution of the initial 3D pore-scale governing equations considering the bilirubin oxydase as the catalyst. The relevance and accuracy of the macroscale model are proved allowing a considerable simulation speedup. It is further employed to successfully predict experimental voltammetry results obtained with porous gold electrodes functionnalized with a bilirubin oxidase mutant (BOD S362C). This model represents a breakthrough by providing an operational simple way of understanding and further optimizing porous electrodes functioning in DET mode.

Published
2022
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2. Solvation force and adsorption isotherm of a fluid mixture in nanopores of complex geometry based on fundamental measure theory

Author

Q D Ha, I Panfilov, Tien Dung Le, C Moyne, Laboratoire Énergies et Mécanique Théorique et Appliquée (LEMTA ), and Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Adsorption Isotherm, Materials science, Discretization, [SPI.FLUID]Engineering Sciences [physics]/Reactive fluid environment, Solvation, Thermodynamics, 02 engineering and technology, 021001 nanoscience & nanotechnology, Condensed Matter Physics, 01 natural sciences, Ellipsoid, Solvation Force, Nanopore, Complex geometry, Adsorption, Gas Mixture Adsorption, 0103 physical sciences, General Materials Science, Density functional theory, Deformation (engineering), Physics::Chemical Physics, 010306 general physics, 0210 nano-technology, Density Functional Theory, Fundamental Measure Theory
Abstract

International audience; A novel method based on the Fundamental Measure Theory (FMT) is developed to calculate the solvation force and adsorption isotherm of a Lennard-Jones fluid mixture in complex geometries. Fast Fourier Transform and 3D-voxel discretization are used for accurately computing the confined fluid densities in a closed pore of arbitrary geometry. Given the fluid densities, the solvation force distribution at the solid surface can be calculated using a new formulation from either mechanical or thermodynamic approach. Understanding the solvation force behavior, which depends on many factors such as pore geometry, confined density distribution, molecule size, is very important to analyze the pore deformation from a poromechanical point of view. Special attention in the numerical simulations is given to the adsorption problem of CH 4 and CO 2 gas mixture in ellipsoidal pore.

Published
2021
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3. A modelling study to evaluate the mechanisms of root iron uptake by Noccaea caerulescens

Author

Thibault Sterckeman, Tien Dung Le, Christian Moyne, Laboratoire Sols et Environnement (LSE), Université de Lorraine (UL)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE), Laboratoire Énergies et Mécanique Théorique et Appliquée (LEMTA ), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), and ANR-11-CESA-0008,SIM TRACES,Simulateur numérique de l'accumulation par les cultures des éléments traces minéraux contaminants du sol(2011)

Subjects
0106 biological sciences, [SDV.SA]Life Sciences [q-bio]/Agricultural sciences, Soil Science, Plant Science, 01 natural sciences, Modelling, Metal, Alkali soil, chemistry.chemical_compound, Iron hydroxide dissolution, medicine, [SDV.BV]Life Sciences [q-bio]/Vegetal Biology, Dissolution, Ironnutrition, Rhizosphere, Ligand, Chemistry, Ironchelate, Root exudation, 04 agricultural and veterinary sciences, Environmental chemistry, visual_art, Soil water, 040103 agronomy & agriculture, visual_art.visual_art_medium, 0401 agriculture, forestry, and fisheries, Ferric, Hydroxide, 010606 plant biology & botany, medicine.drug
Abstract

International audience; Purpose: This work is a quantitative evaluation of current hypotheses of iron acquisition by higher plants. Methods: The outputs of three root uptake models were compared to the iron uptake of a single plant species grown in three different soils. Iron hydroxide dissolution kinetics by organic ligands were formalised in the reactive transport modelling, together with ligand and ferric complex degradation. A global sensitivity analysis was performed. Results: Iron uptake by Noccaea caerulescens does not appear to differ from that of other higher plants. The solubility of soil iron hydroxides alone cannot satisfy the plant iron requirements, even in an acidified rhizosphere. For this reason, all plants growing in aerated soils should suffer extreme iron deficiencies, not only those in alkaline soils. The dissociation rate of an Fe3+ complex (for instance with an aminopolycarboxilate ligand) in solution near the root cell membrane is not sufficient to provide the metal needed by the plant. In contrast, the adsorption of the ferric complex on the root cell membrane, before Fe3+ reduction and the absorption of Fe2+ appears to be a very efficient process. This is also the case for iron acquisition through the root secretion of an iron organic ligand dissolving soil iron hydroxides, the rate of ligand excretion being a key parameter. Conclusions: Mechanistic modelling supports the hypothesis of the reduction at the root cell membrane of a ferric complex resulting of iron hydroxide dissolution by a soil- or root-borne organic ligand.

