Mechanistic Model with Empirical Pitting Onset Approach for Detailed and Efficient Virtual Analysis of Atmospheric Bimetallic Corrosion
Abstract
:1. Introduction
2. Theory and Model Development
2.1. Electrochemical Reactions
2.2. Mass Transport and Chemical Reactions
2.3. The Liquid Film—Solid Corrosion Products Interaction
2.3.1. Precipitation and Dissolution of Solid Species
2.3.2. Metal Dissolution Sites
2.4. The Liquid Film—Atmosphere Interface
2.5. Model Geometry
3. Model Calibration Strategy
4. Calibration Cell Work
4.1. Specifications
4.2. Exposure Procedure
4.3. Post-Exposure Measurements
4.3.1. Geometrical Surface Characterization—Mapping of Localized Corrosion
4.3.2. FT-IR Microscopy
5. Results and Discussion
5.1. Calibration Cell Work
5.1.1. Exposure
5.1.2. Geometrical Characteristics of Localized Corrosion
5.1.3. FT-IR Microscopy
5.2. Model
5.2.1. Calibrated Model Characteristics
5.2.2. Evaluation of Model Restrictions
Geometry Description
Corrosion Products
6. Conclusions
- The description was set up in a manner that reduced the computation time, enabled analysis of local chemical behavior, and highlighted material damage as a single pit depth.
- Analysis of many underlying phenomena associated with atmospheric corrosion was possible for a certain NaCl load at three different RHs. The behavior of aqueous species, corrosion products, and the largest pit depth could be simulated for a 5 h long exposure.
- A well-structured calibration strategy was shown to be of utmost importance. A combination of post-exposure (geometrical mapping of pits and FT-IR) and in operando (galvanic current) measurements were necessary. These were all performed on an experimental calibration cell.
- The empirical pitting onset approach, although dictated by several simplifications, showed to be promising to simulate the galvanic system in a realistic way. The limitations were mainly observed when simulating the beginning of the exposure and were linked to the spread in pitting onset over time. The model matched the experimental measurements better for the two higher RHs (91% and 97%). An explanation for this can be linked to the simplified pit shape approximation.
- The simulated corrosion products could be correlated to experiments. However, quantitative means of measuring the products should be aimed to fully elucidate the behavior.
- It was seen that the calibration cell requires the exposures to be repeated, due to some reproducibility issues, especially when RH was decreased. Uneven wetting was the most likely cause for the inconsistency.
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
Abbreviations
a | Activity | [mol/m3] |
c | Concentration | [mol/m3] |
D | Diffusion coefficient | [m2/s] |
dpit | Pit depth | [m] |
F | Faraday’s constant, 96487 | [As/mol] |
H | Henry’s constant | [M/atm] |
I | Ionic strength | [mol dm−3] |
i | Current density | [A m−2] |
K | Equilibrium constant | [Mn] |
Ks | Solubility product constant | [Mn] |
L | Distance | [m] |
kprec | Precipitation of solid corrosion products | [mol m−2 · s−1] |
m0 | Total amount of solid corrosion product per monolayer area | [mol m−2] |
mAl | Amount of aluminum dissolved per area | [mol m−2] |
m′Al | Amount of chloride- corrected aluminum dissolution per area | [mol m−2] |
ms | Amount of solid corrosion product per area | [mol m−2] |
M | Molar mass | [kg mol−1] |
N | Flux in electrolyte/liquid | [mol m−2 · s−1] |
n | Number of electrons in electrochemical reaction | [-] |
Nb | Flux boundary | [mol m−2 · s−1] |
Nm | Number of monolayers | [-] |
Npit | Number of conically shaped pits | [-] |
R | Universal gas constant, 8.3143 | [J mol−1 K−1] |
Ri | Volumetric reaction term for i | [mol m−3 t−1] |
rpit | Radius conically shaped pits | [m] |
Sb | Source term chemical reactions | [mol m−3 t−1] |
S′b | Source term electrochemical reactions | [mol m−3 t−1] |
T | Temperature | [K] |
t | Time | [s] |
x | Length dimension | [m] |
z | Ion charge number | [-] |
V | Potential in electrolyte | [V] |
α | Transfer coefficient | [-] |
γ | Activity coefficient | [-] |
δ | Thickness of | |
θ | Degree of coverage | [-] |
θall | Degree of coverage of pit/corroding surface | [-] |
κ | Liquid conductivity | [S m−1] |
ν | Stoichiometric coefficient | [-] |
ρ | Density | [kg m−3] |
τ | Total molar amount of alumina per area consumed | [-] |
χ | Open pit fraction | [-] |
Subscripts | ||
aq | Aqueous | |
cell | Galvanic corrosion cell | |
cs | Corroding surface | |
i | Index for species | |
R | Reaction indication | |
ref | Reference | |
s | Solid corrosion product | |
sat | Saturated | |
tot | Total |
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Reaction | Property and Value | Comment |
---|---|---|
O2(g) ↔ O2(aq) | = 0.26875 mol/m3 | For 0.21 bar, temperature and NaCl dependent [60,61] 1 |
CO2(g) ↔ CO2(aq) | H= 3.39 · 10−2 M/atm | For 324 ppm (1 bar atmosphere), temperature [62] and NaCl [63] dependent 1 |
H2O ↔ H+ + OH− | logK = −14 | [64] |
H2CO3 ↔ HCO3- + H+ | logK = −6.34 | [64] |
HCO3- ↔ CO32- + H+ | logK = −6.34 | [64] |
Al3+ + H2O ↔ AlOH2+ + H+ | logK = −4.97 | [64] |
Al3+ + 2H2O ↔ Al(OH)2+ + 2H+ | logK = −9.3 | [65] |
Al3+ + 3H2O ↔ Al(OH)3(aq) +3H+ | logK = −16.791 | [65] |
Al3+ + 4H2O ↔ Al(OH)4- +4H+ | logK = −23 | [64] |
2Al3+ + 2H2O ↔ Al2(OH)24+ + 2H+ | logK = −7.7 | [65] |
AlOH2+ + Cl− ↔ Al(OH)Cl+ | logK = 0.516 | [66] |
Al3+ + Cl− ↔ AlCl2+ | logK = 0.477 | [66] |
Al(OH)3(aq) ↔ Al(OH)3(s) | logKs = 8.41 | Derived from [64,65,67] |
NaAlCO3(OH)2(s) + 2H2O ↔ Al(OH)4- + HCO3- + Na+ + H+ | logKs= −17.86 | [68] |
Al(OH)Cl+ + H2O ↔ Al(OH)2Cl(s) + H+ | logKs = −21.03 | Estimation from Foley and Nguyen [66] |
AlCl2+ + 2H2O → Al(OH)2Cl(s) + 2H+ Al(OH)Cl+ + H2O → Al(OH)2Cl(s) + H+ | k = 4 · 10−6 s−1 | Two irreversible reactions, same rate constant [32]. Full precipitation of formed Al(OH)2Cl assumed. |
Property | Value | Comment |
---|---|---|
1.33 · 10−9 m2/s | [69] | |
2.03 · 10−9 m2/s | [69] | |
5.41 · 10−10 m2/s | [31] | |
9.30 · 10−9 m2/s | [69] | |
5.30 · 10−9 m2/s | [69] | |
9.22 · 10−10 m2/s | [69] | |
1.18 · 10−9 m2/s | [69] | |
1.92 · 10−9 m2/s | [70] | |
2.42 · 10−9 m2/s | NaCl concentration dependent [30]. Value for infinitely diluted solution. |
Property | Value | Comment |
---|---|---|
pH | 7 | Initial pH. |
MAl | 2.698 · 10−2 kg/mol | Density aluminum at 25 °C. |
ρAl | 2710 kg/m3 | Molar mass aluminum at 25 °C. |
Nm · m0 | 1.5 · 10−4 mol/m2 | From model calibration. Total molar site availability per area for precipitation. |
kprec | 1 · 10−8 mol/(m2s) | From model calibration. Rate constant for precipitation (and dissolution) of solid corrosion products/precipitates. is the total concentration of aluminum ions. |
τ | 9.22 · 10−10 m2/s | From model calibration. Total molar amount of aluminum metal per area consumed at the pit for it to be fully open. |
θall | 1.18 · 10−9 m2/s | From model calibration. Allowed span for coverage of pit opening. |
Property | Value | ||
---|---|---|---|
85% RH | 91% RH | 97% RH | |
3600 mol/m3 | 2600 mol/m3 | 900 mol/m3 | |
δ | 4.21 · 10−6 m | 5.83 · 10−6 m | 1.68 · 10−5 m |
Property | Pit Depth/μm | Projected Area/mm2 | ||||
---|---|---|---|---|---|---|
85% RH | 91% RH | 97% RH | 85% RH | 91% RH | 97% RH | |
Total projected area pits | - | - | - | 2.886.10–2 | 4.226.10–1 | 1.620.10–1 |
Five deepest pit average (FDPA) | 6.11 | 9.70 | 29.18 | 5.254.10–3 | 6.694.10–2 | 5.912.10–3 |
Name | Chemical Formula | Location |
---|---|---|
Dawsonite | NaAlCO3(OH)2 | Outer parts and outside of localized corrosion attack. |
Amorphous aluminum hydroxide cont. carbonate | Al(OH)3−2x(CO3)x | At the localized corrosion attack. |
Aluminum hydroxy chlorides | Al2(OH)5Cl·2H2O Al(OH)Cl2, Al(OH)2Cl | At the localized corrosion attack. |
Sodium carbonate | Na2CO3 · xH2O | On the stainless-steel surface. |
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Zavalis, T.G.; Ström, M.; Persson, D.; Wendel, E.; Ahlström, J.; Törne, K.B.; Taxén, C.; Rendahl, B.; Voltaire, J.; Eriksson, K.; et al. Mechanistic Model with Empirical Pitting Onset Approach for Detailed and Efficient Virtual Analysis of Atmospheric Bimetallic Corrosion. Materials 2023, 16, 923. https://doi.org/10.3390/ma16030923
Zavalis TG, Ström M, Persson D, Wendel E, Ahlström J, Törne KB, Taxén C, Rendahl B, Voltaire J, Eriksson K, et al. Mechanistic Model with Empirical Pitting Onset Approach for Detailed and Efficient Virtual Analysis of Atmospheric Bimetallic Corrosion. Materials. 2023; 16(3):923. https://doi.org/10.3390/ma16030923
Chicago/Turabian StyleZavalis, Tommy G., Mats Ström, Dan Persson, Erik Wendel, Johan Ahlström, Karin Beaussant Törne, Claes Taxén, Bo Rendahl, Joakim Voltaire, Katarina Eriksson, and et al. 2023. "Mechanistic Model with Empirical Pitting Onset Approach for Detailed and Efficient Virtual Analysis of Atmospheric Bimetallic Corrosion" Materials 16, no. 3: 923. https://doi.org/10.3390/ma16030923