Electrochemical Species Model Reference

The Electrochemical Species model is an optional electrochemistry model which is available to use with the Electrostatic Potential model or the Electrodynamic Potential model. You can also use the Electrochemical Species model with the Electrodynamic Potential and Electrochemical Reactions models to simulate electrochemical surface reactions which take into account electrochemical species flux due to electrochemical species concentrations.

You can select either a coupled solver or a segregated solver specifically for the Electrochemical Species model. This functionality allows you to, for example, solve a coupled system of equations between the electrochemical species while maintaining a segregated approach to solving electric potential.

When using the Electrochemical Species model with the Electrochemical Reactions model, the Electrochemical Reactions model computes the contributions to the electric current from the species concentrations, the electrochemical species flux, and flux derivatives. The electric current is passed to the Electrodynamic Potential model and the species flux, and flux derivatives, are passed to the Electrochemical Species model.

Table 1. Electrochemical Species Model Reference
Theory	See Electrochemical Species.
Provided By	[physics continuum] > Models > Electrochemistry
Example Node Path	Continua > Physics 1 > Models > Electrochemical Species Model
Requires	Space: any Material: one of Gas, Liquid Optional Models: Electrochemistry
Properties	Key properties are: Electrochemical Species Solver Option. See Electrochemical Species Model Properties.
Activates	Physics Models	Flow
	Model Controls (child nodes)	Electrochemical Species Components. See Electrochemical Species Components Reference.
	Initial Conditions	Molar Concentration. See Electrochemical Species Initial Conditions.
	Boundary Inputs	Wall Electrochemical Species Option, Wall Electrochemical Species Flux Derivative Option. See Electrochemical Species Boundary Settings.
	Region Inputs	See Electrochemical Species Region Settings.
	Solvers	Electrochemical Species, Coulomb Force. See Electrochemical Species Solvers and Coulomb Force Solver.
	Field Functions	See Electrochemical Species Field Functions.

Electrochemical Species Model Properties

If you change between using the Electrodynamic Potential model and the Electrostatic Potential model, the Electrochemical Species model property settings for Charged Species Mobility Dimension and Concentration Dimension, are modified automatically. The Output window displays the modifications, for example:

Electrochemical Species Model: Charged Species Mobility Dimension has been set to Area / Electric Potential Time

Electrochemical Species Model: Concentration Dimension has been set to Number Density

Electrochemical Species Solver Option

Allows you to specify if the electrochemical species model uses a Coupled or Segregated solver to solve for the electrochemical species molar concentrations. If you switch between these options, any solver properties that are set are not maintained.

By default, the Electrochemical Species model is set to use the Coupled Electrochemical Species Solver unless you are using a simulation file in Simcenter STAR-CCM+ v11.04 or later that was saved in an earlier version of Simcenter STAR-CCM+. In which case, the Segregated solver is used—until you specify otherwise. If you modify the choice of solver, update the solver properties—as properties are not transferred between solvers.

Convection

In transport equations, you can choose from a range of schemes that calculate the convection term at a cell face. This calculation requires Simcenter STAR-CCM+ to compute the face value of a quantity from the surrounding cell values. The method used for computing this face value has a profound effect on the stability and accuracy of the numerical scheme. For guidance on selecting a convection scheme, see Convective Flux.

1st-order: First-order convection scheme.
2nd-order: Second-order convection scheme.

Secondary Gradients

Neglect or include the boundary secondary gradients for diffusion and/or the interior secondary gradients at mesh faces.

On: Default value. Solves for interior and boundary types of secondary gradient.
Off: Does not solve for either type of secondary gradient.
Interior Only: Solves for the interior secondary gradients only.
Boundaries Only: Solves for the boundary secondary gradients only.

Electroneutrality option

Specifies if the overall ionic charge density is strictly enforced as zero or not. When simulating corrosion applications, maintain the default option (Scaling).

