The Tertiary Current Distribution, Nernst-Planck Interface
The Tertiary Current Distribution, Nernst-Planck (tcd) interface (), found under the Electrochemistry branch () when adding a physics interface, describes the current and potential distribution in an electrochemical cell taking into account the individual transport of charged species (ions) and uncharged species in the electrolyte due to diffusion, migration and convection using the Nernst-Planck equations. The physics interface supports different descriptions of the coupled charge and mass transport in the electrolyte (see Electrolyte Charge Conservation below). The electrode kinetics for the charge transfer reactions can be described by using arbitrary expressions or by using the predefined Butler-Volmer and Tafel expressions.
Ohm’s law is used in combination with a charge balance to describe the flow of currents in the electrodes. The charge transfer reactions can be defined as boundary conditions or as sources or sinks within a domain in order for the case of porous electrodes.
Settings
The Label is the physics interface node name that will be shown in the model builder tree.
The Name is used primarily as a scope prefix for variables defined by the physics interface. Refer to such physics interface variables in expressions using the pattern <name>.<variable_name>. In order to distinguish between variables belonging to different physics interfaces, the name string must be unique. Only letters, numbers, and underscores (_) are permitted in the Name field. The first character must be a letter.
The default Name (for the first physics interface in the model) is tcd.
Domain Selection
The domains that do not conduct current should be omitted from the selection list, for example, the gas channels in a fuel cell.
Out-of-Plane Thickness
For 2D components, the Thickness field (default value: 1 m) defines a parameter for the thickness of the geometry perpendicular to the two-dimensional cross-section. The value of this parameter is used, among other things, to automatically calculate the total current from the current density vector. The analogy is valid for other fluxes.
Cross-sectional Area
For 1D components, enter a Cross-sectional area Ac (SI unit: m2) to define a parameter for the area of the geometry perpendicular to the 1D component. The value of this parameter is used, among other things, to automatically calculate the total current from the current density vector. The analogy is valid for other fluxes. The default is 1 m2.
Electrolyte Charge Conservation
The physics interface features five different descriptions of the coupled charge and mass transport in the electrolyte.
Use the Electroneutrality or the Electroneutrality, water based charge conservation option to model cells with significant concentration gradients of the current-carrying species (ions). The electroneutrality condition implicitly assumes that all major current-carrying ions are included in the model. In addition to the electroneutrality condition, the Electroneutrality, water based option also adds the water auto-ionization equilibrium condition, including proton and hydroxide transport, when defining the electrolyte equations. Note that this option adds the concentration variables for protons (tcd.cH) and hydroxide (tcd.OH) automatically, and that dependent variables for these two species should not be added under Dependent Variables below.
A Supporting electrolyte describes a situation where the major part of the charge is transferred by ions whose concentration can be described as constant.
Use the Electroanalysis (no potential gradients) option to model electroanalytical problems with electrolyte solutions containing a large quantity of inert supporting electrolyte, with a conductivity so high that ohmic losses can be assumed to be negligible. The electroanalysis option will not solve for the electrolyte potential as a dependent variable, setting it to a constant value of 0. Migration effects are hence neglected. Domain and boundary nodes only applicable to the electrolyte phase potential will be disabled when using electroanalysis.
The Poisson option couples the Nernst-Planck equations for mass transport to the Poisson equation for describing the potential distribution in the electrolyte, without any assumption of electroneutrality. This option is typically used when modeling problems where charge separation effects are of interest, typically within nanometers from an electrode surface.
For the Electroneutrality option, the From electroneutrality list sets the species that is calculated from the corresponding condition. Note that the choice of species to be taken from electroneutrality affects the specific boundary conditions that can be set on the eliminated species. For example, flux and concentration settings cannot be set for the eliminated species, and initial values cannot be provided. The choice can also have an impact on the numerics of the problem.
A general advice is to choose a relatively inert ion with high mole fraction to be taken from electroneutrality for best numerical results.
Dependent Variables
This physics interface defines these dependent variables (fields), the Concentrations of the species, the Electrolyte potential, and the Electric potential.
The names can be changed but the names of fields and dependent variables must be unique within a model.
Discretization
Concentrations basis function orders higher than Quadratic are not recommended if transport by convection is dominating in the model.
To see all settings in this section, click the Show More Options button () and select Advanced Physics Options from the Show More Options dialog box.
Consistent Stabilization and Inconsistent Stabilization
To display these sections, click the Show More Options button () and select Stabilization from the Show More Options dialog box. There are two consistent stabilization methods available and selected by default — Streamline diffusion and Crosswind diffusion. There is one inconsistent stabilization method, Isotropic diffusion, which is not selected by default. Any settings unique to this physics interface are listed below.
When the Crosswind diffusion check box is selected, a weak term that reduces spurious oscillations is added to the transport equation. The resulting system is nonlinear. There are two options for Crosswind diffusion type:
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Do Carmo and Galeão — the default option. This type of crosswind diffusion reduces undershoot and overshoot to a minimum but can in rare cases give equations systems that are difficult to fully converge.
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Codina. This option is less diffusive compared to the Do Carmo and Galeão option but can result in more undershoot and overshoot. It is also less effective for anisotropic meshes. The Codina option activates a text field for the Lower gradient limit glim (SI unit: mol/m4). It defaults to 0.1[mol/m^3)/tds.helem, where tds.helem is the local element size.
For both consistent stabilization methods, select an Equation residual. Approximate residual is the default setting and it means that derivatives of the diffusion tensor components are neglected. This setting is usually accurate enough and is faster to compute. If required, select Full residual instead.
In the COMSOL Multiphysics Reference Manual see Table 2-4 for links to common sections and Table 2-5 to common feature nodes. You can also search for information: press F1 to open the Help window or Ctrl+F1 to open the Documentation window.
Vanadium Redox Flow Battery: Application Library path Batteries_and_Fuel_Cells_Module/Flow_Batteries/v_flow_battery