Galvanized Nail

This tutorial example serves as an introduction to the Corrosion Module and models the metal oxidation and oxygen reduction current densities on the surface of a galvanized nail, surrounded by a piece of wet wood, which acts as electrolyte.

The protecting zinc layer on the nail is not fully covering, so that at the tip of the nail the underlaying iron surface is exposed. First the electrolyte conductivity and the electrode reaction kinetics are modeled to obtain a secondary current distribution (concentration variations in the cell are not accounted for), in a second part the oxygen transport is included to model a tertiary current distribution.

Figure 1: Modeled geometry (2D axisymmetric). The nail surface has two parts: the main part is protected by zinc, on the tip the underlaying iron is exposed. The top boundary is in contact with the atmosphere.

Model Definition

Figure 1 shows the model geometry. Due to the symmetry of the problem the geometry is made 2D axisymmetric, and consists of one single domain, the electrolyte. The actual nail is not included in the model geometry as a domain since the metal electric potential can be considered constant due to the high conductivity of the metal, in combination with the low expected current densities.

The surface of the nail consists two parts, the zinc covered part, and the tip, where the zinc has been scratched off to expose the underlaying iron. The top electrolyte boundary is in contact with the atmosphere, all other boundaries are insulating.

Electrolyte charge transport

The currents expected are small in relation to the total amount of charge carrying ions in the electrolyte. This implies that a constant conductivity can be assumed, use the Secondary Current Distribution interface to solve for the electrolyte potential,

(SI unit: V), according to:

where il (SI unit: A/m2) is the electrolyte current density vector and σl (SI unit: S/m) is the electrolyte conductivity. Use the default insulating conditions for all boundaries except the nail surface:

Where n is the normal vector, pointing out of the domain.

Metal oxidation reactions

The nail is not included as a domain in the model, therefore use the Electrode Surface boundary node to model the nail surface, and set the potential of the metal phase

(SI unit: V) to 0 on this boundary.

The Electrode Surface sets the boundary condition for the electrolyte potential to

where iloc,m (SI unit: A/m2) are the local individual electrode reaction current densities.

Add Electrode Reaction nodes to the Electrode Surface to define the individual electrode reactions.

On the zinc surface, oxidation occurs according to

whereas on the exposed iron surface, iron is oxidized according to

where Eeq,m (SI unit: V) is the equilibrium potential of the electrode reaction.

Use an anodic Tafel expression to model these reactions, this sets the local current density to

for each reaction, where i0,m is the exchange current density, Am (SI unit: V) is the Tafel slope and the overpotential η (SI unit: V) is calculated from

(1)

Oxygen reduction and Oxygen transport

Oxygen is reduced on both the zinc and iron electrode surfaces according to

Use a cathodic Tafel expression to model this reaction, which sets the local current density to

Since zinc and iron have different catalytic properties for oxygen reduction, use different parameter values for AO2 and i0,O2 on the different surfaces.

It is often good modeling practice to solve for a secondary current distribution first, before adding mass transfer. Once one has obtained a satisfactory solution for the secondary problem, one can proceed to increase the complexity of the model.

For this model, solve for the Secondary Current Distribution interface first then add a Transport of Diluted Species interface to model oxygen transport by Fickian diffusion:

where c (SI unit: mol/m3) is the oxygen concentration, N (SI unit: mol/(m2·s)) the flux vector, and D (SI unit: m2/s) the diffusion coefficient.

Use the default No Flux conditions for the right and bottom boundary:

The top boundary is in contact with the surrounding air, set the concentration to a fixed value on this boundary.

On the nail surface, couple the oxygen flux over the boundary to the oxygen reduction current density by using an Electrode-Electrolyte Interface Coupling boundary condition. This sets the flux to be proportional to the electrode current density according to Faraday’s law:

where F is Faraday’s constant (96,485 C/mol), ν the stoichiometric coefficient for oxygen in the reduction reaction and n the number of electrons in the reaction.

The sign convention for ν is that it should be negative for reactants and positive for products in a reduction reaction (A reaction with the electrons participating as reactants). n is always positive. Set ν to -1 and n to 4 for this model.

When including oxygen transport in the model, also change the electrode kinetics for the oxygen reduction reaction to the following expression:

Results and Discussion

Figure 2 shows the electrode reaction current densities for the secondary current distribution model. Zinc oxidation dominates on the zinc surface, with a maximum at the point between the iron and zinc surfaces. Oxygen reduction dominates on the iron surface.

Figure 2: Individual electrode reaction current densities.

Figure 3 shows the concentration of oxygen for the second study step when oxygen transport has been included in the model, for the tertiary current distribution. The concentration of oxygen decreases toward the tip of the nail.

Figure 3: Oxygen concentration in the electrolyte.

Figure 4 shows a comparison of the iron oxidation current densities between the secondary and tertiary current distribution models. The current density decreases slightly when including oxygen transport in the model.

Figure 4: Iron oxidation current densities. Effect of including oxygen transport in the model.

Notes About the COMSOL Implementation

The initial value for the electrolyte potential is set to −Eeq,Zn to reduce the computational time. It is generally good practice to set initial values for the potentials, if they can be derived.

In this case it was assumed that the zinc reaction would be governing due to the larger area of the zinc surface, and the faster reaction kinetics of the zinc reaction in relation to the oxygen reduction reaction. Assuming zero overpotential for the zinc reaction, and using Equation 1, the initial value for the electrolyte potential can be calculated according to: