An electrochemical charge-transfer reaction is a chemical reaction between neutral species, charged ions, and electrons. Phenomena associated with electrochemistry include batteries, fuel cells, corrosion and electro-deposition. Charge-transfer reactions occur at phase-interfaces between electrodes (anode or cathode) and an electrolyte. This interface is referred to as a Faradaic surface.

The general form of the ^th electrochemical reaction is:

(7–117)

where:
	represents liquid or solid species
	is the total number of species
	and are the stoichiometric coefficients of the th species as reactant and product in the reaction , respectively
	is the charge number of the th species
	represents electron

For neutral species, the charge number is zero.

In Ansys Fluent, the charge-transfer reaction rate for the electrochemical reaction at Faradaic interfaces is determined by the Butler-Volmer equation:

(7–118)

or by its alternative form using Tafel slopes:

(7–119)

where:
	= Faradaic current density (A/m2)
	= exchange current density (A/m2)
	= total number of chemical species
	= activation energy (J/kmol)
	= Universal Gas Constant (J/kmolK)
	= Temperature (K)
	= reference temperature (K)
	= molar concentration of species in reaction
	= reference molar concentration of species in reaction
	= rate exponent of species
	= anodic charge transfer coefficient
	= cathodic charge transfer coefficient
	= Tafel slope for anodic reaction (V)
	= Tafel slope for cathodic reaction (V)
	= Faraday constant (C/kmol)
	= overpotential (V)

The overpotential is calculated as:

(7–120)

where and are the electrode and electrolyte potentials (V), respectively, and is the equilibrium potential (V).

The general reaction shown in Equation 7–117 occurs in both forward and backward directions simultaneously. The anodic reaction occurs in the direction where electrons are produced, while the cathodic reaction occurs in the direction where electrons are consumed.

The first term in Equation 7–118 is the rate of the anodic direction, while the second term is the rate of the cathodic direction. The difference between these two rates gives the net rate of reactions. The net direction of reaction depends on the sign of the surface overpotential. If overpotential is positive, the overall reaction moves in the direction of the anodic reaction, and if it is negative, it moves in the direction of the cathodic reaction.

The general reaction (Equation 7–117) also shows that electric current is proportional to the species production/consumption rate in an electrochemical reaction. This correlation for the species in the ^th reaction is expressed by Faraday’s law:

(7–121)

where is the species production/consumption rate, is the species molecular weight, and is the total number of electrons produced by the electrochemical reaction calculated as:

(7–122)

The total species production/consumption rate for specie due to all electrochemical reactions can be computed as:

(7–123)

As follows from Faraday’s law (Equation 7–121), the rate of an electrochemical reaction can be expressed in terms of either electric current or species mass change, since these two quantities are directly proportional.

According to the Butler-Volmer equation (Equation 7–118), the driving force for the electrochemical reaction is the potential difference across the electrode-electrolyte interface. The electric potential in the medium can be derived from the charge conservation law:

(7–124)

where is the electric current density vector.

In a solid phase, the current density and the gradient in potential are related by Ohm’s law:

(7–125)

where is the electric conductivity, and is the electric potential.

Therefore, the potential field is governed by a Laplace equation:

(7–126)

In a liquid (or electrolyte) phase, electric current is the net flux of charged species:

(7–127)

where:
	= flux density of species generated by species diffusion, species convection, and the migration of species (solid or liquid) in the electric field
	= velocity of the flow field
	= concentration of species
	= diffusion coefficient of species
	= mobility of species

In general, the treatment of electrochemical theory is too complicated to be practical. To simplify Equation 7–127, charge neutrality is usually assumed:

(7–128)

This eliminates the second term in Equation 7–127.

In addition, the first term in Equation 7–127 is usually considered negligible compared to the last term. This is a valid assumption for mixtures that are well-mixed or mixtures with a high electrolyte concentration. As a result, only the last term remains in Equation 7–127.

Defining the ionic conductivity as,

(7–129)

the charge conservation equation (Equation 7–127) reduces to:

(7–130)

Therefore, the same Laplace equation is solved in both solid and liquid zones.

Charge neutrality is not explicitly enforced. Instead, it is assumed that there are unrepresented species of identical opposite charge that cancel the represented species charge.

The electric field may exert a force on the charged species in the electrolyte. This results in an additional term in the species transport equation (Equation 7–1):

(7–131)

Electrochemistry can contribute two distinct sources of heat to the energy equation (Equation 5–1).

The first term is due to the charge-transfer reaction at the Faradaic interface and is modeled as:

(7–132)

where is Faradaic current density, and is the over-potential (see Equation 7–120).

The second term is Joule heating due to motion of charges:

(7–133)