Transcription
Corrosion ModuleUser’s Guide
Corrosion Module User’s Guide 1998–2018 COMSOLProtected by patents listed on www.comsol.com/patents, and U.S. Patents 7,519,518; 7,596,474;7,623,991; 8,457,932; 8,954,302; 9,098,106; 9,146,652; 9,323,503; 9,372,673; and 9,454,625. Patentspending.This Documentation and the Programs described herein are furnished under the COMSOL Software LicenseAgreement (www.comsol.com/comsol-license-agreement) and may be used or copied only under the termsof the license agreement.COMSOL, the COMSOL logo, COMSOL Multiphysics, COMSOL Desktop, COMSOL Server, andLiveLink are either registered trademarks or trademarks of COMSOL AB. All other trademarks are theproperty of their respective owners, and COMSOL AB and its subsidiaries and products are not affiliatedwith, endorsed by, sponsored by, or supported by those trademark owners. For a list of such trademarkowners, see www.comsol.com/trademarks.Version: COMSOL 5.4Contact InformationVisit the Contact COMSOL page at www.comsol.com/contact to submit generalinquiries, contact Technical Support, or search for an address and phone number. You canalso visit the Worldwide Sales Offices page at www.comsol.com/contact/offices foraddress and contact information.If you need to contact Support, an online request form is located at the COMSOL Accesspage at www.comsol.com/support/case. Other useful links include: Support Center: www.comsol.com/support Product Download: www.comsol.com/product-download Product Updates: www.comsol.com/support/updates COMSOL Blog: www.comsol.com/blogs Discussion Forum: www.comsol.com/community Events: www.comsol.com/events COMSOL Video Gallery: www.comsol.com/video Support Knowledge Base: www.comsol.com/support/knowledgebasePart number: CM023001
C o n t e n t sChapter 1: IntroductionAbout the Corrosion ModuleWhat Can the Corrosion Module Do?16. . . . . . . . . . . . . . 16Corrosion Module Physics Interface Guide . . . . . . . . . . . . . 17Common Physics Interface and Feature Settings and Nodes . . . . . . 20Where Do I Access the Documentation and Application Libraries? . . . . 21Overview of the User’s Guide25Chapter 2: Modeling with ElectrochemistryIntroduction to Electrochemistry Modeling28What is Electrochemistry? . . . . . . . . . . . . . . . . . . . 28Electrochemical Applications . . . . . . . . . . . . . . . . . . 29Fundamentals of Electrochemistry Modeling . . . . . . . . . . . . 29Current Distribution Cases and Choosing the Right Interface to Model anElectrochemical Cell . . . . . . . . . . . . . . . . . . . . 31Understanding the Different Approximations for Conservation of Charge inElectrolytes . . . . . . . . . . . . . . . . . . . . . . . 32Modeling Electrochemical Reactions . . . . . . . . . . . . . . . 36Double Layer Capacitance . . . . . . . . . . . . . . . . . . . 43Porous Electrodes . . . . . . . . . . . . . . . . . . . . . . 44Boundary Conditions for Running and Controlling Electrochemical Cells. 45Modeling Cyclic Voltammetry . . . . . . . . . . . . . . . . . . 46Common Simplifications when Modeling Electrochemical Cells . . . . . 46Before You Start Building Your Model. . . . . . . . . . . . . . . 48CONTENTS 3
Meshing Advice . . . . . . . . . . . . . . . . . . . . . . . 50Solving Electrochemical Models . . . . . . . . . . . . . . . . . 50Postprocessing Your Solution . . . . . . . . . . . . . . . . . . 55Chapter 3: Electrochemistry InterfacesShared Physics Features in the Electrochemistry Interfaces58Domain, Boundary, Pair, Edge, and Point Nodes for the ElectrochemistryInterfaces . . . . . . . . . . . . . . . . . . . . . . . . 58Electrode. . . . . . . . . . . . . . . . . . . . . . . . . . 60Electrode Current Source . . . . . . . . . . . . . . . . . . . 