Published
2021
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4. Limits of Classical Homogenization Procedure for Coupled Diffusion-Heterogeneous Reaction Processes in Porous Media

Author

Olivier Millet, Mohamed Khaled Bourbatache, Tien Dung Le, Christian Moyne, Laboratoire de Génie Civil et Génie Mécanique (LGCGM), Université de Rennes 1 (UR1), Université de Rennes (UNIV-RENNES)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Université de Rennes (UNIV-RENNES)-Institut National des Sciences Appliquées (INSA), Laboratoire Énergies et Mécanique Théorique et Appliquée (LEMTA ), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Laboratoire des Sciences de l'Ingénieur pour l'Environnement - UMR 7356 (LaSIE), Université de La Rochelle (ULR)-Centre National de la Recherche Scientifique (CNRS), NEEDS program, Université de Rennes (UR)-Institut National des Sciences Appliquées - Rennes (INSA Rennes), Institut National des Sciences Appliquées (INSA)-Institut National des Sciences Appliquées (INSA), and La Rochelle Université (ULR)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Homogenization, Materials science, General Chemical Engineering, 010102 general mathematics, 0211 other engineering and technologies, Diffusion-reaction, 02 engineering and technology, Mechanics, 01 natural sciences, Homogenization (chemistry), Catalysis, Reaction rate, Damköhler numbers, Damkohler number, [SPI]Engineering Sciences [physics], Orders of magnitude (time), Mass transfer, 0101 mathematics, Chemical equilibrium, Diffusion (business), Porous medium, 021101 geological & geomatics engineering
Abstract

International audience; Upscaling of coupled diffusion-heterogeneous reaction problem in porous media is developed for different orders of magnitude of the Damkohler number. At the pore-scale, the mass transfer of two dilute species is ruled by a diffusion mechanism characterized by different diffusion coefficients. The pore-scale model is completed by reversible linear reaction occurring at the solid-fluid interface. Classical homogenization technique is then used to upscale the pore-scale model under three different scenarios: slow, moderate and high reaction rates corresponding to three orders of magnitude of the Damkohler number. The results show that the macroscopic model obtained for a slow reaction rate predicts accurately the coupled diffusion-reaction process at the macroscale in the range of small Damkohler number. However, the classical homogenization procedure for moderate and high reaction rates fails to capture correctly the complex physics at short time when chemical equilibrium is not reached. In these cases, upscaled models impose strictly the chemical equilibrium at the first order due to the dominance of reaction over diffusion. Numerical simulations highlight the error of the macroscopic models compared to direct numerical simulations.

Published
2021
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5. Upscaled Model for Multicomponent Gas Transport in Porous Media Incorporating Slip Effect

Author

Christian Moyne, Gaël Maranzana, Tien Dung Le, Laboratoire d'Energétique et de Mécanique Théorique Appliquée (LEMTA ), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), and Laboratoire Énergies et Mécanique Théorique et Appliquée (LEMTA )

Subjects
Materials science, Hydrogeology, Molar mass, Hydrogen, General Chemical Engineering, 0208 environmental biotechnology, chemistry.chemical_element, 02 engineering and technology, Mechanics, Slip (materials science), 010502 geochemistry & geophysics, Electrochemistry, 01 natural sciences, Homogenization (chemistry), Catalysis, [SPI.MECA.MEFL]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Fluids mechanics [physics.class-ph], Physics::Geophysics, 020801 environmental engineering, [CHIM.THEO]Chemical Sciences/Theoretical and/or physical chemistry, [SPI]Engineering Sciences [physics], chemistry, Porous medium, Gas compressor, ComputingMilieux_MISCELLANEOUS, 0105 earth and related environmental sciences
Abstract

