The Electrochemistry Module Physics Interfaces
The module has a number of physics interfaces, which describe the transport and reaction of charged and neutral ions in aqueous electrolytes, surface reactions (electrochemical and chemical) and the formation of adsorbed species or coatings on metal surfaces. It also describes transport of current in electrolytes and metals, transport of current in thin metal structures (treated as shells), fluid flow, and heat transfer.
Figure 3
shows the available physics interfaces in the Electrochemistry branch as displayed in the Model Wizard for a 3D model.
Figure 3:
The 3D physics interfaces for the Electrochemistry Module, as shown in the Model Wizard, with the Electrochemistry branch fully expanded.
The Current Distribution interfaces
The Electrochemistry interfaces include the generic Primary Current Distribution (
), Secondary Current Distribution (
), and Tertiary Current Distribution, Nernst Planck (
) interfaces.
The Primary Current Distribution interface neglects the activation losses for the charge transfer reactions. It may only be used in the cases where the activation losses are substantially smaller than the conductivity losses. The Secondary Current Distribution interface accounts for the activation losses for the charge transfer reactions.
The Primary and Secondary Current Distribution interfaces may be combined with a Chemical Species Transport interface (described below) in order to incorporate kinetics effects of active species in the electrolyte or adsorbed species on an electrode surface.
The Tertiary Current Distribution, Nernst Planck (
) interface accounts for the transport of species through diffusion, migration, and convection and is therefore able to describe the effects of variations in composition on the electrochemical processes. Four different alternatives to handle electrolyte charge conservation (Electroneutrality, Water-Based with Electroneutrality, Supporting Electrolyte, and Poisson) are available. The kinetics expressions for the electrochemical reactions account for both activation and concentration overpotential.
The Aqueous Electrolyte Transport (
) interface computes the potential and species concentration fields in a dilute aqueous electrolyte. The interface targets modeling of aqueous electrolytes featuring weak acids, weak bases, ampholytes, and generic complex species. This includes, but is not limited to, electrochemical systems and phenomena containing multiple homogeneous reactions coupled to electrode kinetics. The transport is defined by the Nernst-Planck equations in combination with electroneutrality and water autoprotolysis.
The Concentrated Electrolyte Transport interface (
) is a generic interface for defining electrolyte transport. The electrolyte transport model is based on concentrated solution theory and can be applied to any type of electrochemical cell for an arbitrary number of electrolyte species. In contrast to the Tertiary Current Distribution, Nernst-Planck interfaces, the Concentrated Electrolyte Transport interface does not assume the presence of a neutral solvent, or a supporting electrolyte, of constant concentration.
The Electroanalysis Interface
The Electroanalysis interface (
) models mass transport of diluted species in electrolytes using the diffusion-convection equation, solving for electroactive species concentrations. The physics interface is applicable for electrolyte solutions containing a large quantity of excess (supporting) electrolyte. Ohmic losses in the electrolyte are assumed to be negligible. The physics interface includes tailor-made functionality for setting up cyclic voltammetry problems.
The Chemical Species Transport
The Transport of Diluted Species interface (
) is available under the Chemical Species Transport branch. This physics interface can be used to model transport of species due to diffusion, migration, and convection.
The Nernst-Planck-Poisson Equations (
) interface option combines an Electrostatic interface (
) with a Transport of Diluted Species interface (
). This combination can be used for investigation of charge and ion distributions within the electrochemical double layer where charge neutrality cannot be assumed. A requisite here is that the double layer, which typically is in the range of tens nanometers, is fully resolved in the mesh. The equations solved for are identical to the Electrochemistry>Tertiary Current Distribution, Poisson interface.
The Transport of Diluted Species in Porous Media interface (
) is also available and describes species transport between the fluid, solid, and gas phases in saturated and variably saturated porous media. The interface can for instance be used to model mass transport of noncharged particles within porous electrodes filled with aqueous electrolyte.
The Electrophoretic Transport (
) interface can be used to investigate the transport of weak acids, bases, and ampholytes in aqueous solvents. The physics interface is typically used to model various electrophoresis modes, such as zone electrophoresis, isotachophoresis, isoelectric focusing, and moving boundary electrophoresis, but is applicable to any aqueous system involving multiple acid-base equilibria.
The Surface Reactions interface (
) can be used model reactions and translateral transport of surface (adsorbed) species.
The Chemistry interface (
) can be used to define systems of reacting species, electrode reactions and ordinary chemical reactions. As such, it serves as a reaction kinetics and material property provider to the space dependent transport interfaces, such as the Tertiary Current Distribution or Transport of Diluted Species interfaces.