60Electrolyte Current Source . . . . . . . . . . . . . . . . . . . 60Porous Electrode Reaction . . . . . . . . . . . . . . . . . . . 61Porous Matrix Double Layer Capacitance . . . . . . . . . . . . . 61Insulation. . . . . . . . . . . . . . . . . . . . . . . . . . 62Symmetry . . . . . . . . . . . . . . . . . . . . . . . . . 62Electrode Surface. . . . . . . . . . . . . . . . . . . . . . 62Electrode Reaction . . . . . . . . . . . . . . . . . . . . . . 65Double Layer Capacitance . . . . . . . . . . . . . . . . . . . 68Internal Electrode Surface . . . . . . . . . . . . . . . . . . . 69Thin Electrode Surface. . . . . . . . . . . . . . . . . . . . 70Electrolyte Potential . . . . . . . . . . . . . . . . . . . . . 70Electrolyte Current . . . . . . . . . . . . . . . . . . . . . . 71Electrolyte Current Density. . . . . . . . . . . . . . . . . . 71Thin Electrode Layer . . . . . . . . . . . . . . . . . . . . . 71Electrode-Electrolyte Boundary Interface. . . . . . . . . . . . . 72Electric Ground . . . . . . . . . . . . . . . . . . . . . . . 73Electric Potential . . . . . . . . . . . . . . . . . . . . . . . 73Electrode Current Density . . . . . . . . . . . . . . . . . . . 73Electrode Current . . . . . . . . . . . . . . . . . . . . . . 73Electrode Power . . . . . . . . . . . . . . . . . . . . . . . 74CONTENTS 4
Harmonic Perturbation . . . . . . . . . . . . . . . . . . . . 74Electrode Potential . . . . . . . . . . . . . . . . . . . . . . 75External Short . . . . . . . . . . . . . . . . . . . . . . . . 75Initial Values for Dissolving-Depositing Species . . . . . . . . . . . 76Non-Faradaic Reactions . . . . . . . . . . . . . . . . . . . . 76Reference Electrode . . . . . . . . . . . . . . . . . . . . . 76Electric Reference Potential. . . . . . . . . . . . . . . . . . . 76Circuit Terminal . . . . . . . . . . . . . . . . . . . . . . . 77The Primary and Secondary Current Distribution Interfaces78The Primary Current Distribution and Secondary Current DistributionInterfaces . . . . . . . . . . . . . . . . . . . . . . . . 78Electrolyte . . . . . . . . . . . . . . . . . . . . . . . . . 81Initial Values. . . . . . . . . . . . . . . . . . . . . . . . 81Porous Electrode. . . . . . . . . . . . . . . . . . . . . . . 82Periodic Condition . . . . . . . . . . . . . . . . . . . . . . 83Infinite Electrolyte . . . . . . . . . . . . . . . . . . . . . . 83Thin Electrolyte Layer . . . . . . . . . . . . . . . . . . . . . 84Edge Electrode. . . . . . . . . . . . . . . . . . . . . . . 84Electrode Line Current Source . . . . . . . . . . . . . . . . . 86Electrolyte Line Current Source . . . . . . . . . . . . . . . . . 86Electrode Symmetry Axis Current Source . . . . . . . . . . . . . 86Electrolyte Symmetry Axis Current Source . . . . . . . . . . . . . 87Electrode Point Current Source . . . . . . . . . . . . . . . . . 87Electrolyte Point Current Source. . . . . . . . . . . . . . . . 87Sacrificial Edge Anode . . . . . . . . . . . . . . . . . . . . . 87Wiring Edges . . . . . . . . . . . . . . . . . . . . . . . . 88The Current Distribution, Boundary Elements Interface90The Current Distribution, Boundary Elements Interface . . . . . . . . 90Edge Features in 3D for the Current Distribution, Boundary ElementsInterface. . . . . . . . . . . . . . . . . . . . . . . . . 92CONTENTS 5