A two-scale model for multicomponent gas transport in porous media is developed. At the pore-scale, Stefan–Maxwell formulation is used to describe the multi-gas transport together with the mass and momentum conservation equations, whereas on the solid/fluid interface, a slip velocity according to the Kramers–Kistemaker condition is taken into account. The pore-scale equations are then upscaled using a formal homogenization procedure. The macroscopic model shows that the total average velocity is modified by a slip velocity which depends mostly on the diffusive flux of the light gas in the mixture. Application to hydrogen transport in electrochemical devices such as fuel cell, electrochemical hydrogen purifier/compressor, in which considerable contrast of molar mass between the gases occurs, is carried out. As a result, the gas slip effect can modify considerably the gas transport behavior within the porous medium of the devices. This is an important result because the gas transport mechanisms play a crucial role in their efficiency.

Published
2020
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6. Digitization and image-based structure-properties relationship evaluation of a porous gold micro-electrode

Author

Cristina Carucci, Gerard L. Vignoles, Didier Lasseux, Alexander Kuhn, Tien Dung Le, Guillaume Couégnat, Nicolas Mano, Anthony Baux, Laboratoire des Composites Thermostructuraux (LCTS), Centre National de la Recherche Scientifique (CNRS)-Snecma-SAFRAN group-Université de Bordeaux (UB)-Institut de Chimie du CNRS (INC)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Institut de Mécanique et d'Ingénierie de Bordeaux (I2M), Institut National de la Recherche Agronomique (INRA)-Université de Bordeaux (UB)-École Nationale Supérieure d'Arts et Métiers (ENSAM), Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS), Institut des Sciences Moléculaires (ISM), Université Montesquieu - Bordeaux 4-Université Sciences et Technologies - Bordeaux 1-École Nationale Supérieure de Chimie et de Physique de Bordeaux (ENSCPB)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS), Centre de recherches Paul Pascal (CRPP), Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS), Laboratoire Énergies et Mécanique Théorique et Appliquée (LEMTA ), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), ANR-17-CE08-0005,MOMA,Modélisation d'électrodes poreuses pour leur conception optimisée(2017), Université de Bordeaux (UB)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut de Chimie du CNRS (INC)-Snecma-SAFRAN group-Centre National de la Recherche Scientifique (CNRS), Institut de Mécanique et d'Ingénierie (I2M), Université de Bordeaux (UB)-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS)-Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement (INRAE)-Arts et Métiers Sciences et Technologies, HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM), and Université Montesquieu - Bordeaux 4-Université Sciences et Technologies - Bordeaux 1 (UB)-École Nationale Supérieure de Chimie et de Physique de Bordeaux (ENSCPB)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS)

Subjects
Materials science, Stacking, 02 engineering and technology, 010402 general chemistry, 7. Clean energy, 01 natural sciences, Specific surface area, lcsh:TA401-492, General Materials Science, porous material, Composite material, Porosity, defects, Mechanical Engineering, pore network, [CHIM.MATE]Chemical Sciences/Material chemistry, FIB-SEM, 021001 nanoscience & nanotechnology, Crystallographic defect, 0104 chemical sciences, Sphere packing, Mechanics of Materials, digitization, Electrode, SPHERES, lcsh:Materials of engineering and construction. Mechanics of materials, 0210 nano-technology, Porous medium
Abstract

International audience; The advantage of using porous materials for biofuel cells and biosensors is their very large internal surface area (where electron exchange takes place) compared to the overall material volume, yielding much larger current densities than on a bare solid electrode of the same size. However, limitations occur because of mass transfer resistance through the pores. We describe here a bottom-up approach to optimize the design of such materials, through the analysis and modeling of their porous structure. Electrodes prepared by replicating stacked Langmuir-Blodgett films, with 1-µm diameter interconnected spherical pores, were studied. Since pore window dimensions are around 100 nm, Focused Ion Beam-Scanning Electron Microscopy (FIB-SEM) has been performed to obtain a 3D reconstruction of the porous medium. Then, a determination of the geometrical characteristics has been achieved through image analysis. The structure of the sphere packing, the shape and size of the connections between spheres, the distances between spheres, the sphere diameters and the specific surface area have been analyzed. The porous medium is close to a face-centered cubic arrangement of spherical pores, but several deviations from ideality are present: missing pores (point defects), stacking errors (dislocations), and incomplete connection between spheres (only 50% of the ideal sphere connections are present). The consequence of such defects on transport are studied through image-based simulations of mass diffusion in the actual porous medium and in similar ideal media.

