Como calcular numero de Wagner Wa distribución corriente

Calcula numero de Wagner Wa = (kappa*R_pol)/L ratio resistencia cinética vs ohmica electroquimica. Wa<<1 primary ohmica; Wa>>1 secondary uniforme. Carl Wagner Alemania 1901-1977 + 1951. SEAT VW Stellantis batería + Almirall + Solvay aplicaciones.

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Numero de Wagner Wa ratio adimensional resistencia cinética vs ohmica electroquimica: Wa = (kappa*R_pol)/L.

Wa<0.1 primary; 1-10 secondary; Wa>10 strong. Tafel slope 60-120 mV/decade. Historia: Carl Wagner (Leipzig Alemania 1901 - Gottingen 1977) MPI Gottingen 1953-1972 + 1951 Plating Surface Finish 38:997 + Wagner-Schottky + Wagner-Hauffe. Tafel 1905. Newman Berkeley 1991. Bard UT Austin 1980.

España investigación: CSIC Madrid 11000 + ICMM IDAEA; UPM Madrid 40000 ETSII + Antonio Crespo + Manuel Martin Bartolome catalysis; UPC Barcelona 30000 LEAM + ETSEIB; UPV Valencia 35000 IIE + ITQ Avelino Corma zeolite world-leading; Universidad Sevilla 70000 ESI; Universidad Granada UGR 56000; Universidad Autonoma Madrid UAM 1968 35000 + ICMM CSIC partnership; CIEMAT Madrid 1500 + battery + fuel cells; CENER Pamplona 200; Tecnalia 1500; IK4 Research Alliance Bilbao 1500; ICN2 Catalan Institute Nanoscience BCN 200.

España industria automotive battery + EV: SEAT Volkswagen Martorell BCN 14000 + Cupra Born BEV + VW ID hatchback + battery cell production planned; Stellantis España Vigo Madrid Zaragoza Valladolid 12000 + Citroen e-C4 + Peugeot e-2008 + Opel Corsa-e BEV; Renault España Valladolid 5000 + Renault ZOE legacy + Megane E-Tech + Kangoo van; Ford Almussafes Valencia 8000; BasqueVolt Vitoria 2022 100 planned + solid state battery Gigafactory; Inobat Iberica + Mercedes-Benz partnership; Iberdrola Bilbao 40000 + battery storage grid + EV charging; Endesa Madrid 9000; Naturgy Madrid 7000; Acciona 38000; Antolin 18000 + EV interior; Gestamp 38000; CIE Automotive 25000.

España fuel cells PEM SOFC + idrogeno: H2B2 Sevilla 200 + green hydrogen + electrolysis; Iberdrola Puertollano 100 MW green hydrogen; Naturgy + Repsol green hydrogen; Acciona Energía 38000; Tecnicas Reunidas 9000; Sener Bilbao 2400; Indra Madrid 57000.

España chlor-alkali: Solvay Iberica Tarragona Rosignano 600 + chlor-alkali + Nafion membranes; Ercros Tarragona 1908 1500 + chlor-alkali + chlorine derivatives; Industrias Quimicas del Valles IQV Tarragona 600; Aragonesas BASF 600.

España semiconduttori Cu plating BEOL: STMicroelectronics España 200; Soitec Iberia Madrid 100; NXP Semiconductors España 200; Infineon España 200.

España cathodic protection oil&gas: Repsol Madrid 25000 + raffinerie 5 sites + cathodic protection; Cepsa 11000; BP España 1000; Enagas Madrid 1972 1500 + gasdotti + cathodic protection; Iberdrola 40000; Sener 2400 + cathodic offshore.

Formula Wagner

Definición: Wa = (kappa*R_pol)/L.

Historia

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

España investigación: CSIC 11000; UPM 40000 ETSII Crespo; UPC 30000; UPV 35000 ITQ Corma; Sevilla 70000; Granada 56000; Carlos III 22000; UAM 35000; CIEMAT 1500; Tecnalia 1500; ICN2 200.

España automotive: SEAT VW Martorell 14000 Cupra Born + VW ID; Stellantis Vigo Madrid Zaragoza 12000; Renault Valladolid 5000 ZOE Megane E-Tech; Ford Almussafes 8000; BasqueVolt Vitoria 100 solid state; Iberdrola 40000 battery storage; Endesa 9000; Antolin 18000; Gestamp 38000.

España fuel cells: H2B2 Sevilla 200 green hydrogen; Iberdrola Puertollano 100 MW; Naturgy Repsol; Acciona 38000; Tecnicas Reunidas 9000; Sener 2400; Indra 57000.

España chlor-alkali: Solvay Tarragona 600; Ercros 1500; IQV 600.

España semiconduttori: STM España 200; Soitec 100; NXP 200; Infineon 200.

España cathodic protection: Repsol 25000; Cepsa 11000; Enagas Madrid 1500 gasdotti; Iberdrola 40000.