The Current Distribution, Shell Interface93Feature Nodes in the Current Distribution, Shell Interface . . . . . . . 93The Tertiary Current Distribution, Nernst-Planck Interface94The Tertiary Current Distribution, Nernst-Planck Interface . . . . . . 94Electrolyte . . . . . . . . . . . . . . . . . . . . . . . . . 98Porous Electrode. . . . . . . . . . . . . . . . . . . . . . . 99Separator. . . . . . . . . . . . . . . . . . . . . . . . . 99Reactions. . . . . . . . . . . . . . . . . . . . . . . . .100Initial Values. . . . . . . . . . . . . . . . . . . . . . .100Ion Exchange Membrane . . . . . . . . . . . . . . . . . . .101Ion Exchange Membrane Boundary . . . . . . . . . . . . . . .101Thin Electrolyte Layer . . . . . . . . . . . . . . . . . . . .102The Electrode, Shell Interface103Boundary, Edge, Point, and Pair Nodes for the Electrode, Shell Interface .104Electrode. . . . . . . . . . . . . . . . . . . . . . . . .105Initial Values. . . . . . . . . . . . . . . . . . . . . . .106Corroding Electrode . . . . . . . . . . . . . . . . . . . .106External Current Density . . . . . . . . . . . . . . . . . .107Current Source . . . . . . . . . . . . . . . . . . . . . .107Normal Current Density . . . . . . . . . . . . . . . . . . .107Electric Insulation . . . . . . . . . . . . . . . . . . . . .108Boundary Current Source . . . . . . . . . . . . . . . . . .108Ground . . . . . . . . . . . . . . . . . . . . . . . . .108Electric Potential . . . . . . . . . . . . . . . . . . . . . .108The Electroanalysis Interface110Domain, Boundary, and Pair Nodes for the Electroanalysis Interface . .111Transport Properties . . . . . . . . . . . . . . . . . . . .113Initial Values. . . . . . . . . . . . . . . . . . . . . . .114Electrode Surface in the Electroanalysis Interface. . . . . . . . . .115CONTENTS 6
Electrode Reaction . . . . . . . . . . . . . . . . . . . . .117Theory for the Current Distribution Interfaces119The Nernst-Planck Equations . . . . . . . . . . . . . . . . .119Domain Equations for Primary and Secondary Current Distributions . .120Electrochemical Reactions and the Difference Between a Primary and aSecondary Current Distribution . . . . . . . . . . . . . . .121Domain Equations for Tertiary Current Distributions Using the Nernst-PlanckEquations and Electroneutrality . . . . . . . . . . . . . . .123Mass Fluxes and Sources Due to Electrochemical Reactions . . . . .125Stochiometric Coefficients for Double Layer Capacitive Charging . . .126Film Resistance . . . . . . . . . . . . . . . . . . . . . .127Electrode Kinetics Expressions . . . . . . . . . . . . . . . .127Theory for Specific Current Distribution Feature Nodes. . . . . . .129Theory for Electrochemical Heat Sources138Joule Heating Due to Charge Transport . . . . . . . . . . . . .139Heating Due to Electrochemical Reactions . . . . . . . . . . . .139Heating Due to Heat of Mixing . . . . . . . . . . . . . . . .140Theory for the Electrode, Shell Interface141Governing Equations . . . . . . . . . . . . . . . . . . . .141Coupling to Other Physics Interfaces . . . . . . . . . . . . . .141Theory for the Electroanalysis Interface143Electroanalytical Methods . . . . . . . . . . . . . . . . . .143Supporting Electrolyte . . . . . . . . . . . . . . . . . . . .144Domain Equations for the Electroanalysis Interface . . . . . . . . .145Electrodes in the Electroanalysis Interface . . . . . . . . . . . .146The Electroanalytical Butler–Volmer Equation . . . . . . . . . . .148Counter Electrodes and Overall Charge Balance . . . . . . . . . .149CONTENTS 7
Electrode Potentials and Reference Electrodes150Reference Electrodes . . . . . . . . . . . . . . . . . . . .150Boundary Conditions Using Reference Electrode Potentials. . . . .151Nodes for Handling Electrode Potentials and Reference Electrodes. . .151Chapter 4: Corrosion, Deformed Geometry InterfacesAbout the Corrosion Interfaces154Modeling Deformation of an Electrode Surface . . . . . . . . . .154Tangential Velocities at the Intersection Between a Depositing and aNoncorroding Boundary . . . . . . . . . . . . . . . . .155Chapter 5: Chemical Species Transport InterfacesThe Transport of Diluted Species Interface160The Transport of Diluted Species in Porous Media Interface . . . . .164Domain, Boundary, and