Comment calculer nombre de Wagner Wa distribution courant

Calcule nombre de Wagner Wa = (kappa*R_pol)/L rapport resistance cinétique vs ohmique electrochimie. Wa<<1 primary ohmique; Wa>>1 secondary uniforme. Carl Wagner Allemagne 1901-1977 + 1951. Renault Stellantis Verkor batterie + Air Liquide hydrogen + Solvay applications.

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Nombre de Wagner Wa rapport adimensionnel resistance cinétique vs ohmique electrochimie: Wa = (kappa*R_pol)/L.

Wa<0.1 primary; 1-10 secondary; Wa>10 strong. Tafel 60-120 mV/decade. Histoire: Carl Wagner (Leipzig Allemagne 1901 - Gottingen 1977) MPI Gottingen 1953-1972 + 1951 + Wagner-Schottky + Wagner-Hauffe. Tafel 1905. Newman 1991. Bard 1980.

France recherche: CEA Saclay 16000 + battery + fuel cells + LITEN Grenoble world-leading; CNRS 11000; Mines Paris PSL CES Sophia 2000; IFPEN 1700; EDF R&D 158000; IRSN 1740; ANDRA 660; Synchrotron SOLEIL 500; CEA-LITEN Grenoble 1100 + battery world-leading + fuel cells PEM SOFC + Verkor partnership.

France universites: Sorbonne Paris 55000 LIMSI; PSL 17000 ENS ESPCI Mines + Tarascon + Le Bideau battery + Catherine Faulkner; X Polytechnique 3500 LadHyX; Centrale Supelec 7000 EM2C; INSA Lyon 6000 LMFA + LAGEPP; Toulouse III 35000 IMFT; Aix-Marseille 80000; UGA Grenoble 60000 LITEN + LEPMI + Christophe Coperet; ENSAM 6000; Bordeaux 50000 ICMCB battery + Materials Science; Strasbourg 50000 ICPEES; Universite Picardie Jules Verne Amiens + RS2E Reseau Storage Electrochemical Energy + Jean-Marie Tarascon battery + Christian Masquelier world-leading; College de France Tarascon; ENS Lyon Coperet.

France industrie automotive battery + EV: Stellantis France Velizy 65000 + Sochaux + Mulhouse + Poissy + Hordain + Rennes + Citroen e-C4 + Peugeot e-2008 + Opel Corsa-e BEV + ACC Automotive Cells Company battery joint venture Stellantis Mercedes; Renault Group Boulogne-Billancourt 105000 + Renault ZOE legacy + Megane E-Tech + Kangoo van + R5 E-Tech + Verkor partnership Dunkirk Gigafactory; Verkor Dunkirk 2020 5000 planned + 50 GWh Gigafactory + Renault customer + 2025 production; ACC Automotive Cells Company Stellantis Mercedes-Benz TotalEnergies 1500 + 3 Gigafactories Douvrin France + Kaiserslautern Germany + Termoli Italy; Faurecia Forvia Nanterre 110000; Plastic Omnium 30000; Valeo 113000 + thermal management + battery; Michelin Clermont-Ferrand 132000; Hutchinson 41000; BorgWarner France Tulle 4000.

France industrie fuel cells PEM SOFC + idrogeno: Air Liquide Paris 67000 + green hydrogen + Albi liquid hydrogen + ITER partner LHe; Engie Courbevoie 100000; EDF 158000; McPhy Energy La Motte-Fanjas 100 + green hydrogen electrolyzer + 1 GW factory planned; Symbio Saint-Fons 200 + fuel cells PEM partnership Faurecia Michelin Stellantis + Symbio Forvia hydrogen heavy duty; HRS Champagne-au-Mont-d'Or 100 + hydrogen refueling stations; H2sys Belfort 200 + hydrogen fuel cells; Hyvia Renault Plug Power JV 200; Faurecia Forvia 110000 + hydrogen heavy duty trucks.

