The Tertiary Current Distribution, Nernst-Planck Interface

The interface (

), found under the 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 Charge Conservation model 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.

The is the physics interface node name that will be shown in the model builder tree.

The 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 field. The first character must be a letter.

The default (for the first physics interface in the model) is tcdee.

The domains that do not conduct current should be omitted from the selection list, for example, the gas channels in a fuel cell.

For 2D components, the 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.

For 1D components, enter a 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, amongst 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.

The physics interface features four different descriptions of the coupled charge and mass transport in the electrolyte.

Use the or the 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 option also adds the water auto-ionization equilibrium condition, including proton and hydroxide transport, when defining the electrolyte equations.

A describes a situation where the major part of the charge is transfered by ions whose concentration can be described as constant.

The 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 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.

This physics interface defines these dependent variables (fields), the s of the species, the , and the .

The names can be changed but the names of fields and dependent variables must be unique within a model.

To display this section, click the button (

) and select .

basis function orders higher than are not recommended if transport by convection is dominating in the model.

To display these sections, click the button (

) and select . There are two consistent stabilization methods available and selected by default— and . There is one inconsistent stabilization method, , which is not selected by default. Any settings unique to this physics interface are listed below.

•

When the 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 :

—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.

. 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 glim (SI unit: mol/m4). It defaults to 0.1[mol/m^3)/tds.helem, where tds.helem is the local element size.

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For both consistent stabilization methods, select an 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 instead.