Pair Nodes for the Transport of Diluted SpeciesInterface. . . . . . . . . . . . . . . . . . . . . . . .165Transport Properties . . . . . . . . . . . . . . . . . . . .167Turbulent Mixing . . . . . . . . . . . . . . . . . . . . . .169Initial Values. . . . . . . . . . . . . . . . . . . . . . .170Mass-Based Concentrations. . . . . . . . . . . . . . . . . .170Reactions. . . . . . . . . . . . . . . . . . . . . . . . .170No Flux . . . . . . . . . . . . . . . . . . . . . . . . .172Inflow . . . . . . . . . . . . . . . . . . . . . . . . . .172Outflow . . . . . . . . . . . . . . . . . . . . . . . . .173Concentration . . . . . . . . . . . . . . . . . . . . . . .173Flux . . . . . . . . . . . . . . . . . . . . . . . . . . .173Symmetry . . . . . . . . . . . . . . . . . . . . . . . .174CONTENTS 8
Flux Discontinuity . . . . . . . . . . . . . . . . . . . . .174Partition Condition . . . . . . . . . . . . . . . . . . . . .175Periodic Condition . . . . . . . . . . . . . . . . . . . . .176Line Mass Source . . . . . . . . . . . . . . . . . . . . . .176Point Mass Source . . . . . . . . . . . . . . . . . . . . .177Open Boundary . . . . . . . . . . . . . . . . . . . . . .178Thin Diffusion Barrier . . . . . . . . . . . . . . . . . . . .178Thin Impermeable Barrier . . . . . . . . . . . . . . . . . .178Equilibrium Reaction . . . . . . . . . . . . . . . . . . . .179Surface Reactions. . . . . . . . . . . . . . . . . . . . .180Surface Equilibrium Reaction . . . . . . . . . . . . . . . . .180Fast Irreversible Surface Reaction . . . . . . . . . . . . . . .181Porous Electrode Coupling . . . . . . . . . . . . . . . . . .181Reaction Coefficients . . . . . . . . . . . . . . . . . . . .182Electrode Surface Coupling . . . . . . . . . . . . . . . . . .182Porous Media Transport Properties. . . . . . . . . . . . . . .183Adsorption . . . . . . . . . . . . . . . . . . . . . . . .185Partially Saturated Porous Media . . . . . . . . . . . . . . . .186Volatilization . . . . . . . . . . . . . . . . . . . . . . .188Reactive Pellet Bed . . . . . . . . . . . . . . . . . . . . .189Reactions. . . . . . . . . . . . . . . . . . . . . . . . .192Species Source. . . . . . . . . . . . . . . . . . . . . . .193Hygroscopic Swelling . . . . . . . . . . . . . . . . . . . .194Fracture . . . . . . . . . . . . . . . . . . . . . . . . .195The Transport of Diluted Species in Fractures Interface196Boundary, Edge, Point, and Pair Nodes for the Transport of DilutedSpecies in Fractures Interface . . . . . . . . . . . . . . . .198Adsorption . . . . . . . . . . . . . . . . . . . . . . . .199Concentration . . . . . . . . . . . . . . . . . . . . . . .200Flux . . . . . . . . . . . . . . . . . . . . . . . . . . .200Fracture . . . . . . . . . . . . . . . . . . . . . . . . .200Inflow . . . . . . . . . . . . . . . . . . . . . . . . . .201No Flux . . . . . . . . . . . . . . . . . . . . . . . . .202Outflow . . . . . . . . . . . . . . . . . . . . . . . . .202Reactions. . . . . . . . . . . . . . . . . . . . . . . . .202Species Source. . . . . . . . . . . . . . . . . . . . . . .203CONTENTS 9
The Chemistry Interface204Feature Nodes Available for the Chemistry Interface . . . . . . . .207Reaction . . . . . . . . . . . . . . . . . . . . . . . . .207Species. . . . . . . . . . . . . . . . . . . . . . . . .211Reversible Reaction Group . . . . . . . . . . . . . . . . . .213Equilibrium Reaction Group. . . . . . . . . . . . . . . . . .214Species Group . . . . . . . . . . . . . . . . . . . . . . .216Reaction Thermodynamics . . . . . . . . . . . . . . . . . .216Species Activity . . . . . . . . . . . . . . . . . . . . . .216Species Thermodynamics. . . . . . . . . . . . . . . . . . .216The Nernst-Planck-Poisson Equations Interface218The Electrophoretic Transport