Not Enforced: Not Enforced is the default option when using the Electrostatic Potential Model. A uniform zero ionic charge density is not enforced. However, depending on the setup of other parameters, the overall ionic charge density may already equal zero. This option is appropriate for non-corrosion related applications which do not require electroneutrality.
Scaling: Scaling is the default option when using the Electrodynamic Potential Model. This method ensures that the overall ionic charge density is equal to zero by scaling the ionic charge densities for each species proportionally. When the species have equal charge numbers, the total concentration is not changed by scaling. Simcenter STAR-CCM+ checks the concentration profiles that are set using the concentration dimension property and provides a warning if they are not electrically neutral. This option is appropriate for applications that feature electroneutrality, such as corrosion and etching. See Eqn. (4077).

Transport

Defines how the Electrochemical Species model is coupled to other models and so defines the transport equations that Simcenter STAR-CCM+ solves.

Species <> Electric Potential: Physical two-way coupling of flux contributions between the Electrochemical Species and Electric Potential models.
Electric Potential > Species: One-way coupling including drift flux / migrative contributions from the Electric Potential model to the Electrochemical Species model.
Species > Electric Potential: One-way transfer of contributions from the Electrochemical Species model to the Electric Potential model.
- When using the Electrostatic Potential model, the contributions are for the space charge density.
- When using the Electrodynamic Potential model, the contributions are for the diffusive current.
No Electric Potential Coupling: The Electrochemical Species model and the Electric Potential model act independently.

Charged Species Mobility Dimension

Allows you to set the dimension of the charged species mobility. When the Electrodynamic Potential Model is selected, the default setting for this property is set as Area Quantity/Energy Time, and when the Electrostatic Potential model is selected, the default setting for this property is set as Area/Electric Potential Time.

Area Quantity/Energy Time: Allows you to specify the mobility of electrochemical species components in dimensions of Area Quantity/Energy Time, or default SI units of $m^{2} k m o l / J s$
denoted by $u_{i}$ in Eqn. (4080) and Eqn. (4092).
Area/Electric Potential Time: Allows you to specify the mobility of electrochemical species components in dimensions of Area/Electrical Potential Time or default SI units of $m^{2} / V s$ .
denoted by $K_{i}$ in Eqn. (4092).

Concentration Dimension

Allows you to specify how the concentration of molecules / particles is defined. When the Electrodynamic Potential Model is selected, the default setting for this property is set as Molar Concentration, and when the Electrostatic Potential model is selected, the default setting for this property is set as Number Density. If the Electroneutrality property is set to Scaling, Simcenter STAR-CCM+ checks the concentration profiles that are set and provides a warning if they are not electrically neutral.

Molar Concentration: Specifies the concentration of molecules/particles using the molar concentration in $k m o l / m^{3}$
Number Density: Specifies the molecule/particle concentration in $1 / m^{3}$ using the actual number of particles—which is the molar concentration multiplied by the Avogadro constant, $N_{A}$

Electrochemical Species Model Initial Conditions

Molar Concentration: Allows you to specify a composite or constant value for the molar concentration, $c_{i}$ for species $i$ in Eqn. (4072) of each electrochemical species component that is specified under the Electrochemical Species model.

Electrochemical Species Model Boundary Settings

Wall Boundary

Wall Electrochemical Species Option

The wall electrochemical species option for a boundary allows you to define what happens at that boundary regarding electrochemical species.

Method	Corresponding Physics Value Nodes
Impermeable Specifies zero flux at the boundary.	None
Specified Flux You can specify the Value as a Constant or Composite array. The physics condition, Wall Electrochemical Species Flux Derivative Option also becomes available to specify.	One of the following nodes appears depending on what you set for Concentration Dimension on the Electrochemical Species model. You can specify the Value as a Constant or Composite array. Molar Concentration Flux Number Density Flux
Specified Value	One of the following nodes appears depending on what you set for Concentration Dimension on the Electrochemical Species model. You can specify the Value as a Constant or Composite array. Molar Concentration Number Density

Wall Electrochemical Species Flux Derivative Option

The Wall Electrochemical Species Flux Derivative Option allows you to specify the derivative of the Molar Concentration Flux of species

i

(or Number Density Flux) with respect to the molar concentration of species

i

(or number density) at the wall. The Concentration Flux Derivative represents:

\frac{d N_{n, s, i}}{d c_{i}}

and the Number Density Flux Derivative represents:

\frac{d N_{n, s, i}}{d n_{p}}

where

N_{n, s, i}

is the molar concentration flux of electrochemical species,

i

(or number density) at the wall,

c_{i}

is the molar concentration of electrochemical species

i

at the wall, and

n_{p}

is the number density at the wall.

