Your Name Introduction Electrochemical Systems Electrochemical systems are devices or processes in which an ionic conductor mediates the interconversion of chemical and electrical energy The reactions by which this interconversion of energy occurs involve the transfer of charge electrons at ID: 1046871
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1. Modeling in Electrochemical EngineeringYour Name
2. Introduction: Electrochemical SystemsElectrochemical systems are devices or processes in which an ionic conductor mediates the inter-conversion of chemical and electrical energyThe reactions by which this inter-conversion of energy occurs involve the transfer of charge (electrons) at the interface between an electronic conductor (the electrode) and an ionic conductor (the electrolyte)
3. Introduction: Redox ReactionsIndividual electrode reactions are symbolized as reduction-oxidation (redox) processes with electrons as one of the reactants:Ox = oxidized speciesRed = reduced speciese- = electronn = electron stoichiometry coefficient.
4. Introduction: Thermochemical and Electrochemical Processes
5. Introduction: Energy Producing and Energy Consuming Electrochemical Processes
6. Introduction: Spontaneous Processes and Processes that Require Energy Input
7. Introduction: Electrocatalysis
8. Introduction: Anodic and Cathodic Reactions
9. Introduction: Transport and Electrochemical Reactions TransportDiffusion, convection, migration, which is an electrophoretic effect on ions. The mobility and concentration of ions yields the mass transfer and Ohmic resistances in the electrolyteElectrochemical reactionElectrode kinetics for an electron charge transfer step as rate determining step (RDS) yields potential-dependent reaction rate. The overpotential is a measure of the activation energy (Arrhenius equation -> Butler-Volmer equation)
10. Introduction: TransportTransportFlux = diff. + conv. + migrationCurrent densityElectroneutralitysum of charges = 0Perfectly mixedprimary and secondaryConcentrationDiffusivityFlow velocityChargeMobilityIonic potentialFaraday’s constant
11. Introduction: Conservation of Species and ChargeConservation of speciesn-1 species, n:th through chargeconservationConservation of chargeNet charge is not accumulated, produced or consumed in the bulk electrolyteFor primary and secondary casesReaction rate
12. Modeling of Electrochemical CellsPrimary current distributionAccounts only for Ohmic effects in the simulation of current density distribution and performance of the cell:Neglects the influence of concentration variations in the electrolyteNeglects the influence of electrode kinetics on the performance of the cell, i.e. activation overpotential is neglected (losses due to activation energy)Secondary current distributionAccounts only for Ohmic effects and the effect of electrode kinetics in the simulation of current density distribution and performance of the cell:Neglects the influence of concentration variations in the electrolyteTertiary current distributionAccounts for Ohmic effects, effects of electrode kinetics, and the effects of concentration variations on the performance of a cell
13. Modeling of Electrochemical CellsNon-porous electrodesHeterogeneous reactionsTypically used for electrolysis, metal winning, and electrodepositionPorous electrodesReactions treated as homogeneous reaction in models although they are heterogeneous in realityTypically used for batteries, fuel cells, and in some cases also for electrolysisElectrolytesDiluted and supporting electrolytesConcentrated electrolytes”Free” electrolytes with forced and free convection”Immobilized” electrolytes through the use of porous matrixes, negligible free convection, rarely forced convectionSolid electrolytes, no convection
14. Assumptions:Perfectly mixed electrolyteNegligible activation overpotentialNegligible ohmic losses in the anode structureA First Example: Primary Current DistributionAnode: Wire electrodeCathodes: Flat-plateelectrodesCathodes: Flat-plateelectrodesElectrolyte
15. Subdomain:Charge continuityBoundaryElectrode potentialsat electrode surfacesInsulation elsewhereA First Example: Subdomain and Boundary SettingsAnode: Cell voltage = 1.3 VE0 = 1.2 VTotal cell (in this case ohmic) polarization = 100 mVCathodes: Electrode potential = 0 VE0 = 0 V(negligible overpotential)Cathodes: 0 VElectrolyte:Ionic potential
16. A First Example: Some DefinitionsActivation and concentration overpotential = 0Select the cathode as reference pointElectronic potentialCell voltageIonic potentialAt anode, indexAt cathode, index
17. A First Example: Some ResultsCurrent density distribution at tha anode surfaceHighly active catalystInactive catalystPotential distribution in the electrolyte
18. A Second Example: Secondary Current DistributionActivation overpotential taken into accountCharge transfer current at the electrode surfacesNew boundary conditionsExchange current densityFaraday’s constantGas constantCharge transfer coefficient
19. Comparison: Primary and Secondary Current DistributionsCurrent density distribution at the anode surfaceLower current density with equal cell voltage (1.3V) compared to primary casePolarization curvesEffect ofActivationoverpotentialSolid line = PrimaryDashed line = Secondary
20. Comparison: Primary and Secondary Current Density Distribution, 0.1 A Total CurrentDimensionless current density disribution, primary caseDimensionless current density disribution, secondary caseIndependent of total currentDependentof total current
21. Some Results: Mesh ConvergencePolarization curves for three mesh refinements (four mesh cases)Total current, seven mesh cases (up to 799186 elements)
22. Primary and Secondary Current Distributions: Summary and RemarksPrimary case gives less uniform current distribution than the secondary case: The addition of charge transfer resistance through the activation overpotential forces the current to become more uniformSecondary current density distribution is not independent of total current:The charge transfer resistance decreases with increasing current density (overpotential increases proportional to the logarithm of current density for high current density)Home work:The geometry is symmetric in this example. Use this geometry and treat the wire electrode as a bipolar electrode placed in between an anode and a cathode
23. Tertiary Current Density DistributionUse the secondary current distribution case as starting pointAdd the flow equations, in this case from single phase laminar flow Navier-StokesSolve only for the flowAdd equations for mass transport, in this chase the Nernst-Planck equationsIntroduce the concentration dependence on the reaction kineticsSolve the fully coupled material and charge balances using the already solved flow field
24. Results: Concentration and Current Density DistributionMain direction of the flowStagnation in the flowresults in lower concentration
25. Concluding RemarksUse a primary current distribution as the starting pointIntroduce reaction kinetics to obtain secondary current distributionIntroduce a decoupled flow fieldIntroduce material balances and concentration dependency in the reaction kinetics to obtain a tertiary current distributionSeveral options: Supporting electrolyte where the conductivity is independent of concentration All charged species are balanced and are combined in the electroneutrality conditionAll charged species are balanced but they are combined using Poisson’s equation