Published
2020
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7. Current and optimal dimensions predictions for a porous micro‐electrode

Author

Tien Dung Le, Didier Lasseux, Laboratoire Énergies et Mécanique Théorique et Appliquée (LEMTA ), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Transferts, écoulements, fluides, énergétique (TREFLE), Université Sciences et Technologies - Bordeaux 1-École Nationale Supérieure de Chimie et de Physique de Bordeaux (ENSCPB)-Centre National de la Recherche Scientifique (CNRS), and ANR-17-CE08-0005,MOMA,Modélisation d'électrodes poreuses pour leur conception optimisée(2017)

Subjects
[PHYS]Physics [physics], Work (thermodynamics), Materials science, [SPI.FLUID]Engineering Sciences [physics]/Reactive fluid environment, Porous electrode, 02 engineering and technology, Mechanics, Radius, 010402 general chemistry, 021001 nanoscience & nanotechnology, 01 natural sciences, Catalysis, 0104 chemical sciences, [SPI]Engineering Sciences [physics], Volume (thermodynamics), Reagent, Electrode, Upscaling, Electrochemistry, [CHIM]Chemical Sciences, Optimisation, Diffusion (business), Current (fluid), 0210 nano-technology, Porosity
Abstract

International audience; The expression of the current delivered by a cylindrical porous micro-electrode operating a single heterogeneous reaction and mass diffusion of the reagent is an analytically derived in this work from a complete solution of the diffusion/reaction macroscopic problem. This solution is valid regardless of the aspect (thickness to inner radius) ratio. It encompasses the hybrid solution reported elsewhere, valid only when this ratio remains small compared to unity, and, consequently, the case of a planar electrode as well. The asymptotic form of the solution in this latter case is also provided. The complete solution is used to predict the optimal thickness of the electrode and its optimal inner radius (i.e. the supporting wire radius) corresponding to the best compromise between a minimum electrode volume and a maximum current per unit volume. This work hence provides a complete optimization procedure that can be used as predictive tools for the design of porous electrodes.

Published
2020
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8. Optimal Thickness of a Porous Micro-Electrode Operating a Single Redox Reaction

Author

Tien Dung Le, Stéphane Reculusa, Gerard L. Vignoles, Didier Lasseux, Alexander Kuhn, Nicolas Mano, Lin Zhang, Institut de Mécanique et d'Ingénierie de Bordeaux (I2M), Institut National de la Recherche Agronomique (INRA)-Université de Bordeaux (UB)-École Nationale Supérieure d'Arts et Métiers (ENSAM), Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS), Institut des Sciences Moléculaires (ISM), Université Montesquieu - Bordeaux 4-Université Sciences et Technologies - Bordeaux 1-École Nationale Supérieure de Chimie et de Physique de Bordeaux (ENSCPB)-Centre National de la Recherche Scientifique (CNRS), Centre de recherches Paul Pascal (CRPP), Centre National de la Recherche Scientifique (CNRS), Laboratoire des Composites Thermostructuraux (LCTS), Université Sciences et Technologies - Bordeaux 1-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Snecma-SAFRAN group-Centre National de la Recherche Scientifique (CNRS), Centre de Recherche Paul Pascal (CRPP), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), Institut de Mécanique et d'Ingénierie, CNRS, UMR5295, ANR: ANR-10-LABX-0042-AMADEUS,ANR-10-LABX-0042-AMADEUS, ANR-10-IDEX-0003-02/10-IDEX-0003,IDEX BORDEAUX,IdEx Bordeaux(2010), ANR-17-CE08-0005,MOMA,Modélisation d'électrodes poreuses pour leur conception optimisée(2017), ANR-16-CE19-0001,BIO3,Electrodes poreuses biocompatibles et biofonctionnelles pour des biopiles enzymatiques miniaturisées(2016), HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-Arts et Métiers Sciences et Technologies, HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS), Université Montesquieu - Bordeaux 4-Université Sciences et Technologies - Bordeaux 1 (UB)-École Nationale Supérieure de Chimie et de Physique de Bordeaux (ENSCPB)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS), Université de Bordeaux (UB)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS), Université de Bordeaux (UB)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut de Chimie du CNRS (INC)-Snecma-SAFRAN group-Centre National de la Recherche Scientifique (CNRS), ANR-10-LABX-0042,AMADEus,Advanced Materials by Design(2010), ANR-10-IDEX-0003,IDEX BORDEAUX,Initiative d'excellence de l'Université de Bordeaux(2010), Université Montesquieu - Bordeaux 4-Université Sciences et Technologies - Bordeaux 1-École Nationale Supérieure de Chimie et de Physique de Bordeaux (ENSCPB)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS), Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS), Centre National de la Recherche Scientifique (CNRS)-Snecma-SAFRAN group-Université de Bordeaux (UB)-Institut de Chimie du CNRS (INC)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), and Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Sciences et Technologies - Bordeaux 1-Snecma-SAFRAN group