This derivative is used for linearization.

This option is available when the Wall Electrochemical Species Option boundary condition is set to Specified Flux.

Method	Corresponding Physics Value Nodes
None The derivative of the Concentration Flux is not calculated. This is the default option.	None
Specified Allows you to specify the concentration flux derivative that is used for linearization.	Concentration Flux Derivative Allows you to specify the concentration flux derivative as a Constant or Composite array. For a stable set-up, make sure that the flux derivative has a negative value.

Electrochemical Species Model Region Settings

Electrochemical Species Source Option

Method	Corresponding Physics Value Nodes
deactivated	None
activated Allows you to provide additional physics in Eqn. (4072) to represent a specific molar concentration or number density.	Electrochemical Species Source Jacobian Use this node to specify the Jacobian, $d (S_{c_{i}}) / d (c_{i})$ , of each of the defined species as a scalar array profile. Electrochemical Species Sources Use this node to specify the species source, $S_{c_{i}}$ , of each of the defined species as a scalar array profile. The units that are specified are dependent upon the Concentration Dimension setting of the Electrochemical Species model.

Method

Corresponding Physics Value Nodes

deactivated

None

activated: Allows you to provide additional physics in Eqn. (4072) to represent a specific molar concentration or number density.

Electrochemical Species Source Jacobian: Use this node to specify the Jacobian, $d (S_{c_{i}}) / d (c_{i})$ , of each of the defined species as a scalar array profile.
Electrochemical Species Sources: Use this node to specify the species source, $S_{c_{i}}$ , of each of the defined species as a scalar array profile. The units that are specified are dependent upon the Concentration Dimension setting of the Electrochemical Species model.

Electrochemical Species Solver

A Coupled Electrochemical Species Solver and a Segregated Electrochemical Species Solver are available to solve the electrochemical species concentrations independently from solving the electric potential.

You can select which variant of the Electrochemical Species solver to use within the Electrochemical Species model properties. However, when using the Bulk Ion Chemical Reactions model, only the Coupled option is available.

Having the choice of electrochemical species solvers allows you to solve for the electrochemical species concentrations in the most appropriate way, independent of the method that is used to solve any other factor. For example, electric potential is solved for using a segregated approach, however, you can choose a coupled implementation for solving electrochemical species concentrations.

The Segregated Electrochemical Species Solver runs faster than the Coupled Electrochemical Species Solver. However, for certain problems, especially depletion conditions at high current densities, the coupled solver converges when the segregated solver does not.

The Coupled Electrochemical Species Solver is intended for use with the Electrochemical Reactions model or the Bulk Ion Chemical Reactions model. If you use the coupled solver without these models, the runtime increases considerably—without any benefit.

Since elements cannot be created or destroyed, Simcenter STAR-CCM+ guarantees conservation of each type of atom when using the coupled solver. However, when source terms and boundary fluxes are provided using field functions, the segregated solver does not guarantee the conservation of elements. Using the segregated approach, the source terms that are computed for each electrochemical species concentration are not computed consistently using the concentrations from the same Newton iteration. Therefore, elements are not conserved at each Newton iteration when field functions are involved with the segregated approach. To guarantee conservation of elements, either use the coupled solver, or use the segregated solver and run Newton's method until it is fully converged for a steady simulation, or for each time-step in an unsteady simulation.

If necessary, you can also stop a simulation and change between the coupled and segregated solver options. Since the Coupled Electrochemical Species Solver provides stability, you can start a simulation with this solver. When the simulation begins to converge, you can change to the Segregated Electrochemical Species Solver—which runs quicker. Switching between solver options removes any solver settings that are defined. Therefore, if you switch solver options, update the solver settings.