Interface220Common Settings for the Species nodes in the Electrophoretic. . . . . . . . . . . . . . . . . . .223Diffusion and Migration Settings . . . . . . . . . . . . . . . .Transport Interface225Domain, Boundary, and Pair Nodes for the Electrophoretic TransportInterface. . . . . . . . . . . . . . . . . . . . . . . .Solvent. . . . . . . . . . . . . . . . . . . . . . . . .Porous Matrix Properties10 C O N T E N T S226227. . . . . . . . . . . . . . . . . .227Fully Dissociated Species . . . . . . . . . . . . . . . . . . .227Uncharged Species . . . . . . . . . . . . . . . . . . . . .227Weak Acid . . . . . . . . . . . . . . . . . . . . . . . .228Weak Base . . . . . . . . . . . . . . . . . . . . . . . .228Ampholyte . . . . . . . . . . . . . . . . . . . . . . . .228Protein. . . . . . . . . . . . . . . . . . . . . . . . .229Current Source . . . . . . . . . . . . . . . . . . . . . .229Initial Potential. . . . . . . . . . . . . . . . . . . . . . .229Current . . . . . . . . . . . . . . . . . . . . . . . . .229Current Density . . . . . . . . . . . . . . . . . . . . . .229Insulation . . . . . . . . . . . . . . . . . . . . . . . . .230Potential . . . . . . . . . . . . . . . . . . . . . . . . .230Species Source. . . . . . . . . . . . . . . . . . . . . . .230Initial Concentration . . . . . . . . . . . . . . . . . . . .231Concentration . . . . . . . . . . . . . . . . . . . . . . .231No Flux . . . . . . . . . . . . . . . . . . . . . . . . .231Flux . . . . . . . . . . . . . . . . . . . . . . . . . . .231
Inflow . . . . . . . . . . . . . . . . . . . . . . . . . .232Outflow . . . . . . . . . . . . . . . . . . . . . . . . .232The Surface Reactions Interface233Boundary, Edge, Point, and Pair Nodes for the Surface ReactionsInterface. . . . . . . . . . . . . . . . . . . . . . . .234Surface Properties . . . . . . . . . . . . . . . . . . . . .235Initial Values236. . . . . . . . . . . . . . . . . . . . . . .Reactions. . . . . . . . . . . . . . . . . . . . . . . . .236Surface Concentration . . . . . . . . . . . . . . . . . . . .237Theory for the Transport of Diluted Species Interface238Mass Balance Equation . . . . . . . . . . . . . . . . . . . .239Equilibrium Reaction Theory . . . . . . . . . . . . . . . . .240Convective Term Formulation. . . . . . . . . . . . . . . . .242Solving a Diffusion Equation Only. . . . . . . . . . . . . . .Mass Sources for Species Transport. . . . . . . . . . . . . .242243Adding Transport Through Migration . . . . . . . . . . . . . .244Supporting Electrolytes . . . . . . . . . . . . . . . . . . .246Crosswind Diffusion . . . . . . . . . . . . . . . . . . . .247Danckwerts Inflow Boundary Condition . . . . . . . . . . . . .248Mass Balance Equation for Transport of Diluted Species in PorousMedia . . . . . . . . . . . . . . . . . . . . . . . . .248Convection in Porous Media . . . . . . . . . . . . . . . . .250Diffusion in Porous Media . . . . . . . . . . . . . . . . . .252Dispersion . . . . . . . . . . . . . . . . . . . . . . . .253Adsorption . . . . . . . . . . . . . . . . . . . . . . . .254Reactions. . . . . . . . . . . . . . . . . . . . . . . . .256Mass Transport in Fractures . . . . . . . . . . . . . . . . .256References . . . . . . . . . . . . . . . . . . . . . . . .257Theory for the Electrophoretic Transport Interface259Theory for the Surface Reactions Interface265Governing Equations for the Surface Concentrations . . . . . . . .265Governing Equations for the Bulk Concentrations . . . . . . . . .266ODE Formulations for Surface Concentrations . . . . . . . . . .268Surface Reaction Equations on Deforming Geometries . . . . . . .269CONTENTS 11