Subjects
Work (thermodynamics), Materials science, Thermodynamics, 02 engineering and technology, 010402 general chemistry, 01 natural sciences, Catalysis, Diffusion layer, volume averaging method, redox chemistry, Electrochemistry, computational chemistry, optimization, porous electrodes, redox chemistry, volume averaging method, Porosity, Voltammetry, [SPI.FLUID]Engineering Sciences [physics]/Reactive fluid environment, Radius, porous electrodes, [CHIM.CATA]Chemical Sciences/Catalysis, 021001 nanoscience & nanotechnology, computational chemistry, 0104 chemical sciences, Volume (thermodynamics), Electrode, 0210 nano-technology, [CHIM.OTHE]Chemical Sciences/Other, Current density, optimization
Abstract

International audience; This article reports on a procedure to predict the optimal thickness of cylindrical porous electrodes operating a single redox reaction. This is obtained from a macroscopic model for the coupled diffusion-reaction process that is first validated with voltammetry experiments of the H2O2/H2O reductionreaction carried out with a series of porous electrodes elaborated in this work. An analytical solution to this model is developed in the steady regime and for electrodes featuring a thickness to mean radius ratio small enough compared to unity. An analytical expression of the optimal electrode thickness is derived corresponding to the crossover value of two asymptotic regimes characterizing the dependence of the volume currentdensity produced by the electrode upon its thickness. The predictive tool of the optimal thickness is general, regardless of the porous microstructure. The case of the electrodes used in the reported experiments illustrates that the optimal thickness is not intrinsic to the microsctructure characterized by the size of the representative volume, its specific area and effective diffusion coefficient. It also depends on the operating conditions reflected in the kinetic number, Ki, and the thickness of the diffusion layer surrounding the electrode. The dependence of the optimal thickness on these two parameters is quite significant in a range of very small values of Ki but remains quasi constant beyond a threshold value.

Published
2019
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9. Upscaled model for diffusion and serial reduction pathways in porous electrodes

Author

Gerard L. Vignoles, Tien Dung Le, Nicolas Mano, Didier Lasseux, Alexander Kuhn, Lin Zhang, Institut de Mécanique et d'Ingénierie de Bordeaux (I2M), Institut National de la Recherche Agronomique (INRA)-Université de Bordeaux (UB)-École Nationale Supérieure d'Arts et Métiers (ENSAM), Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS), Institut des Sciences Moléculaires (ISM), Université Montesquieu - Bordeaux 4-Université Sciences et Technologies - Bordeaux 1-École Nationale Supérieure de Chimie et de Physique de Bordeaux (ENSCPB)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS), Centre de Recherche Paul Pascal (CRPP), Université de Bordeaux (UB)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS), Laboratoire des Composites Thermostructuraux (LCTS), Centre National de la Recherche Scientifique (CNRS)-Snecma-SAFRAN group-Université de Bordeaux (UB)-Institut de Chimie du CNRS (INC)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA), ANR-17-CE08-0005,MOMA,Modélisation d'électrodes poreuses pour leur conception optimisée(2017), Université Montesquieu - Bordeaux 4-Université Sciences et Technologies - Bordeaux 1-École Nationale Supérieure de Chimie et de Physique de Bordeaux (ENSCPB)-Centre National de la Recherche Scientifique (CNRS), Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), Université Sciences et Technologies - Bordeaux 1-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Snecma-SAFRAN group-Centre National de la Recherche Scientifique (CNRS), HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-Arts et Métiers Sciences et Technologies, HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS), Université Montesquieu - Bordeaux 4-Université Sciences et Technologies - Bordeaux 1 (UB)-École Nationale Supérieure de Chimie et de Physique de Bordeaux (ENSCPB)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS), and Université de Bordeaux (UB)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut de Chimie du CNRS (INC)-Snecma-SAFRAN group-Centre National de la Recherche Scientifique (CNRS)