France chlor-alkali: Arkema Lavera 21000 + chlor-alkali + Pebax Rilsan; Kemone Berre-l'Etang 1500 + PVC chlor-alkali; Solvay France Tavaux 17000 + chlor-alkali + Solef PVDF; Inovyn Tavaux 600; Vencorex Le Pont-de-Claix 600.

France semiconduttori Cu plating: STMicroelectronics Crolles + Tours + Le Mans + Rousset 6500 + Cu plating BEOL + 300 mm wafer 28/22 nm; Soitec Bernin Isere 2200; X-FAB Corbeil-Essonnes 700; NXP Semiconductors France 1100; Infineon France 200.

France cathodic protection oil&gas: Total Énergies 102000 + raffinerie Donges Gonfreville Lavera Feyzin + cathodic protection offshore; Petroineos Lavera 1500; Esso France 1500; BP France 800; GRTgaz Bois-Colombes 1500 + gasdotti + cathodic; Storengy Bois-Colombes 1500 + gas storage cathodic; EDF 158000 + nuclear cathodic protection condensers.

Formule Wagner

Définition: Wa = (kappa*R_pol)/L.

Histoire

Carl Wagner (Leipzig 1901 - Gottingen 1977) MPI Gottingen 1953-1972 + 1951 + Wagner-Schottky + Wagner-Hauffe. Tafel 1905. Newman Berkeley 1991. Bard UT Austin 1980.

France recherche: CEA Saclay 16000 + LITEN Grenoble battery world-leading; CNRS 11000; Mines Paris PSL 2000; IFPEN 1700; EDF R&D 158000; IRSN 1740; SOLEIL 500; CEA-LITEN Grenoble 1100 battery world-leading + Verkor partnership.

France universites: Sorbonne 55000 LIMSI; PSL 17000 ENS ESPCI Tarascon Le Bideau battery; X 3500 LadHyX; Centrale Supelec 7000; INSA Lyon 6000; Toulouse III 35000 IMFT; Aix-Marseille 80000; UGA Grenoble 60000 LITEN + LEPMI + Coperet; ENSAM 6000; Bordeaux 50000 ICMCB battery; Strasbourg 50000 ICPEES; Picardie Amiens + RS2E Tarascon Masquelier world-leading; College de France Tarascon; ENS Lyon Coperet.

France automotive battery: Stellantis France Velizy 65000 Sochaux Mulhouse Poissy + Citroen e-C4 + Peugeot e-2008 + Opel Corsa-e + ACC battery JV; Renault Group Boulogne 105000 ZOE Megane E-Tech R5 E-Tech + Verkor partnership; Verkor Dunkirk 5000 planned 50 GWh Gigafactory; ACC Stellantis Mercedes TotalEnergies 1500 3 Gigafactories Douvrin Kaiserslautern Termoli; Faurecia 110000; Plastic Omnium 30000; Valeo 113000; Michelin 132000; Hutchinson 41000; BorgWarner Tulle 4000.

France fuel cells hydrogen: Air Liquide 67000 green hydrogen Albi LH2 + ITER LHe; Engie 100000; EDF 158000; McPhy Energy 100 1 GW factory planned; Symbio Saint-Fons 200 Faurecia Michelin Stellantis JV; HRS Champagne-au-Mont-d'Or 100; H2sys Belfort 200; Hyvia Renault Plug Power 200; Faurecia hydrogen 110000.

France chlor-alkali: Arkema Lavera 21000; Kemone Berre 1500; Solvay Tavaux 17000; Inovyn Tavaux 600; Vencorex 600.

France semiconduttori: STMicroelectronics Crolles 6500 Cu plating BEOL; Soitec Bernin 2200; X-FAB Corbeil 700; NXP France 1100; Infineon France 200.