Reference for the Surface Reactions Interface . . . . . . . . . . .270Theory for the Coupling of Mass Transport toElectrochemical Reactions271Molar Sources and Sinks . . . . . . . . . . . . . . . . . . .271Mass Sources and Sinks . . . . . . . . . . . . . . . . . . .272Chapter 6: Fluid Flow InterfacesThe Brinkman Equations Interface274Domain, Boundary, Point, and Pair Nodes for the BrinkmanEquations Interface . . . . . . . . . . . . . . . . . . . .276Fluid and Matrix Properties . . . . . . . . . . . . . . . . . .277Forchheimer Drag . . . . . . . . . . . . . . . . . . . . .278Mass Source. . . . . . . . . . . . . . . . . . . . . . .278Volume Force . . . . . . . . . . . . . . . . . . . . . . .279Initial Values. . . . . . . . . . . . . . . . . . . . . . .279Fluid Properties . . . . . . . . . . . . . . . . . . . . . .279The Darcy’s Law Interface281Domain, Boundary, Edge, Point, and Pair Nodes for the Darcy’s12 C O N T E N T SLaw Interface . . . . . . . . . . . . . . . . . . . . . .282Fluid and Matrix Properties . . . . . . . . . . . . . . . . . .284Mass Source. . . . . . . . . . . . . . . . . . . . . . .285Initial Values. . . . . . . . . . . . . . . . . . . . . . .285Porous Electrode Coupling . . . . . . . . . . . . . . . . .285Electrode Surface Coupling . . . . . . . . . . . . . . . . . .286Pressure . . . . . . . . . . . . . . . . . . . . . . . . .286Mass Flux. . . . . . . . . . . . . . . . . . . . . . . . .287Inlet . . . . . . . . . . . . . . . . . . . . . . . . . . .287Symmetry . . . . . . . . . . . . . . . . . . . . . . . .288No Flow . . . . . . . . . . . . . . . . . . . . . . . . .288Flux Discontinuity . . . . . . . . . . . . . . . . . . . . .288Outlet . . . . . . . . . . . . . . . . . . . . . . . . . .289Cross Section . . . . . . . . . . . . . . . . . . . . . . .289Thickness. . . . . . . . . . . . . . . . . . . . . . . . .289
The Free and Porous Media Flow Interface290Domain, Boundary, Point, and Pair Nodes for the Free and PorousMedia Flow Interface . . . . . . . . . . . . . . . . . . .291Fluid Properties . . . . . . . . . . . . . . . . . . . . . .292Fluid and Matrix Properties . . . . . . . . . . . . . . . . . .293Volume Force . . . . . . . . . . . . . . . . . . . . . . .294Forchheimer Drag . . . . . . . . . . . . . . . . . . . . .294Porous Electrode Coupling . . . . . . . . . . . . . . . . . .294Initial Values. . . . . . . . . . . . . . . . . . . . . . .295Electrode-Electrolyte Interface Coupling . . . . . . . . . . . . .295Wall296. . . . . . . . . . . . . . . . . . . . . . . . . .Theory for the Brinkman Equations InterfaceAbout the Brinkman Equations297. . . . . . . . . . . . . . . .297Brinkman Equations Theory. . . . . . . . . . . . . . . . . .297References for the Brinkman Equations Interface. . . . . . . . . .299Theory for the Darcy’s Law Interface300Darcy’s Law — Equation Formulation . . . . . . . . . . . . . .300Theory for the Free and Porous Media Flow Interface302Reference for the Free and Porous Media Flow Interface. . . . . . .302Theory for the Coupling of Fluid Flow to ElectrochemicalReactionsMomentum Sources and Sinks . . . . . . . . . . . . . . . . .303303Chapter 7: Heat Transfer InterfacesCoupling of Heat Transfer to Electrochemical Reactions306Joule Heating Due to Charge Transport . . . . . . . . . . . . .307Heating Due to Electrochemical Reactions . . . . . . . . . . . .307CONTENTS 13