Subjects
Work (thermodynamics), Speedup, Scale (ratio), Chemistry, General Chemical Engineering, Volume averaging method, [SPI.FLUID]Engineering Sciences [physics]/Reactive fluid environment, 02 engineering and technology, Mechanics, 010402 general chemistry, 021001 nanoscience & nanotechnology, 01 natural sciences, 0104 chemical sciences, Analytical Chemistry, Oxygen reduction reaction, Reduction (complexity), Porous micro-electrode, Electrode, Upscaling, Electrochemistry, Diffusion (business), 0210 nano-technology, Porosity, Voltammetry, Diffusion reaction macroscopic model
Abstract

International audience; Multiscale modelling of coupled diffusion and serial reduction reactions in porous micro-electrodes is developed in this work. The governing coupled equations at the pore scale in the case of two reduction reactions, as for instance, the serial reaction pathway for oxygen reduction to hydrogen peroxide and subsequently to water, are upscaled to obtain a macroscopic model describing the process in an effective medium at the electrode scale. This new macroscopic model, obtained from the volume averaging technique, is validated through comparisons with results of 3D Direct Numerical Simulations of the pore-scale model. The excellent agreement between the two approaches proves the relevance of the macroscale model which reduces to a 1D problem in the configuration under concern, providing a drastic speedup in the computation of the solution. Numerical results obtained with the macroscopic model are successfully compared to experimental data obtained by voltammetry with porous gold electrodes of different thicknesses operating the serial pathway of oxygen reduction to water. Results highlight the ability of this new macroscopic model to predict the electrode behavior and show that the second reduction reaction of hydrogen peroxide plays an important role in the current production.

Published
2019
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10. Multi-scale modeling of diffusion and electrochemical reactions in porous micro-electrodes