France cathodic protection: Total Énergies 102000 raffinerie Donges Gonfreville Lavera; Petroineos 1500; Esso France 1500; BP France 800; GRTgaz 1500 gasdotti; Storengy 1500; EDF 158000 nuclear.

Tableau valeurs

  • Wa = (kappa*R_pol)/L
  • Wa<0.1 primary
  • 1-10 secondary
  • Wa>10 strong
  • Wagner Allemagne 1901-1977
  • Wagner 1951
  • Tafel 1905
  • Newman Berkeley 1991
  • Bard Austin 1980
  • France CEA-LITEN Grenoble 1100: battery world-leading
  • France RS2E Picardie Tarascon: world-leading
  • France College de France Tarascon
  • France Verkor Dunkirk 5000: 50 GWh
  • France ACC Stellantis Mercedes 1500: 3 Gigafactories
  • France Stellantis 65000: e-C4 e-2008 BEV
  • France Renault 105000: ZOE Megane E-Tech R5
  • France Air Liquide 67000: green hydrogen LHe ITER
  • France Symbio 200: Faurecia Michelin Stellantis JV
  • France McPhy 100: 1 GW electrolyzer
  • France HRS 100: hydrogen refueling
  • France Arkema Lavera 21000: chlor-alkali
  • France Solvay Tavaux 17000
  • France STM Crolles 6500: Cu plating BEOL
  • France Total Énergies 102000: cathodic
  • France GRTgaz 1500: gasdotti cathodic

Exemples numériques

Exemple 1 - Chlor-alkali. Wa=3. France: Arkema Lavera + Solvay Tavaux + Kemone Berre.

Exemple 2 - Li-ion. Wa=100. France: Verkor Dunkirk 50 GWh + ACC Douvrin + Stellantis e-C4 + Renault Megane E-Tech R5.

Exemple 3 - PEM fuel cell. Wa=0.5. France: Symbio + McPhy + HRS + Hyvia Plug Power + Air Liquide.

Exemple 4 - Cu plating. Wa=0.5. France: STM Crolles 6500 + Soitec Bernin + X-FAB Corbeil.

Exemple 5 - Cathodic protection. Wa=5000. France: Total Énergies + GRTgaz + Storengy + EDF nuclear.

Limites

  1. Linearized Butler-Volmer.
  2. Tertiary mass transfer.
  3. Convection Levich.
  4. Multiple reactions.
  5. Geometry corner.
  6. Ionic Nernst-Planck.
  7. Bubble void.
  8. Membrane Nafion.
  9. Time-dependent EIS.
  10. Température.

Erreurs courantes

Wa vs Damkohler.

Primary vs secondary.

R_pol Tafel.

Throwing power.

Kappa ionique.

Applications

  1. Chlor-alkali France: Arkema Lavera 21000 + Kemone Berre 1500 + Solvay Tavaux 17000 + Inovyn + Vencorex.
  2. Li-ion battery Gigafactory France: Verkor Dunkirk 5000 50 GWh + ACC Stellantis Mercedes TotalEnergies Douvrin Kaiserslautern Termoli + Stellantis e-C4 e-2008 + Renault ZOE Megane E-Tech R5 + Faurecia Forvia + Valeo + Plastic Omnium.
  3. Fuel cells PEM hydrogen France: Air Liquide 67000 + Symbio 200 Faurecia Michelin Stellantis JV + McPhy 100 1 GW + HRS + H2sys + Hyvia Renault Plug Power + Faurecia heavy duty trucks.
  4. EV charging hydrogen station France: HRS Champagne-au-Mont-d'Or + Hyvia + Air Liquide hydrogen stations.
  5. Cathodic protection France: Total Énergies 102000 raffinerie offshore + Petroineos + Esso + BP France + GRTgaz 1500 gasdotti + Storengy 1500 gas storage + EDF nuclear.
  6. Semiconduttori Cu plating France: STM Crolles 6500 BEOL + Soitec Bernin 2200 + X-FAB Corbeil 700 + NXP France 1100.
  7. Battery storage grid France: EDF + Engie + Total Énergies + Veolia + Suez.
  8. Hydrogen Air Liquide ITER LHe partner.
  9. Universites: Sorbonne LIMSI + ESPCI Tarascon + Centrale Supelec + UGA LITEN LEPMI + Bordeaux ICMCB + Picardie RS2E Tarascon Masquelier world-leading + College de France Tarascon.
  10. Solar storage France: EDF Renouvelables + TotalEnergies + ACC + Verkor.