Chapter 8: Mathematics, Moving Interface BranchThe Level Set Interface312Domain, Boundary, and Pair Nodes for the Level Set Interface . . . .313Level Set Model . . . . . . . . . . . . . . . . . . . . . .314Initial Values. . . . . . . . . . . . . . . . . . . . . . .314Inlet . . . . . . . . . . . . . . . . . . . . . . . . . . .315Initial Interface . . . . . . . . . . . . . . . . . . . . . . .316No Flow . . . . . . . . . . . . . . . . . . . . . . . . .316Thin Barrier. . . . . . . . . . . . . . . . . . . . . . . .316Theory for the Level Set Interface317The Level Set Method . . . . . . . . . . . . . . . . . . . .317Conservative and Nonconservative Form . . . . . . . . . . . .319Initializing the Level Set Function . . . . . . . . . . . . . . . .319Variables For Geometric Properties of the Interface . . . . . . . .320Reference for the Level Set Interface . . . . . . . . . . . . . .320Chapter 9: Multiphysics Coupling NodesDeforming Electrode Surface . . . . . . . . . . . . . . . . .322Nondeforming Boundary . . . . . . . . . . . . . . . . . . .323Electrochemical Heating . . . . . . . . . . . . . . . . . . .324Flow Coupling . . . . . . . . . . . . . . . . . . . . . . .324Potential Coupling . . . . . . . . . . . . . . . . . . . . .325Space Charge Density Coupling . . . . . . . . . . . . . . . .325Temperature Coupling325. . . . . . . . . . . . . . . . . . .Chapter 10: GlossaryGlossary of Terms14 C O N T E N T S328
1IntroductionThis guide describes the Corrosion Module, an optional add-on package forCOMSOL Multiphysics intended for the modeling and simulation of corrosionand corrosion protection processes.This chapter introduces you to the capabilities of this module. A summary of thephysics interfaces and where you can find documentation and model examples isalso included. The last section is a brief overview with links to each chapter in thisguide.In this chapter: About the Corrosion Module Overview of the User’s Guide15
About the Corrosion ModuleThese topics are included in this section: What Can the Corrosion Module Do? Corrosion Module Physics Interface Guide Common Physics Interface and Feature Settings and Nodes Where Do I Access the Documentation and Application Libraries?The Physics Interfaces and Building a COMSOL Multiphysics Model inthe COMSOL Multiphysics Reference ManualWhat Can the Corrosion Module Do?The Corrosion Module is intended for the modeling of corrosion and corrosionprotection. The descriptions made available by the module are based on current andpotential distribution in galvanic cells. Its modeling capabilities cover galvaniccorrosion, cathodic protection, anodic protection, and sacrificial anode protection.The Corrosion Module consists of chemical species transport, fluid flow, heat transfer,electrochemistry, and corrosion interfaces. These physics interfaces describe thepotential in the electrolyte and in the corroding or protected metallic structure. Theelectrode reactions can be described using arbitrary electrode kinetic expressions of theoverpotential for the anodic and cathodic reactions. The potential and currentdistribution can also include the influence of mass transport and heat transfer, whichmeans that the Corrosion Module makes it possible to model composition andtemperature in a corrosion cell in detail. The ability to account for mass transport inthe electrolyte allows for modeling of corrosion caused by variations in, for example,salt concentration, oxygen concentration, and pH.The basis of the Corrosion Module is the mass and current balances in the electrolyteand in the corroding or protected metal structure. In the electrolyte, the currentbalance is defined together with individual species balances for the charged species andthe electroneutrality condition. In the metallic structure, the current balance isdescribed using Ohm’s law for the current density. The electron transfer reactions, atthe interface between the metallic structure and the electrolyte, couple the transportprocesses in the electrolyte with the current flowing in the metallic structure. The16 CHAPTER 1: INTRODUCTION