Author

X.P. Nguyen, Nicolas Mano, Alexander Kuhn, Tien Dung Le, Didier Lasseux, Gerard L. Vignoles, Institut de Mécanique et d'Ingénierie de Bordeaux (I2M), Institut National de la Recherche Agronomique (INRA)-Université de Bordeaux (UB)-École Nationale Supérieure d'Arts et Métiers (ENSAM), Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-Arts et Métiers Sciences et Technologies, HESAM Université (HESAM)-HESAM Université (HESAM)-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS), ANR-17-CE08-0005,MOMA,Modélisation d'électrodes poreuses pour leur conception optimisée(2017), École Nationale Supérieure d'Arts et Métiers (ENSAM), HESAM Université (HESAM)-HESAM Université (HESAM)-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB)-Institut National de la Recherche Agronomique (INRA), Laboratoire des Composites Thermostructuraux (LCTS), Université de Bordeaux (UB)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Institut de Chimie du CNRS (INC)-Snecma-SAFRAN group-Centre National de la Recherche Scientifique (CNRS), Centre de Recherche Paul Pascal (CRPP), Université de Bordeaux (UB)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS), Institut des Sciences Moléculaires (ISM), Université Montesquieu - Bordeaux 4-Université Sciences et Technologies - Bordeaux 1-École Nationale Supérieure de Chimie et de Physique de Bordeaux (ENSCPB)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS), ANR-10-IDEX-0003,IDEX BORDEAUX,Initiative d'excellence de l'Université de Bordeaux(2010), Centre National de la Recherche Scientifique (CNRS)-École Nationale Supérieure de Chimie et de Physique de Bordeaux (ENSCPB)-Université Sciences et Technologies - Bordeaux 1-Université Montesquieu - Bordeaux 4-Institut de Chimie du CNRS (INC), HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-Arts et Métiers Sciences et Technologies, HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-HESAM Université - Communauté d'universités et d'établissements Hautes écoles Sorbonne Arts et métiers université (HESAM)-Institut Polytechnique de Bordeaux-Centre National de la Recherche Scientifique (CNRS), Université Montesquieu - Bordeaux 4-Université Sciences et Technologies - Bordeaux 1 (UB)-École Nationale Supérieure de Chimie et de Physique de Bordeaux (ENSCPB)-Institut de Chimie du CNRS (INC)-Centre National de la Recherche Scientifique (CNRS), HESAM Université (HESAM)-HESAM Université (HESAM)-Institut Polytechnique de Bordeaux-Institut National de la Recherche Agronomique (INRA)-Centre National de la Recherche Scientifique (CNRS)-Université de Bordeaux (UB), Centre National de la Recherche Scientifique (CNRS)-Commissariat à l'énergie atomique et aux énergies alternatives (CEA)-Université Sciences et Technologies - Bordeaux 1-Snecma-SAFRAN group, Université de Bordeaux (UB)-Centre National de la Recherche Scientifique (CNRS), Université Montesquieu - Bordeaux 4-Université Sciences et Technologies - Bordeaux 1-École Nationale Supérieure de Chimie et de Physique de Bordeaux (ENSCPB)-Centre National de la Recherche Scientifique (CNRS), ANR-10-IDEX-03-02/10-LABX-0042,AMADEus,Advanced Materials by Design(2010), and ANR-10-IDEX-0003-02/10-IDEX-0003,IDEX BORDEAUX,IdEx Bordeaux(2010)

Subjects
[SDV.BIO]Life Sciences [q-bio]/Biotechnology, Materials science, [SDV]Life Sciences [q-bio], General Chemical Engineering, Volume averaging method, Nanotechnology, 02 engineering and technology, 010402 general chemistry, 01 natural sciences, Industrial and Manufacturing Engineering, [SHS]Humanities and Social Sciences, [SPI.MAT]Engineering Sciences [physics]/Materials, Diffusion, [SPI]Engineering Sciences [physics], [CHIM.GENI]Chemical Sciences/Chemical engineering, Upscaling, [SPI.GPROC]Engineering Sciences [physics]/Chemical and Process Engineering, Diffusion (business), Porosity, Heterogeneous reaction, Voltammetry, Microscale chemistry, Applied Mathematics, [SPI.FLUID]Engineering Sciences [physics]/Reactive fluid environment, Porous electrode, General Chemistry, Mechanics, [CHIM.CATA]Chemical Sciences/Catalysis, 021001 nanoscience & nanotechnology, Fick's laws of diffusion, Amperometry, 0104 chemical sciences, [CHIM.THEO]Chemical Sciences/Theoretical and/or physical chemistry, Electrode, 0210 nano-technology, Porous medium
Abstract

International audience; A multi-scale model of diffusion/reaction at play in a porous electrode is developed and solutions to the physico-electro-chemical coupled problem are provided. This represents a key step to progress in the optimization of new efficient and innovative micro-electro-devices that needs to be addressed from a chemical engineering point of view. The pore-scale model based on Fickian diffusion in the porous medium and Nernstian layer and the electrochemical reaction governed by the Buttler-Volmer equation isupscaled using volume averaging to obtain a macroscopic model that describes the process on an effective equivalent medium. The validity and accuracy of the macroscopic model is successfully checked through the comparison with direct numerical simulations of the initial microscale model for amperometry tests. Predictions obtained from the upscaled model on the current intensity versus the scanning potential during voltammetry reveal to be in very good agreement with experimental results reported in the literature. These results show the capability of the macroscopic model to analyze the behavior of the porous electrode. In particular, it provides an efficient tool to study the dependence of the current intensity on the microstructure of the porous material and on the electrochemical parameters with the perspective of optimizing the electrode efficiency.