Porous Media Flow
The Fluid Flow interfaces (
) can be combined with the Electrochemistry Module interfaces to model free and forced convection in electrochemical cells.
The Darcy’s Law interface (
) is used to model fluid movement through interstices in a porous medium where a homogenization of the porous and fluid media into a single medium is done. Together with the continuity equation and equation of state for the pore fluid (or gas) this physics interface can be used to model low velocity flows, for which the pressure gradient is the major driving force. The penetration of electrolyte through a porous electrode is a classic example for the use of Darcy’s Law in electrochemical engineering.
Darcy’s law can be used in porous media where the fluid is mostly influenced by the frictional resistance within the pores. Its use is within very low flows, or media where the porosity is very small. Where the size of the interstices is larger, and the fluid is also influenced by itself, the gradients in fluid velocity, pressure, and gravity must be considered. This is done in the Brinkman Equations interface.
The Brinkman Equations interface (
) is used to model compressible flow at speeds of less than Mach 0.3, but control over the density and any of the mass balances that are deployed must be maintained to help with this.
The Free and Porous Media Flow, Brinkman interface (
) and the Free and Porous Media Flow, Darcy interface (
) are useful for equipment that contain domains where free flow is connected to porous media, such as concrete structures immersed in water.
Heat Transfer
The Heat Transfer interfaces (
) have in-built formulations for the contribution of Joule heating, and other electrochemical heat sources, to the thermal balance of electrochemical cells.
The features of the various Heat Transfer interfaces include Heat Transfer in Fluids (
), Heat Transfer in Solids (
), and Heat Transfer in Porous Media (
), and account for conductive and convective heat transfer. These features interact seamlessly and can be used in combination in a single model.
The detailed equations and assumptions that are defined by the physics interfaces are formulated in the
Electrochemistry Module User’s Guide
and the
COMSOL Multiphysics Reference Manual
.
Physics Interface Guide by Space Dimension and Study Type
The table lists the physics interfaces available with this module in addition to those included with the COMSOL Multiphysics basic license.
Physics interface
Icon
Tag
Space Dimension
Available Study Type
Chemical Species Transport
Transport of Diluted Species
tds
all dimensions
stationary; time dependent
Chemistry
chem
all dimensions
stationary; time dependent
Nernst–Planck–Poisson Equations
tds+es
all dimensions
stationary; time dependent; stationary source sweep; small-signal analysis, frequency domain
Electrophoretic Transport
el
all dimensions
stationary; stationary with initialization; time dependent; time dependent with initialization
Transport of Diluted Species in Porous Media
tds
all dimensions
stationary; time dependent
Surface Reactions
sr
all dimensions
stationary (3D, 2D, and 2D axisymmetric models only); time dependent
Reacting Flow
Laminar Flow, Diluted Species
—
3D, 2D, 2D axisymmetric
stationary; time dependent
Electrochemistry
Primary Current Distribution
Secondary Current Distribution
cd
all dimensions
stationary; stationary with initialization; time dependent; time dependent with initialization; AC impedance, initial values; AC impedance, stationary; AC impedance, time dependent
Tertiary Current Distribution, Nernst–Planck (Electroneutrality, Water-Based with Electroneutrality, Supporting Electrolyte, Poisson)
tcd
all dimensions
stationary; stationary with initialization; time dependent; time dependent with initialization; AC impedance, initial values; AC impedance, stationary; AC impedance, time dependent
Aqueous Electrolyte Transport
aqt
all dimensions
stationary; stationary with initialization; time dependent; time dependent with initialization
Concentrated Electrolyte Transport
cet
all dimensions
stationary; stationary with initialization; time dependent; time dependent with initialization;
Electroanalysis
tcd
all dimensions
stationary; time dependent; AC impedance, initial values; AC impedance, stationary; AC impedance, time dependent; cyclic voltammetry
Electrode, Shell
els
3D, 2D, 2D axisymmetric
stationary; time dependent
Fluid Flow
Porous Media and Subsurface Flow
Brinkman Equations
br
3D, 2D, 2D axisymmetric
stationary; time dependent
Darcy’s Law
dl
all dimensions
stationary; time dependent
Free and Porous Media Flow, Brinkman
fp
3D, 2D, 2D axisymmetric
stationary; time dependent
Free and Porous Media Flow, Darcy
—
3D, 2D, 2D axisymmetric
stationary; time dependent
Nonisothermal Flow
Brinkman Equations
—
3D, 2D, 2D axisymmetric
stationary; time dependent; stationary, one-way NITF; time dependent, one-way NITF
Heat Transfer
Heat Transfer in Porous Media
ht
all dimensions
stationary; time dependent