Note	For issues involving the Electrochemical Species Solvers, try reducing the under-relaxation factor on the Electric Potential Solver.

The convergence of the coupled solver varies slightly depending on the ordering of the electrochemical species, since the algebraic multigrid solver is constructed based on the matrix components of the first mixture component.

Both implementations, the Coupled Electrochemical Species Solver and the Segregated Electrochemical Species Solver, have the same properties and expert properties.

Under-Relaxation Factor: In order to promote convergence, this property is used to under-relax changes of the solution during the iterative process. If residuals show solution divergence or do not decrease, reduce the under-relaxation factor.
Solver Frozen: When On, the solver does not update any quantity during an iteration. It is Off by default. This is a debugging option that can result in non-recoverable errors and wrong solutions due to missing storage. See Finite Volume Solvers Reference for details.
Reconstruction Frozen: When On, Simcenter STAR-CCM+ does not update reconstruction gradients with each iteration, but rather uses gradients from the last iteration in which they were updated. Activate Temporary Storage Retained in conjunction with this property. This property is Off by default.
Reconstruction Zeroed: When On, the solver sets reconstruction gradients to zero at the next iteration. This action means that face values used for upwinding (Eqn. (905)) and for computing cell gradients (Eqn. (917) and Eqn. (918)) become first-order estimates. This property is Off by default. If you turn this property Off after having it On, the solver recomputes the gradients on the next iteration.
Temporary Storage Retained: When On, Simcenter STAR-CCM+ retains additional field data that the solver generates during an iteration. The particular data retained depends on the solver, and becomes available as field functions during subsequent iterations. Off by default.

Coulomb Force Solver

You can use the Coulomb Force physics model in addition to the Electrochemical Species and Electrostatic Potential physics models to simulate electrohydrodynamic forces that arise from local ionic charge densities. See Modeling Ionic Species Flux. When the Coulomb Force physics model is used, the Coulomb Force Solver becomes available. The Coulomb Force Solver node allows you to specify an Under-Relaxation factor which you can adjust to help improve stability when simulating ionic wind simulations or plasma actuators. See Coulomb Force Formulation.

Under-Relaxation Factor: In order to promote convergence, this property is used to under-relax changes of the solution during the iterative process. If residuals show solution divergence or do not decrease, reduce the under-relaxation factor.
Solver Frozen: When On, the solver does not update any quantity during an iteration. It is Off by default. This is a debugging option that can result in non-recoverable errors and wrong solutions due to missing storage. See Finite Volume Solvers Reference for details.

Electrochemical Species Field Functions

Charge Number of [Species]: Charge number, $z_{i}$ of species $i$ . A separate scalar field function is available for each species.
Diffusion Current Density: The second term in Eqn. (4077).
Ionic Charge Density: The ionic space charge density, $ρ_{i o n}$ . Scalar function.
Molar Concentration of [Species]: The molar concentration, $c_{i}$ , of species $i$ in $k m o l / m^{3}$ . A separate scalar field function is available for each species.
Molecular Diffusivity of [Species]: Diffusivity, $D_{i}$ , of species $i$ . A separate scalar field function is available for each species.
Number Density of [Species]: Displays the number of particles in $1 / m^{3}$ . Calculated by the molar concentration multiplied by the Avogadro constant, $N_{A}$ . A separate scalar field function is available for each species.

The following field functions are available when using the Electrochemical Species model and Temporary Storage is activated. Using field functions to visualize these quantities can help to diagnose if something is going wrong at a flow boundary, say, where large gradients are not expected. See, Turning On Temporary Storage.

Molar Concentration Residual: The residuals are the imbalance in the discretized equations. Scalar field function.
Molar Concentration Correction: Corrections are added to the solution of the previous iteration to get the updated solution. Scalar function.
Molar Concentration Gradient: Gradients are used to compute values such as diffusion and strain rates. Vector function.
Molar Concentration Recon: Reconstruction gradients are used to interpolate cell values to faces. Vector function.
Molar Concentration Ap: The Ap coefficients are the diagonal coefficients in the matrix of the linear system. Vector function.