Mis à jour en juillet 2026

Questions fréquentes

Qu est-ce que le nombre de Wagner?

Wa = (kappa*R_pol)/L rapport adimensionnel resistance cinétique vs ohmique electrochimie. Wa<0.1 primary; 1-10 secondary; Wa>10 strong. Carl Wagner Allemagne 1901-1977 + 1951 + Wagner-Schottky + Wagner-Hauffe. France: CEA-LITEN Grenoble world-leading battery + Verkor Dunkirk 50 GWh + ACC Stellantis Mercedes + Air Liquide hydrogen + Stellantis Renault.

Comment calculer Wagner?

Procedure: (1) Wa = (kappa*R_pol)/L; (2) kappa S/m; (3) R_pol Ohm*m^2 Tafel; (4) L m; (5) régime. Chlor-alkali: Wa=3. Li-ion: Wa=100. France: ESPCI Tarascon + UGA LITEN LEPMI + Picardie RS2E Tarascon Masquelier + College de France.

Qu est-ce que primary vs secondary?

Primary Wa->0 ohmique géométrique; Secondary Wa intermediaire Butler-Volmer cinétique uniforme; Tertiary Wa large mass transfer Nernst. France: Arkema Lavera chlor-alkali + Verkor Dunkirk + Symbio Faurecia Michelin Stellantis.

Quels régimes classifie Wa?

Wa<0.1 primary; 0.1-1 mixed; 1-10 secondary; Wa>10 strong. France: Solvay chlor-alkali + Verkor Dunkirk + Symbio PEM + Total Énergies cathodic protection + STM Crolles Cu plating BEOL.

Qui etait Carl Wagner?

Carl Wagner (Leipzig Allemagne 1901 - Gottingen 1977) Universitat Leipzig PhD 1924 + Hamburg 1928-1933 + Jena 1933-1945 + Gottingen 1953-1972 emeritus + Max-Planck-Institut Physikalische Chemie Gottingen director 1953-1972 + Wagner Award ECS; 1951 Plating Surface Finish 38:997 Wagner number eponyme + Wagner-Schottky defects + Wagner-Hauffe rule + 1924 'Thermodynamics of Solids' classique.

Qu est-ce que Tafel kinetics?

Tafel kinetics Julius Tafel Switzerland 1862-1918 + 1905 paper Z Phys Chem 50:641 + eta = a + b*log(i) + Tafel slope 60-120 mV/decade + Butler-Volmer linearized + R_pol = b/(2.303*i). France: Picardie RS2E Tarascon world-leading + ESPCI Tarascon + UGA LEPMI.

Quelles applications de Wagner?

Applications: chlor-alkali Arkema Lavera 21000 + Solvay Tavaux 17000 + Kemone Berre + Vencorex; Li-ion battery Verkor Dunkirk 50 GWh + ACC Stellantis Mercedes TotalEnergies Douvrin Kaiserslautern Termoli + Renault ZOE Megane E-Tech R5 + Stellantis e-C4 e-2008; fuel cells PEM hydrogen Symbio 200 Faurecia Michelin Stellantis + McPhy 1 GW + HRS + Air Liquide 67000 + Hyvia Renault Plug Power; cathodic protection Total Énergies 102000 + GRTgaz 1500 gasdotti + Storengy + EDF nuclear; Cu plating BEOL STM Crolles 6500 + Soitec Bernin 2200.

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