Tabla valores

  • Wa = (kappa*R_pol)/L
  • Wa<0.1 primary
  • 1-10 secondary
  • Wa>10 strong
  • Wagner Alemania 1901-1977
  • Wagner 1951
  • Tafel 1905
  • Newman Berkeley 1991
  • Bard Austin 1980
  • España CSIC 11000
  • España UPM ETSII 40000
  • España SEAT VW Martorell 14000
  • España Renault ZOE Megane 5000
  • España BasqueVolt Vitoria 100: solid state
  • España Iberdrola 40000: battery storage
  • España H2B2 Sevilla 200: hydrogen
  • España Iberdrola Puertollano 100 MW
  • España Solvay Tarragona 600: chlor-alkali
  • España Ercros 1500
  • España Repsol 25000: cathodic

Ejemplos numericos

Ejemplo 1 - Chlor-alkali. Wa=3. España: Solvay Tarragona + Ercros + IQV.

Ejemplo 2 - Li-ion. Wa=100. España: SEAT VW Martorell + BasqueVolt Vitoria + Stellantis.

Ejemplo 3 - PEM fuel cell. Wa=0.5. España: H2B2 Sevilla + Iberdrola Puertollano.

Ejemplo 4 - Cu plating. Wa=0.5. España: STM España + Soitec + NXP.

Ejemplo 5 - Cathodic protection. Wa=5000. España: Repsol + Enagas gasdotti + Iberdrola.

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. Temperature.

Errores comunes

Wa vs Damkohler.

Primary vs secondary.

R_pol Tafel.

Throwing power.

Kappa ionica.

Aplicaciones

  1. Chlor-alkali España: Solvay Tarragona + Ercros 1500 + IQV.
  2. Li-ion battery España: SEAT VW Martorell 14000 Cupra Born + Stellantis Vigo Madrid + Renault ZOE Megane E-Tech + Ford Almussafes + BasqueVolt Vitoria 100 solid state.
  3. Fuel cells PEM hydrogen España: H2B2 Sevilla 200 + Iberdrola Puertollano 100 MW + Naturgy + Repsol + Acciona Energía 38000.
  4. Battery storage grid España: Iberdrola 40000 + Endesa + Naturgy + Acciona Energía.
  5. EV charging España: Iberdrola + Endesa X + Repsol Move + Wallbox Cataluna.
  6. Cathodic protection oil&gas España: Repsol 25000 + Cepsa + Enagas 1500 gasdotti + Sener Bilbao.
  7. Semiconduttori Cu plating España: STM España + Soitec + NXP + Infineon.
  8. Solar storage España: Iberdrola Andasol + Sener Gemasolar + Abengoa + 3SUN.
  9. Investigación universitaria: UPM ETSII Crespo + UPV ITQ Corma + UPC LEAM + Sevilla ESI + UAM ICMM partnership.
  10. Hydrogen Iberdrola Puertollano 100 MW world-largest electrolyzer green hydrogen.

Actualizado a julio de 2026

Preguntas frecuentes

Que es el numero de Wagner?

Wa = (kappa*R_pol)/L ratio resistencia cinética vs ohmica electroquimica. Wa<0.1 primary; 1-10 secondary; Wa>10 strong. Carl Wagner Alemania 1901-1977 + 1951 + Wagner-Schottky + Wagner-Hauffe. España: CSIC 11000 + SEAT VW Martorell 14000 + BasqueVolt Vitoria + Iberdrola Puertollano 100 MW hydrogen + Solvay Tarragona.

Como se calcula Wagner?

Procedimiento: (1) Wa = (kappa*R_pol)/L; (2) kappa S/m; (3) R_pol Ohm*m^2 Tafel; (4) L m; (5) regime. Chlor-alkali: Wa=3. Li-ion: Wa=100. España: UPM ETSII + UPC LEAM + UPV ITQ Corma.

Que es primary vs secondary?

Primary Wa->0 ohmica geométrica; Secondary Wa intermedio Butler-Volmer cinética uniforme; Tertiary Wa grande mass transfer Nernst. España: Solvay chlor-alkali + SEAT VW Martorell battery + Iberdrola hydrogen.

Que regimenes clasifica Wa?

Wa<0.1 primary; 0.1-1 mixed; 1-10 secondary; Wa>10 strong. España: Solvay chlor-alkali + SEAT VW Cupra Born battery + H2B2 PEM + Repsol cathodic protection.

Quien fue Carl Wagner?

Carl Wagner (Leipzig Alemania 1901 - Gottingen 1977) Universitat Leipzig PhD 1924 + Hamburg 1928-1933 + Gottingen 1953-1972 + MPI Physikalische Chemie Gottingen director; 1951 Plating Surface Finish 38:997 Wagner number eponym + Wagner-Schottky defects + Wagner-Hauffe rule + Wagner Award ECS.

Que es 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). España: ITQ Corma + UPM Crespo + UAM ICMM.

Que aplicaciones tiene Wagner?

Aplicaciones: chlor-alkali Solvay Tarragona + Ercros + IQV; Li-ion SEAT VW Martorell Cupra Born + Stellantis + Renault ZOE Megane E-Tech + BasqueVolt Vitoria solid state; fuel cells H2B2 Sevilla + Iberdrola Puertollano 100 MW hydrogen world-largest; cathodic protection Repsol 25000 + Cepsa + Enagas gasdotti + Iberdrola; battery storage Iberdrola + Endesa + Naturgy + Acciona; EV charging Iberdrola + Repsol Move + Wallbox Cataluna.

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