module contains predefined formulations for the abovementioned processes. Inaddition, the module can be used together with the heat transfer interfaces usingpredefined terms for heat sources caused by the electrochemical process.Corrosion Module Physics Interface GuideThe Corrosion Module extends the functionality of the physics interfaces of the basepackage for COMSOL Multiphysics. The details of the physics interfaces and studytypes for the Corrosion Module are listed in the table. The functionality of theCOMSOL Multiphysics base package is listed in the COMSOL MultiphysicsReference Manual.In the COMSOL Multiphysics Reference Manual: Studies and Solvers The Physics Interfaces For a list of all the core physics interfaces included with a COMSOLMultiphysics license, see Physics Interface Guide.PHYSICS INTERFACEICONTAGSPACEDIMENSIONAVAILABLE STUDY TYPEChemical Species TransportSurface Reactionssrall dimensionsstationary (3D, 2D, and 2Daxisymmetric models only);time dependentTransport of DilutedSpeciestdsall dimensionsstationary; time dependentTransport of DilutedSpecies in Porous Mediatdsall dimensionsstationary; time dependentTransport of DilutedSpecies in Fracturesdsf3D, 2D, 2Daxisymmetricstationary; time dependentElectrophoretic Transportelall dimensionsstationary; stationary withinitialization; timedependent; time dependentwith initializationABOUT THE CORROSION MODULE 17
PHYSICS INTERFACETAGSPACEDIMENSIONAVAILABLE STUDY TYPEtds esall dimensionsstationary; time dependent;stationary source sweep;small-signal analysis,frequency domain—3D, 2D, 2Daxisymmetricstationary; time dependentcdall dimensionsstationary; stationary withinitialization; timedependent; time dependentwith initialization; ACimpedance, initial values;AC impedance, stationary;AC impedance, timedependentTertiary y,Water-Based withElectroneutrality,Supporting Electrolyte)tcdall dimensionsstationary; stationary withinitialization; timedependent; time dependentwith initialization; ACimpedance, initial values;AC impedance, stationary;AC impedance, timedependentCurrent Distribution,Boundary Elementcdbemall dimensionsstationary; stationary withinitialization; timedependent; time dependentwith initialization; ACimpedance, initial values;AC impedance, stationary;AC impedance, cting FlowLaminar Flow, DilutedSpeciesElectrochemistryPrimary CurrentDistributionSecondary CurrentDistribution18 CHAPTER 1: INTRODUCTION
PHYSICS INTERFACEICONTAGSPACEDIMENSIONAVAILABLE STUDY TYPECurrent Distribution, Shellcdshall dimensionsstationary; stationary withinitialization; timedependent; time dependentwith initialization; ACimpedance, initial values;AC impedance, stationary;AC impedance, timedependentElectroanalysiselanall dimensionsstationary; time dependent;AC impedance, initialvalues; AC impedance,stationary; AC impedance,time dependent; cyclicvoltammetryElectrode, Shellels3D, 2D, 2Daxisymmetricstationary; time dependentsiec dgall dimensionsstationary; stationary withinitialization; timedependent; time dependentwith initialization; ACimpedance, initial values;AC impedance, stationary;AC impedance, timedependenttcdee dgall dimensionsstationary; stationary withinitialization; timedependent; time dependentwith initialization; ACimpedance, initial values;AC impedance, stationary;AC impedance, timedependentCorrosion, Deformed GeometryCorrosion, PrimaryCorrosion, SecondaryCorrosion, Tertiarywith (Electroneutrality,Supporting Electrolyte)ABOUT THE CORROSION MODULE 19
PHYSICS INTERFACEICONTAGSPACEDIMENSIONAVAILABLE STUDY TYPEFluid FlowPorous Media and Subsurface FlowBrinkman Equationsbr3D, 2D, 2Daxisymmetricstationary; time dependentDarcy’s Lawdlall dimensionsstationary; time dependentFree and Porous MediaFlowfp3D, 2D, 2Daxisymmetricstationary
COMSOL Multiphysics intended for the modeling and simulation of corrosion and corrosion protection processes. This chapter introduces you to the capabilities of this module.