Published
2017
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11. Application of a multi-scale form of Terzaghi’s effective stress principle for unsaturated expansive clays to simulate hydro-mechanical behavior during hydration

Author

Marcio A. Murad, Christian Moyne, Julia Mainka, van Duy Tran, Tien Dung Le, Laboratoire Énergies et Mécanique Théorique et Appliquée (LEMTA ), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Laboratorio Nacional de Computação Cientifica [Rio de Janeiro] (LNCC / MCT), and Mainka, Julia

Subjects
lcsh:GE1-350, 021110 strategic, defence & security studies, Chemistry, Capillary action, Effective stress, 0211 other engineering and technologies, Disjoining pressure, Solvation, 02 engineering and technology, Mechanics, [SPI.MECA.SOLID]Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph], Homogenization (chemistry), Microscopic scale, [SPI]Engineering Sciences [physics], medicine, [SPI.MECA.SOLID] Engineering Sciences [physics]/Mechanics [physics.med-ph]/Solid mechanics [physics.class-ph], Geotechnical engineering, Swelling, medicine.symptom, Terzaghi's principle, lcsh:Environmental sciences, ComputingMilieux_MISCELLANEOUS, 021101 geological & geomatics engineering
Abstract

International audience; Our recently developed multi-scale form of Terzaghi’s effective stress principle for unsaturated swelling clays that was rigorously derived by periodic homogenization starting from micro- and nano-mechanical analyses is applied to numerically simulate one-dimensional swelling pressure tests of compacted bentonites during hydration. The total macroscopic stress captures the coupling between disjoining forces at the nanoscopic scale of clay platelets and capillary effects at the microscopic scale of clay aggregates over the entire water content range. The numerical results allow to draw conclusions on the water transfer mechanism between inter- and intra-aggregate pores during hydration and consequently on the evolution of the external swelling pressure resulting from the competition between capillary and disjoining forces. In addition, such application highlights the abilities and the limits of the electrical double-layer theory to compute the disjoining pressure in the nano-pores. For large platelet distances, in the range of osmotic swelling, the nature of the disjoining pressure is electro-chemical and can be computed from Poisson-Boltzmann theory. Conversely, at small distances, in the crystalline swelling, a solvation component has to be added to account for the molecular nature of the solvent. As a first improvement of the nano-scale description the solvent is treated as a hard sphere fluid using Density Functional Theory.

Published
2016
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12. Swelling Pressure in Expansive Porous Media Derived from Nano/Macro Homogenization Including Ion Size Correlation Effects

Author

Marcio A. Murad, Sidarta A. Lima, Tien-Dung Le, Christian Moyne, Laboratoire Énergies et Mécanique Théorique et Appliquée (LEMTA ), Université de Lorraine (UL)-Centre National de la Recherche Scientifique (CNRS), Laboratorio Nacional de Computação Cientifica [Rio de Janeiro] (LNCC / MCT), Vienna University of Technology (TU Wien), Institute for Mechanics of Materials and Structures, Institute for Geotechnical Engineering, Christian Hellmich, Bernhard Pichler, and Dietmar Adam

Subjects
Materials science, Porous media, Thermodynamics, 01 natural sciences, Homogenization (chemistry), [SPI]Engineering Sciences [physics], 0103 physical sciences, Nano, Homogeneity (physics), medicine, Composite material, 010306 general physics, Dynamic pressure, 010304 chemical physics, Statistical mechanics, Nanomechanics, Pore pressure, Condensed Matter::Soft Condensed Matter, Soil pressure, Homogeneity, Density functional theory, Clays, Swelling, medicine.symptom, Porous medium, Expansive soils
Abstract

International audience; In the case of electrically charged porous media as clays, a precise definition of swelling pressure has already been given in our preceding works using the periodic homogenization medium for two scales (nano/macro) (Moyne and Murad, 2002, 2006). The modeling at the nanoscale is based on the Poisson-Boltzmann equation to describe the electrostatics. However, for montmorillonite clays, if for a monovalent compensating cation (eg Na), swelling is always observed. For divalent ions (eg Ca or ions of higher valence), on the contrary, shrinking phenomena can be observed. As the Poisson-Boltzmann equation always predicts swelling, a more precise description of the physics at the nanopore level is needed. Therefore, a pore-scale model is developed within the framework of Statistical Mechanics in conjunction with a thermodynamic approach based on Density Functional Theory.

Published
2013
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