Model Assumptions and Engineering Approaches

While electrochemical simulations can account for the most detailed first-principle physics, most engineering problems can be diagnosed successfully based on simplified setups.

Current Distribution Methodology

Electrochemical engineers and scientists categorize simulations according to the current distribution concept. The three main aspects here lie in the consideration or neglect of:

electrical transport losses due to resistance in the electrolyte solution or in metal phases
activation overpotentials
concentration dependent reaction rates and overpotentials

Primary Current Distribution: Primary current distribution setups account solely for electrical transport losses due to resistance (1.), but (2.) and (3.) are neglected. These simulations refrain from solving species concentrations and only need to resolve electric potentials. When temperatures are fixed as well, only one partial differential equation (PDE) is solved for the electric potential, thus reducing the computational effort significantly. Also, the computation is sped-up due to the absence of coupling effects between electric potentials and species concentrations. In Simcenter STAR-CCM+, such setups are approximated using only the Electrodynamic Potential model in conjunction with the Electrochemical Reactions model—where maximum specific exchange currents are applied to minimize activation overpotentials.; Neglecting activation overpotentials corresponds to assuming an infinite electrochemical reaction rate where all significant losses occur in the electrolyte and/or in the metal transport of charge carriers. For reactions that are significantly faster than the species transport, this assumption leads to contradictory behaviour in situations where real reactions with a chemical equilibrium at high progress rates are likely to suffer from reactant depletion, decreasing their rate. However, primary current distribution setups do not consider any concentration effects. Therefore, these setups are not ideal for simulating reactions that are significantly faster than species transport.; The methodology nevertheless serves well when reactions are impeded by the metal/solution transport, as in many (anti-) corrosion setups. Despite being a computationally performant modeling technique, you are recommended to use secondary current distribution with Simcenter STAR-CCM+.
Secondary Current Distribution: Secondary current distribution setups build on the foundation of primary current distribution, but additionally account for activation overpotentials (2.). With the same Simcenter STAR-CCM+ model set as primary current distribution setups, but with more realistic parameters for the specific exchange currents, this treatment performs equally well with respect to computational expense, but delivers more realistic results and is therefore recommended.; Secondary current distribution setups are limited in that they do not resolve species concentrations. As such, a secondary treatment assumes a perfectly mixed electrolyte. However, a certain level of saturation effects is considered in electrochemical reaction rates, usually leading to decreased, more realistic extremal values. Prefer using this treatment when electrochemical reactions do not lead to significant changes in molar concentrations of reactants, for example when reactants are in excess (such as salt in seawater), and the timescales of the reaction are relatively large in comparison to the convective and diffusive flow timescales.
Tertiary Current Distribution: The most detailed modelling is represented by tertiary current distribution modelling where reaction rates and overpotentials are concentration dependent. In this scenario, all of (1.) (2.) and (3.) are considered.; While providing the best quality and highest fidelity of the results, this scenario requires the highest computational effort, and the highest demand on parameterizing the simulation model.; For isothermal tertiary current setups, one partial differential equation is solved for each species. These partial differential equations depend on the flow velocities, therefore, three additional equations are solved for the velocity components, plus one for pressure. These equations are solved in addition to the partial differential equation for the electric potential. Thus, the tertiary current distribution setup requires the solution of at least 5+n partial differential equations whereas the primary and the secondary current distribution setups are required to solve only one. It is generally recommended to include solution of an additional partial differential equation for temperature variations as this comes with minor additional computational cost compared to the overall computational effort.


	Primary	Secondary (recommended)	Tertiary
Considerations	Electrical Transport Losses	Electrical Transport Losses Activation Overpotential	Electrical Transport Losses Activation Overpotential Concentration Dependence
Relevant Simcenter STAR-CCM+ Models	Electrodynamic Potential Model Electrochemical Reactions*	Electrodynamic Potential Model Electrochemical Reactions	Electrodynamic Potential Model Electrochemical Reactions either: Electrochemical Species Multi-Component Gas Multi-Component Liquid
Number of Partial Differential Equations Solved (isothermal)	1	1	5 + number of species
Accessible Solution Quantities	Electric Potential $ϕ$ Electrical Currents $j$	Electric Potential $ϕ$ Electrical Currents $j$ Surface Overpotential $η$	Electric Potential $ϕ$ Electrical Currents $j$ Surface Overpotential $η$ Molar Concentrations $c_{i}$ Velocity $v$

* When simulating an electrochemical interface, the Electrochemical Reactions model is required in order to model the difference in equilibrium potentials between the solid and the electrolyte.

The parameterization requirements are also considerable. Reactions need to be known and parameterized to account for their dependence on concentrations. Simple measurements like cyclic voltammetry will not suffice to parameterize the setup but detailed knowledge is required about the reaction mechanisms involved in the process, involving not only stoichiometries but also rate constants and exchange current densities for each single reaction.

Detailed parameterization of models provides superior results when reactant concentrations significantly influence the rate of reactions—which is usually the case when the reaction rate is not infinite, but time scales are equal or smaller than the ones of diffusion/convection, that is, when reactants cannot be fed fast enough to the reaction site, or products cannot be removed fast enough to sustain the reaction at unchanged rates. This is the case for many technical applications like fuel cells or batteries in critical load scenarios, or some wet-etching simulations where manufacturing speed is crucial for achieving low production costs.

Temperature Effects

Electrochemical reaction rates are clearly temperature dependent. Nevertheless, solving for temperature can be neglected for engineering problems occurring at constant temperature levels.

Consider, for example, the corrosion of a water pipeline that lies buried in permafrost ground. Temperature is controlled by heating elements, but when investigating corrosion rates, this temperature can be considered as fixed.

Other applications require solving for temperature. In oil processing pipelines, metals are subjected to both spatially and temporally varying temperatures. If electrochemical reaction rates are still low, for example, when considering unwanted corrosion effects, the electrochemical heating can still be neglected as it only contributes negligibly to the overall temperature.

Neglecting temperature effects has significant runtime impact when looking at primary and secondary current distribution setups, where only a single partial differential equation needs to be solved then. Solving for temperature in tertiary setups will represent an additional partial differential equation to the 5+n existing partial differential equations. Therefore, neglect of solving for temperature yields only minimal savings, and is not recommended in favor of accurate results.