COMSOL 6.4 - Corrosion Under an Evans Droplet

An Evans droplet experiment is a century-old corrosion experiment for demonstrating oxygen transport-limited corrosion. A droplet of water is placed on a metal surface, and over time the surface features differences in the radial direction of the surface in terms of amount of corroded material and deposited corrosion products.

This tutorial model defines corrosion of an iron surface in contact with an aqueous sodium-chloride solution droplet in a surrounding atmosphere containing both carbon dioxide and oxygen. The model accounts for charge and mass transport of multiple species as well as iron dissolution, oxygen reduction, carbonic acid equilibria, iron hydrolysis, and precipitation of ferrous hydroxide and ferrous carbonate corrosion products.

The model computes the transient and spatial distributions of the various species within the droplet. A spatial gradient in pH is demonstrated and is attributed to the complex dynamic interplay between the dissolved iron, corrosion products, and dissolved atmospheric gases.

The model is based on several journal papers (Ref. 1–Ref. 4).

Model Definition

Figure 1 shows the model geometry, defining an elliptical electrolyte droplet (with a 90° wetting angle) covering an iron metal surface. The geometry is defined in 2D with axial symmetry. As an assumption, the geometry is fixed throughout the simulation.

Figure 1: Model geometry.

The model is defined using the interface, solving for the electrolyte phase potential and the concentrations of the electrolyte species H+, OH-, Fe2+, FeOH+, Fe(OH)2(aq), FeCO3(aq), O2(aq), CO2(aq), H2CO3, HCO3-, CO32-, Na+, and Cl-.

Oxygen reduction occurs on the metal surface, which, due to limited oxygen diffusion, is more dominant toward the periphery of the droplet:

(1)

Iron is oxidized to counterbalance the oxygen reduction reaction:

(2)

Butler–Volmer electrode kinetics expressions are used for both the oxygen-reduction and iron-dissolution reactions. The combination of these two reactions gives rise to a mixed electrode potential of the metal surface.

Dissolved iron precipitates as ferrous hydroxide and ferrous carbonate corrosion products at the electrode surface due to the following reactions:

(3)

(4)

The reactions are defined as irreversible and precipitation takes place once the solubility product is exceeded. The corrosion products are said to cover the metallic surface and are assumed to only inhibit the metal dissolution, that is, the products passivate the iron. The corrosion-product coverage degree, θ, is computed with the expression

(5)

With the use of the above expression, the coverage can reach a maximum value of 1 with precipitation. ctot,s is the total molar amount per surface area of precipitated corrosion products and cavailable,s is the molar availability per surface area and monolayer for corrosion-product precipitation. The inhibition of the metal dissolution is modeled by multiplying the local current density of the metal dissolution reaction with the uncovered surface fraction, 1 − θ. Note that with the expression above more than cavailable,s needs to precipitate for full passivation.

Equilibrium Reactions

The following equilibrium reactions are accounted for in the electrolyte:

(6)

K1 through K7 are the equilibrium constants. Values have been chosen for temperatures near room temperature (293.15 K).

The water dissociation equilibrium reaction is built-in for the Aqueous Electrolyte Transport interface. All three carbonic acid reactions can be captured by adding the Carbonic Acid feature to the Electrolyte domain node. The Ampholyte feature is used to model the two iron hydrolysis reactions. Finally, the Complex Species feature allows for easy representation of the iron carbonate species. These equilibrium reaction features simultaneously calculate the concentration of all aqueous species based on equilibrium expressions, which are based on the reaction stoichiometry and the equilibrium constant Kk according to

(7)

where ci (SI unit: mol/m3) is the concentration of species i and vik is the stoichiometric coefficient of species i in reaction k.

As a result of the above equilibrium reactions, the gaseous CO2 dissolved at the droplet surface forms carbonic acid, which generally lowers the pH.

The model is solved using a time-dependent solver, simulating the transient and spatial evolution of the species considered for 300 seconds. Inward fluxes of O2 and CO2 are set relatively high at the upper droplet boundary facing the surrounding atmosphere such that the gas concentrations are approximately constant and equal to the saturation concentrations (O2(aq, sat) and CO2(aq, sat)) at the droplet surface.

Results and Discussion

Figure 2 shows the iron ion concentration distribution within the Evans droplet at 10 s (left) and 300 s (right). It can be seen that the concentration is lower within a ring expanding inward from the droplet periphery compared to the central parts of the droplet. At the 300 s, this ring with lower iron ion concentration has become approximately 1 mm wide.

Figure 2: Iron ion concentration distribution within the droplet at t = 10 s (left) and t = 300 s (right).

In Figure 3, the current density distributions and the corrosion-product coverage degree along the iron surface underneath the droplet at 300 s are displayed. The observed lower iron-ion concentration can be explained by the lower anodic metal-dissolution reaction which in turn is affected by the higher corrosion-product coverage degree at the same location. The short-time behavior in Figure 2 (left) is likewise explained by the coverage, which is less and means that the iron dissolution initially is present over almost the whole droplet covered surface.

The cathodic oxygen reduction is larger near the rim of the droplet due to limited oxygen transport, in combination with the limited electrolyte conductivity. The total current density shows that the anodic activity dominates the central parts of the droplet and the cathodic the periphery of the droplet.

Note that the droplet rim has a different behavior due to the acidifying CO2 from the atmosphere. This acidity counteracts any corrosion-product precipitation.

Figure 3: Iron dissolution, oxygen reduction, and total current density distributions along the iron surface at t = 300 s.

Figure 4 shows the CO2(aq) concentration distribution within the droplet at 10 s (left) and 300 s (right). It can be seen that the concentration is reduced close to the iron surface, since it is consumed in a homogeneous reaction.

Figure 4: CO2 concentration distribution within the droplet at t = 10 s (left) and t = 300 s (right).

Figure 5 shows the pH distribution within the droplet at 10 s (left) and 300 s (right). The pH changes over time are substantial. It can also be seen that the pH is increased in the vicinity of the metal surface, when compared to the pH closer to the droplet periphery. At the droplet rim, the pH is the lowest due to the CO2 in the atmosphere. The pH changes are generally attributed to the dissolution of iron atoms which need to be counter-balanced by hydroxide ions from water autoprotolysis. The iron hydrolysis is insufficient to acidify the electrolyte near the iron surface.

Figure 5: pH distribution within the droplet at t = 10 s (left) and t = 300 s (right).

Figure 6 shows the surface plot of precipitated corrosion products per area along the iron surface underneath the droplet and the streamline plot of the electrolyte current density over the droplet domain at 300 s. Most has precipitated in the ring region where the low iron-ion concentration is observed. A comparison with the coverage degree in Figure 3 indicates that ferrous carbonate almost exclusively makes up the coverage in that region. The access to carbonates in the form of carbonate ions near the droplet periphery is the main cause for this. The streamlines show the ionic current flow from the core toward the rim of the droplet.